Skip to content

Instantly share code, notes, and snippets.

@eamartin

eamartin/ipython_notebook

Last active August 29, 2015 14:02
Show Gist options
  • Save eamartin/66b23cfdb84cbd30e5c7 to your computer and use it in GitHub Desktop.
Save eamartin/66b23cfdb84cbd30e5c7 to your computer and use it in GitHub Desktop.
Download ZIP
American Options Pricing project
Raw
ipython_notebook
{
"metadata": {
"language": "Julia",
"name": "",
"signature": "sha256:52758898c2403685db8d857c76083099a23d7889718b8185d62e48903a88e488"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is a summary and implementation of \"An Operator Splitting Method for Pricing American Options\" by Samuli Ikonen and Jari Toivanen."
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"American put options"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An American put option is a contract on an underlying asset that gives the option buyer the right to sell the underlying asset (also known as exercising the option) at any time before the expiration date at a fixed \"strike\" price. To formalize this, an American put option purchased at $t=0$ with strike price $K$ and expiration $t=T$ allows the option holder to exercise the option at any time $0\\le t \\le T$. The payoff for the option holder of exercising the option at time $t$ is $K - s(t)$, where $s(t)$ is the value of the underlying asset at time $t$. Note the option holder does not need to exercise the option and can let it expire, which gives the option holder 0 payoff.\n",
"\n",
"Although not directly relevant to this project, a call option (as oppposed to a put) allows the option holder to buy an underlying asset at the strike price rather than sell the asset. A European option (as opposed to an American option) only allows the option holder to exercise the option at the expiration date rather than any time before the expiration date."
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Options pricing and the Black-Scholes PDE"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A fundamental problem for options markets is determining at which price to sell options. That is, given a strike price $K$ and an expiration $T$, how much should the potential option buyer have to pay for the right to sell the asset at price $K$ before time $T$?\n",
"\n",
"One can see that the value of an American put option must always be greater than or equal to the value of a European put option because the holder of the American option has more opportunities to exercise the option. By similar logic, one can also see that the partial derivative of the option price with respect to time must also be negative.\n",
"\n",
"One way to address this problem is to attempt to come up with an option price that can be \"hedged\" perfectly, that is a price such that any gains or losses can be completed made up for with a risk-free strategy. The Black-Scholes model does exactly this, but requires a large number of assumptions about the market. Deriving the Black-Scholes model is out of the scope of this project (and beyond my non-existant knowledge of stochastic calculus), but the assumptions of the model are\n",
"\n",
"* the price of the underlying asset is geometric Brownian motion\n",
"* the volatility of the asset $\\sigma$ is fixed with time\n",
"* the asset pays no dividends (although a simple alteration to the model can account for dividends)\n",
"* no opportunities for arbitrage (risk-free profit) exist in the market\n",
"* there are no transaction costs in the market and one can buy/sell any quantity of the asset and borrow/loan any quantity of money at interest rate $r$\n",
"\n",
"This model leads to the Black-Scholes equation:\n",
"\\begin{align*}\n",
"v_t = A_{\\text{BS}}v \\equiv -\\frac{1}{2}\\sigma^2 s^2 v_{ss} - rsv_s + rv\n",
"\\end{align*}\n",
"Here $v(t, s)$ is the price of the option at time $t$ given the asset price $s(t)$. Under this forumlation, the option price is $v(0, s(0))$.\n",
"\n",
"This method will not be used in this project, but a simple change of variables can change the Black-Scholes equation into the heat equation."
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Boundary conditions and Linear Complementarity Problems"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's consider the boundary conditions of the American put option pricing problem.\n",
"\n",
"\\begin{align*}\n",
"v(T, s) = g(s) \\equiv \\max(K-s, 0)\n",
"\\end{align*}\n",
"because at the expiration time the option owner will sell the asset for $K$ and make $K-s$ if $K-s > 0$, or will do nothing if exercising the option would lead to a loss.\n",
"\n",
"\\begin{align*}\n",
"v(t, 0) = K\n",
"\\end{align*}\n",
"because the owner of the option will immediately exercise the option and receive a payoff of its full strike price.\n",
"\n",
"\\begin{align*}\n",
"\\lim_{s\\to\\infty} v(t, s) = 0\n",
"\\end{align*}\n",
"\n",
"By more stochastic calculus, one can show for the American put option that\n",
"\\begin{align*}\n",
"v_t - A_{\\text{BS}}v \\le 0\n",
"\\end{align*}\n",
"\n",
"Let's consider where the Black-Scholes equation applies for an American put option. Let the continuation region of the domain be the values of $(t, s)$ where it is not optimal to exercise the option and the stopping region be the values of $(t, s)$ where immediate evaluation of the option is favorable. In the continuation region, $v(t, s) \\ge g(s)$ (otherwise we would evaluate immediately), and in the stopping region $v(t, s) = g(s)$. In the continuation region, all is still the same as in the European option case, so the Black-Scholes equation $v_t = A_{\\text{BS}}v$ holds. For reasons I don't fully understand, in the stopping region, $v_t - A_{\\text{BS}}v \\le 0$.\n",
"\n",
"This and the above observation that $v \\ge g$ gives the following system of equations:\n",
"\\begin{align*}\n",
"v_t - A_{\\text{BS}}v \\le 0 \\\\\n",
"\\left(v_t - A_{\\text{BS}}v \\right)(v - g) = 0 \\\\\n",
"v \\ge g\n",
"\\end{align*}\n",
"which is called a linear complementarity problem (LCP) and is a problem from the optimization literature.\n",
"\n",
"We can combine all of the constraints and introduce the slack variable $\\lambda$ to get\n",
"\\begin{align*}\n",
"v_t - A_{\\text{BS}}v &= \\lambda \\\\\n",
"\\lambda (v-g) &= 0 \\\\\n",
"\\lambda &\\le 0 \\\\\n",
"v &\\ge g \\\\\n",
"v(T, s) &= \\max(K-s, 0) \\\\\n",
"v(t, 0) &= K \\\\\n",
"\\lim_{s\\to\\infty} v(t, s) &= 0\n",
"\\end{align*}"
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Time and Space/Price Discretization"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note $A_{\\text{BS}}$ only takes partial derivatives with respect to $s$. This means we can discretize $A_{\\text{BS}}$ with respect solely to $s$. Note that the original LCP is defined for $s\\in [0, \\infty)$, but to handle the scheme with finite differences a finite domain is necesssary. Therefore we'll take the standard finite difference options pricing approach and only consider values of $s$ up to $s_{\\max}$, where $s_{\\max}$ is several times larger the strike price $K$. Another slightly strange aspect of finite difference methods for option pricing is that the final condition $v(T, s)$ is unknown, but the initial condition $v(s, 0)$ is unknown (and what we want to solve for this). This is the opposite of the typical finite differencing siutation and leads to us marching backwards in time rather than forwards. \n",
"\n",
"Although the paper works through the finite difference approximations working with a non-uniform grid, I'm going to do all of the derivations assuming $\\Delta t = k$ and $\\Delta s = h$. Let $s_i = ih$ and $s_M = Mh = s_{\\max}$. Similarly let $t_n = nk$ and $t_N = Nk = T$.\n",
"\n",
"We'll approximate with the standard second order \n",
"\\begin{align*}\n",
"v_{ss}(t, s_i) &\\approx \\frac{1}{h^2} \\left(v(t, s_{i+1}) - 2v(t, s_i) + v(t, s_{i-1})\\right) \\\\\n",
"v_{s}(t, s_i) &\\approx \\frac{1}{2h} \\left(v(t, s_{i+1}) - v(t, s_{i-1})\\right)\n",
"\\end{align*}\n",
"\n",
"These approximations give\n",
"\\begin{align*}\n",
"(Av)_i &= -\\frac{\\sigma^2s_i^2}{h^2}\\left(v_{i+1}-2v_i+v_{i-1}\\right) - \\frac{rs_i}{2h}\\left(v_{i+1}-v_{i-1}\\right) + rv_i \\\\\n",
"&= \\left(-\\frac{\\sigma^2s_{i-1}^2}{h^2} + \\frac{rs_{i-1}}{2h}\\right)v_{i-1} + \\left(\\frac{2\\sigma^2s_i^2}{h^2} + r \\right)v_i + \\left(-\\frac{\\sigma^2s_{i+1}^2}{h^2} - \\frac{rs_{i+1}}{2h}\\right)v_{i+1} \\\\\n",
"&= \\left(-\\sigma^2(i-1)^2 + \\frac{r(i-1)}{2}\\right)v_{i-1} + \\left(2\\sigma^2i^2 + r \\right)v_i + \\left(-\\sigma^2(i+1)^2 - \\frac{r(i+1)}{2}\\right)v_{i+1}\n",
"\\end{align*}\n",
"as an approximation to $A_{\\text{BS}}$ where $v_i = v(t, s_i)$. Note $A$ is a tridiagonal matrix. For a spatial/price grid with $m + 1$ grid points (from $i=0$ to $i=m$), we have an $(m-1)\\times(m-1)$ matrix where the top and bottom grid values come from the boundary values, which can be done by adding in a vector $f$ where the first component is\n",
"\\begin{align*}\n",
"\\left(-\\frac{\\sigma^2s_1^2}{h^2} + \\frac{rs_1}{2h}\\right)K = \\left(\\frac{r}{2} - \\sigma^2\\right)K\n",
"\\end{align*}\n",
"and all of the rest of the components are 0 (because only the boundary condition at $s=0$ is non-zero). Thus we can approximate $A_{\\text{BS}}v = Av + f$.\n",
"\n",
"A modification of the Crank-Nicolson scheme known as the Rannacher scheme will be used for marching backwards in time. The Rannacher scheme will be used instead of Crank-Nicolson because the final condition at $v(T, s)$ is not smooth and the Crank-Nicolson scheme does not dampen oscillations very well. The Rannacher time-stepping scheme consists of running the first several time-steps with the implicit Euler scheme (which can be thought of as Crank-Nicolson with $\\theta=1$) and the rest of the steps with the standard Crank-Nicolson method (with $\\theta=1/2$). \n",
"\n",
"Note with the Rannacher scheme we have\n",
"\\begin{align*}\n",
"v_t - A_{\\text{BS}}v &= \\lambda \\\\\n",
"\\frac{v^{n+1} - v^n}{k} - \\theta_n Av^n - (1-\\theta_n) Av^{n+1} - f &= \\lambda^n \\\\\n",
"v^{n+1} - v^n - \\theta_n kAv^n - (1-\\theta_n) kAv^{n+1} - kf &= k \\lambda^n \\implies \\\\\n",
"\\left(I - (1-\\theta_n)kA\\right)v^{n+1} - \\left(I + \\theta_n k A\\right)v^n - kf &= k \\lambda^n \\\\\n",
"Cv^{n+1} - Bv^n - kf &= k\\lambda^n\n",
"\\end{align*}\n",
"where\n",
"\\begin{align*}\n",
"\\theta_n &= \\left\\{\n",
" \\begin{array}{lr}\n",
" 1 & : n = N-1, ..., N-4 \\\\\n",
" 1/2 & : n = N-5, ..., 0\n",
" \\end{array}\n",
" \\right. \\\\\n",
"B &= I + \\theta_n k A \\\\\n",
"C &= I - (1 - \\theta_n)k A\n",
"\\end{align*}\n",
"\n",
"After discretization, we now have the system of equations\n",
"\\begin{align*}\n",
"Cv^{n+1} - Bv^n - kf &= k\\lambda^n \\\\\n",
"\\left(\\lambda^n\\right)^T (v^n-g) &= 0 \\\\\n",
"\\lambda^n &\\le 0 \\\\\n",
"v^n &\\ge g \\\\\n",
"v_i^N &= \\max(K-s_i, 0) \\\\\n",
"\\end{align*}\n",
"\n",
"Note $\\left(\\lambda^n\\right)^T (v^n-g) = 0$ along with $\\lambda^n \\le 0$ and $v^n \\ge g$ implies that for $\\lambda^n_i(v_i^n - g_i^n) = 0$ for all $i$."
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Solving the system with an operator splitting method"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Ikonen and Toivanen present an operator spliting approach to approximately solving the above linear complementarity problem in two partial time steps. The first step invovles solving a system of linear equations and the second step involves setting values for $\\lambda^n$ and $v^n$ so that they meet the constraints.\n",
"\n",
"The first step is\n",
"\\begin{align*}\n",
"B\\tilde{v}^n = Cv^{n+1} - kf - k\\lambda^{n+1}\n",
"\\end{align*}\n",
"and the second step is solving\n",
"\\begin{align*}\n",
"v^n + k \\lambda^n &= \\tilde{v}^n + k\\lambda^{n+1} \\\\\n",
"\\lambda_i^n(v_i^n - g_i) &= 0 \\; \\text{ for all } i\\\\\n",
"\\lambda^n &\\le 0 \\\\\n",
"v^n &\\ge g\n",
"\\end{align*}\n",
"\n",
"The first step involves solving a tridiagonal system. Although the second step looks more complex, it is actually computationally easier because the update can be computed componentwise (there are no spatial couplings, so solving the system takes linear time).\n",
"\n",
"Note for the second step, each equation depends only on a single component of each vector. This means in the following algebra it is valid to treat $\\lambda^n$ as a scalar (just let it be $\\lambda_i^n)$.\n",
"\n",
"The first equation implies $v^n = \\tilde{v}^n + k\\lambda^{n+1} - k\\lambda^n$. Plugging this into the second equation gives\n",
"$\\lambda^n(\\tilde{v}^n + k\\lambda^{n+1} - k\\lambda^n - g) = 0$, which implies one of two solutions:\n",
"\\begin{align*}\n",
"\\left\\{\n",
" \\begin{array}{lr}\n",
" \\lambda^n = 0 \\\\\n",
" v^n = \\tilde{v}^n + k \\lambda^{n+1}\n",
" \\end{array}\n",
" \\right. \\\\\n",
"&\\text{or} \\\\\n",
"\\left\\{\n",
" \\begin{array}{lr}\n",
" \\lambda^n = \\lambda^{n+1} + \\frac{\\tilde{v}^n - g}{k} \\\\\n",
" v^n = g\n",
" \\end{array}\n",
" \\right. \\\\\n",
"\\end{align*}\n",
"\n",
"Note we still have to satisfy the the $\\lambda^n \\le 0$ and the $v^n \\ge g$ constraints. As long as one of these sets of solutions satisfies these constraints, then the problem has a solution. Consider the first set of solutions. If $v^n = \\tilde{v}^n + k \\lambda^{n+1} \\ge g$, then the problem is satisfied. Thus assume $\\tilde{v}^n + k\\lambda^{n+1} < g$. Now consider the second set of solutions. $v^n=g$ clearly satisfies one of the constraints, and $\\lambda^n = \\lambda^{n+1} + \\frac{\\tilde{v}^n - g}{k} = \\frac{k \\lambda^{n+1} + \\tilde{v}^n - g}{k} < 0$ by the above assumption, which means the second set of solutions satisfies both constraints. Thus one of these two sets of solutions always will satisfy all of the constraints.\n",
"\n",
"If $\\tilde{v}^n + k\\lambda^{n+1} \\ge g$, then\n",
"\\begin{align*}\n",
"\\left\\{\n",
" \\begin{array}{lr}\n",
" \\lambda^n = 0 \\\\\n",
" v^n = \\tilde{v}^n + k \\lambda^{n+1}\n",
" \\end{array}\n",
" \\right.\n",
"\\end{align*}, otherwise\n",
"\\begin{align*}\n",
"\\left\\{\n",
" \\begin{array}{lr}\n",
" \\lambda^n = \\lambda^{n+1} + \\frac{\\tilde{v}^n - g}{k} \\\\\n",
" v^n = g\n",
" \\end{array}\n",
" \\right. \\\\\n",
"\\end{align*}"
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Implementation"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"using PyPlot\n",
"\n",
"function make_A(num_points, s_max, sigma, r)\n",
" h = s_max / (num_points - 1)\n",
" s = [h:h:s_max - h]\n",
"\n",
" # second order values\n",
" d = r + (2 .* sigma.^2 .* s.^2) ./ h.^2\n",
" dl = -(sigma.^2 .* s.^2 ./ h.^ 2) + (r .* s ./ (2 .* h))\n",
" du = -(sigma.^2 .* s.^2 ./ h.^ 2) - (r .* s ./ (2 .* h))\n",
"\n",
" # first order values here to ensure M-matrix\n",
" #dl = -sigma.^2 .* s.^2 ./ h.^2\n",
" #d = (2 .* sigma.^2 .* s.^2 ./ h.^2) + (r .* s ./ h) + r\n",
" #du = (-sigma.^2 .* s.^2 ./ h.^2) - r .* s ./ h\n",
"\n",
" Tridiagonal(dl[1:end-1], d, du[2:end])\n",
"end\n",
"\n",
"function solver(num_space_points, s_max, num_time_points, T, sigma, r, K)\n",
" RANNACHER_SWITCH = 0\n",
"\n",
" A = make_A(num_space_points, s_max, sigma, r)\n",
" k = T ./ (num_time_points - 1)\n",
" h = s_max ./ (num_space_points - 1)\n",
"\n",
" mat_size = size(A, 1)\n",
" tri_I = Tridiagonal(zeros(mat_size - 1), ones(mat_size), zeros(mat_size - 1))\n",
"\n",
" # use this B and C just for first few iterations\n",
" B = tri_I + A * k\n",
" C = tri_I\n",
"\n",
" # use these B and C later\n",
" B_later = tri_I + A * (0.5 .* k)\n",
" C_later = tri_I + A * (-0.5 .* k)\n",
"\n",
" # initial conditions\n",
" lambda = zeros(size(A, 1))\n",
" g = max(K - h .* [1:num_space_points-2], 0)\n",
" v = copy(g)\n",
"\n",
" for n = num_time_points:-1:1\n",
" assert(all(lambda .<= 0))\n",
" assert(all(v .>= g))\n",
"\n",
" if n == (num_time_points - RANNACHER_SWITCH)\n",
" B = B_later\n",
" C = C_later\n",
" end\n",
"\n",
" # step 1\n",
" v_tilde = C * v - k .* lambda\n",
" # include boundary condition\n",
" #v_tilde[1] -= k .* (-sigma.^2 + r ./ 2) .* K\n",
" v_tilde = B \\ v_tilde\n",
" \n",
" # step 2\n",
" for i = 1:size(v_tilde, 1)\n",
" if v_tilde[i] + k .* lambda[i] >= g[i]\n",
" v[i] = v_tilde[i] + k .* lambda[i]\n",
" lambda[i] = 0.0\n",
" else\n",
" lambda[i] += (v_tilde[i] - g[i]) ./ k\n",
" v[i] = g[i]\n",
" end\n",
" end\n",
" end\n",
" linspace(0.0, s_max, num_space_points), [K, v, 0.0]\n",
"end"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 1,
"text": [
"solver (generic function with 1 method)"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's check this code by using the same parameters as in the paper: $\\sigma=0.25, r=0.1, T=0.25, K=10$."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# 1000 space and 1000 time grid points, s_max=40\n",
"s, v = solver(1000, 40, 10000, 0.25, 0.25, 0.1, 10.0);"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(s, v)\n",
"xlabel(\"Asset price at \\$t=0\\$\")\n",
"ylabel(\"Option price\")\n",
"title(\"\\$\\\\sigma=0.25, r=0.1, T=0.25, K=10\\$\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "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",
"svg": [
"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Created with matplotlib (http://matplotlib.sourceforge.net/) -->\n",
"<svg height=\"404pt\" version=\"1.1\" viewBox=\"0 0 501 404\" width=\"501pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
" <defs>\n",
" <style type=\"text/css\">\n",
"*{stroke-linecap:square;stroke-linejoin:round;}\n",
" </style>\n",
" </defs>\n",
" <g id=\"figure_1\">\n",
" <g id=\"patch_1\">\n",
" <path d=\"\n",
"M0 404.653\n",
"L501.512 404.653\n",
"L501.512 0\n",
"L0 0\n",
"z\n",
"\" style=\"fill:#ffffff;\"/>\n",
" </g>\n",
" <g id=\"axes_1\">\n",
" <g id=\"patch_2\">\n",
" <path d=\"\n",
"M40.9688 367.736\n",
"L487.369 367.736\n",
"L487.369 22.136\n",
"L40.9688 22.136\n",
"z\n",
"\" style=\"fill:#ffffff;\"/>\n",
" </g>\n",
" <g id=\"line2d_1\">\n",
" <path clip-path=\"url(#p338691d578)\" d=\"\n",
"M40.9688 79.736\n",
"L41.4156 71.8915\n",
"L68.2264 149.514\n",
"L72.248 160.437\n",
"L81.6318 184.673\n",
"L139.275 333.218\n",
"L141.509 338.132\n",
"L143.744 342.45\n",
"L145.978 346.228\n",
"L148.212 349.518\n",
"L150.446 352.369\n",
"L152.68 354.828\n",
"L154.915 356.939\n",
"L157.149 358.741\n",
"L159.383 360.272\n",
"L161.617 361.567\n",
"L164.298 362.852\n",
"L166.98 363.89\n",
"L170.107 364.845\n",
"L173.682 365.666\n",
"L177.704 366.328\n",
"L182.172 366.829\n",
"L187.981 367.232\n",
"L195.578 367.508\n",
"L206.749 367.668\n",
"L230.432 367.731\n",
"L452.068 367.736\n",
"L487.369 367.736\n",
"L487.369 367.736\" style=\"fill:none;stroke:#0000ff;\"/>\n",
" </g>\n",
" <g id=\"matplotlib.axis_1\">\n",
" <g id=\"xtick_1\">\n",
" <g id=\"line2d_2\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L0 -4\" id=\"m0012dd4eef\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_3\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L0 4\" id=\"m476344969c\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_1\">\n",
" <!-- 0 -->\n",
" <defs>\n",
" <path d=\"\n",
"M31.7812 66.4062\n",
"Q24.1719 66.4062 20.3281 58.9062\n",
"Q16.5 51.4219 16.5 36.375\n",
"Q16.5 21.3906 20.3281 13.8906\n",
"Q24.1719 6.39062 31.7812 6.39062\n",
"Q39.4531 6.39062 43.2812 13.8906\n",
"Q47.125 21.3906 47.125 36.375\n",
"Q47.125 51.4219 43.2812 58.9062\n",
"Q39.4531 66.4062 31.7812 66.4062\n",
"M31.7812 74.2188\n",
"Q44.0469 74.2188 50.5156 64.5156\n",
"Q56.9844 54.8281 56.9844 36.375\n",
"Q56.9844 17.9688 50.5156 8.26562\n",
"Q44.0469 -1.42188 31.7812 -1.42188\n",
"Q19.5312 -1.42188 13.0625 8.26562\n",
"Q6.59375 17.9688 6.59375 36.375\n",
"Q6.59375 54.8281 13.0625 64.5156\n",
"Q19.5312 74.2188 31.7812 74.2188\" id=\"DejaVuSans-30\"/>\n",
" </defs>\n",
" <g transform=\"translate(37.9453125 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_2\">\n",
" <g id=\"line2d_4\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"96.76875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_5\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"96.76875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_2\">\n",
" <!-- 5 -->\n",
" <defs>\n",
" <path d=\"\n",
"M10.7969 72.9062\n",
"L49.5156 72.9062\n",
"L49.5156 64.5938\n",
"L19.8281 64.5938\n",
"L19.8281 46.7344\n",
"Q21.9688 47.4688 24.1094 47.8281\n",
"Q26.2656 48.1875 28.4219 48.1875\n",
"Q40.625 48.1875 47.75 41.5\n",
"Q54.8906 34.8125 54.8906 23.3906\n",
"Q54.8906 11.625 47.5625 5.09375\n",
"Q40.2344 -1.42188 26.9062 -1.42188\n",
"Q22.3125 -1.42188 17.5469 -0.640625\n",
"Q12.7969 0.140625 7.71875 1.70312\n",
"L7.71875 11.625\n",
"Q12.1094 9.23438 16.7969 8.0625\n",
"Q21.4844 6.89062 26.7031 6.89062\n",
"Q35.1562 6.89062 40.0781 11.3281\n",
"Q45.0156 15.7656 45.0156 23.3906\n",
"Q45.0156 31 40.0781 35.4375\n",
"Q35.1562 39.8906 26.7031 39.8906\n",
"Q22.75 39.8906 18.8125 39.0156\n",
"Q14.8906 38.1406 10.7969 36.2812\n",
"z\n",
"\" id=\"DejaVuSans-35\"/>\n",
" </defs>\n",
" <g transform=\"translate(93.9384375 380.48475)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_3\">\n",
" <g id=\"line2d_6\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"152.56875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_7\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"152.56875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_3\">\n",
" <!-- 10 -->\n",
" <defs>\n",
" <path d=\"\n",
"M12.4062 8.29688\n",
"L28.5156 8.29688\n",
"L28.5156 63.9219\n",
"L10.9844 60.4062\n",
"L10.9844 69.3906\n",
"L28.4219 72.9062\n",
"L38.2812 72.9062\n",
"L38.2812 8.29688\n",
"L54.3906 8.29688\n",
"L54.3906 0\n",
"L12.4062 0\n",
"z\n",
"\" id=\"DejaVuSans-31\"/>\n",
" </defs>\n",
" <g transform=\"translate(145.99125 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_4\">\n",
" <g id=\"line2d_8\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"208.36875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_9\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"208.36875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_4\">\n",
" <!-- 15 -->\n",
" <g transform=\"translate(201.916875 380.48475)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_5\">\n",
" <g id=\"line2d_10\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"264.16875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_11\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"264.16875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_5\">\n",
" <!-- 20 -->\n",
" <defs>\n",
" <path d=\"\n",
"M19.1875 8.29688\n",
"L53.6094 8.29688\n",
"L53.6094 0\n",
"L7.32812 0\n",
"L7.32812 8.29688\n",
"Q12.9375 14.1094 22.625 23.8906\n",
"Q32.3281 33.6875 34.8125 36.5312\n",
"Q39.5469 41.8438 41.4219 45.5312\n",
"Q43.3125 49.2188 43.3125 52.7812\n",
"Q43.3125 58.5938 39.2344 62.25\n",
"Q35.1562 65.9219 28.6094 65.9219\n",
"Q23.9688 65.9219 18.8125 64.3125\n",
"Q13.6719 62.7031 7.8125 59.4219\n",
"L7.8125 69.3906\n",
"Q13.7656 71.7812 18.9375 73\n",
"Q24.125 74.2188 28.4219 74.2188\n",
"Q39.75 74.2188 46.4844 68.5469\n",
"Q53.2188 62.8906 53.2188 53.4219\n",
"Q53.2188 48.9219 51.5312 44.8906\n",
"Q49.8594 40.875 45.4062 35.4062\n",
"Q44.1875 33.9844 37.6406 27.2188\n",
"Q31.1094 20.4531 19.1875 8.29688\" id=\"DejaVuSans-32\"/>\n",
" </defs>\n",
" <g transform=\"translate(257.371875 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-32\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_6\">\n",
" <g id=\"line2d_12\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"319.96875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_13\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"319.96875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_6\">\n",
" <!-- 25 -->\n",
" <g transform=\"translate(313.2975 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-32\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_7\">\n",
" <g id=\"line2d_14\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"375.76875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_15\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"375.76875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_7\">\n",
" <!-- 30 -->\n",
" <defs>\n",
" <path d=\"\n",
"M40.5781 39.3125\n",
"Q47.6562 37.7969 51.625 33\n",
"Q55.6094 28.2188 55.6094 21.1875\n",
"Q55.6094 10.4062 48.1875 4.48438\n",
"Q40.7656 -1.42188 27.0938 -1.42188\n",
"Q22.5156 -1.42188 17.6562 -0.515625\n",
"Q12.7969 0.390625 7.625 2.20312\n",
"L7.625 11.7188\n",
"Q11.7188 9.32812 16.5938 8.10938\n",
"Q21.4844 6.89062 26.8125 6.89062\n",
"Q36.0781 6.89062 40.9375 10.5469\n",
"Q45.7969 14.2031 45.7969 21.1875\n",
"Q45.7969 27.6406 41.2812 31.2656\n",
"Q36.7656 34.9062 28.7188 34.9062\n",
"L20.2188 34.9062\n",
"L20.2188 43.0156\n",
"L29.1094 43.0156\n",
"Q36.375 43.0156 40.2344 45.9219\n",
"Q44.0938 48.8281 44.0938 54.2969\n",
"Q44.0938 59.9062 40.1094 62.9062\n",
"Q36.1406 65.9219 28.7188 65.9219\n",
"Q24.6562 65.9219 20.0156 65.0312\n",
"Q15.375 64.1562 9.8125 62.3125\n",
"L9.8125 71.0938\n",
"Q15.4375 72.6562 20.3438 73.4375\n",
"Q25.25 74.2188 29.5938 74.2188\n",
"Q40.8281 74.2188 47.3594 69.1094\n",
"Q53.9062 64.0156 53.9062 55.3281\n",
"Q53.9062 49.2656 50.4375 45.0938\n",
"Q46.9688 40.9219 40.5781 39.3125\" id=\"DejaVuSans-33\"/>\n",
" </defs>\n",
" <g transform=\"translate(368.9896875 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-33\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_8\">\n",
" <g id=\"line2d_16\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"431.56875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_17\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"431.56875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_8\">\n",
" <!-- 35 -->\n",
" <g transform=\"translate(424.9153125 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-33\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_9\">\n",
" <g id=\"line2d_18\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_19\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_9\">\n",
" <!-- 40 -->\n",
" <defs>\n",
" <path d=\"\n",
"M37.7969 64.3125\n",
"L12.8906 25.3906\n",
"L37.7969 25.3906\n",
"z\n",
"\n",
"M35.2031 72.9062\n",
"L47.6094 72.9062\n",
"L47.6094 25.3906\n",
"L58.0156 25.3906\n",
"L58.0156 17.1875\n",
"L47.6094 17.1875\n",
"L47.6094 0\n",
"L37.7969 0\n",
"L37.7969 17.1875\n",
"L4.89062 17.1875\n",
"L4.89062 26.7031\n",
"z\n",
"\" id=\"DejaVuSans-34\"/>\n",
" </defs>\n",
" <g transform=\"translate(480.425625 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-34\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_10\">\n",
" <!-- Asset price at $t=0$ -->\n",
" <defs>\n",
" <path d=\"\n",
"M25 -2.20312\n",
"Q12.75 -2.20312 8.32812 7.875\n",
"Q3.90625 17.9688 3.90625 31.8906\n",
"Q3.90625 40.5781 5.48438 48.2344\n",
"Q7.07812 55.9062 11.7812 61.25\n",
"Q16.5 66.6094 25 66.6094\n",
"Q31.5938 66.6094 35.7812 63.375\n",
"Q39.9844 60.1562 42.1875 55.0469\n",
"Q44.3906 49.9531 45.1875 44.1094\n",
"Q46 38.2812 46 31.8906\n",
"Q46 23.2969 44.4062 15.7969\n",
"Q42.8281 8.29688 38.1875 3.04688\n",
"Q33.5469 -2.20312 25 -2.20312\n",
"M25 0.390625\n",
"Q30.5625 0.390625 33.2969 6.09375\n",
"Q36.0312 11.8125 36.6719 18.75\n",
"Q37.3125 25.6875 37.3125 33.5\n",
"Q37.3125 41.0156 36.6719 47.3594\n",
"Q36.0312 53.7188 33.3125 58.8594\n",
"Q30.6094 64.0156 25 64.0156\n",
"Q19.3438 64.0156 16.6094 58.8281\n",
"Q13.875 53.6562 13.2344 47.3281\n",
"Q12.5938 41.0156 12.5938 33.5\n",
"Q12.5938 27.9375 12.8594 23\n",
"Q13.1406 18.0625 14.3125 12.8125\n",
"Q15.4844 7.5625 18.0938 3.96875\n",
"Q20.7031 0.390625 25 0.390625\" id=\"Cmr10-30\"/>\n",
" <path d=\"\n",
"M7.51562 13.2812\n",
"Q6.6875 13.2812 6.14062 13.9062\n",
"Q5.60938 14.5469 5.60938 15.2812\n",
"Q5.60938 16.1094 6.14062 16.6875\n",
"Q6.6875 17.2812 7.51562 17.2812\n",
"L70.3125 17.2812\n",
"Q71.0469 17.2812 71.5781 16.6875\n",
"Q72.125 16.1094 72.125 15.2812\n",
"Q72.125 14.5469 71.5781 13.9062\n",
"Q71.0469 13.2812 70.3125 13.2812\n",
"z\n",
"\n",
"M7.51562 32.7188\n",
"Q6.6875 32.7188 6.14062 33.2969\n",
"Q5.60938 33.8906 5.60938 34.7188\n",
"Q5.60938 35.4531 6.14062 36.0781\n",
"Q6.6875 36.7188 7.51562 36.7188\n",
"L70.3125 36.7188\n",
"Q71.0469 36.7188 71.5781 36.0781\n",
"Q72.125 35.4531 72.125 34.7188\n",
"Q72.125 33.8906 71.5781 33.2969\n",
"Q71.0469 32.7188 70.3125 32.7188\n",
"z\n",
"\" id=\"Cmr10-3d\"/>\n",
" <path d=\"\n",
"M34.2812 27.4844\n",
"Q23.3906 27.4844 19.1875 25\n",
"Q14.9844 22.5156 14.9844 16.5\n",
"Q14.9844 11.7188 18.1406 8.90625\n",
"Q21.2969 6.10938 26.7031 6.10938\n",
"Q34.1875 6.10938 38.7031 11.4062\n",
"Q43.2188 16.7031 43.2188 25.4844\n",
"L43.2188 27.4844\n",
"z\n",
"\n",
"M52.2031 31.2031\n",
"L52.2031 0\n",
"L43.2188 0\n",
"L43.2188 8.29688\n",
"Q40.1406 3.32812 35.5469 0.953125\n",
"Q30.9531 -1.42188 24.3125 -1.42188\n",
"Q15.9219 -1.42188 10.9531 3.29688\n",
"Q6 8.01562 6 15.9219\n",
"Q6 25.1406 12.1719 29.8281\n",
"Q18.3594 34.5156 30.6094 34.5156\n",
"L43.2188 34.5156\n",
"L43.2188 35.4062\n",
"Q43.2188 41.6094 39.1406 45\n",
"Q35.0625 48.3906 27.6875 48.3906\n",
"Q23 48.3906 18.5469 47.2656\n",
"Q14.1094 46.1406 10.0156 43.8906\n",
"L10.0156 52.2031\n",
"Q14.9375 54.1094 19.5781 55.0469\n",
"Q24.2188 56 28.6094 56\n",
"Q40.4844 56 46.3438 49.8438\n",
"Q52.2031 43.7031 52.2031 31.2031\" id=\"DejaVuSans-61\"/>\n",
" <path d=\"\n",
"M48.7812 52.5938\n",
"L48.7812 44.1875\n",
"Q44.9688 46.2969 41.1406 47.3438\n",
"Q37.3125 48.3906 33.4062 48.3906\n",
"Q24.6562 48.3906 19.8125 42.8438\n",
"Q14.9844 37.3125 14.9844 27.2969\n",
"Q14.9844 17.2812 19.8125 11.7344\n",
"Q24.6562 6.20312 33.4062 6.20312\n",
"Q37.3125 6.20312 41.1406 7.25\n",
"Q44.9688 8.29688 48.7812 10.4062\n",
"L48.7812 2.09375\n",
"Q45.0156 0.34375 40.9844 -0.53125\n",
"Q36.9688 -1.42188 32.4219 -1.42188\n",
"Q20.0625 -1.42188 12.7812 6.34375\n",
"Q5.51562 14.1094 5.51562 27.2969\n",
"Q5.51562 40.6719 12.8594 48.3281\n",
"Q20.2188 56 33.0156 56\n",
"Q37.1562 56 41.1094 55.1406\n",
"Q45.0625 54.2969 48.7812 52.5938\" id=\"DejaVuSans-63\"/>\n",
" <path id=\"DejaVuSans-20\"/>\n",
" <path d=\"\n",
"M34.1875 63.1875\n",
"L20.7969 26.9062\n",
"L47.6094 26.9062\n",
"z\n",
"\n",
"M28.6094 72.9062\n",
"L39.7969 72.9062\n",
"L67.5781 0\n",
"L57.3281 0\n",
"L50.6875 18.7031\n",
"L17.8281 18.7031\n",
"L11.1875 0\n",
"L0.78125 0\n",
"z\n",
"\" id=\"DejaVuSans-41\"/>\n",
" <path d=\"\n",
"M6.20312 8.10938\n",
"Q6.20312 9.57812 6.5 10.8906\n",
"L13.7188 39.5938\n",
"L3.21875 39.5938\n",
"Q2.20312 39.5938 2.20312 40.9219\n",
"Q2.59375 43.1094 3.51562 43.1094\n",
"L14.5938 43.1094\n",
"L18.6094 59.4219\n",
"Q19 60.75 20.1719 61.6719\n",
"Q21.3438 62.5938 22.7969 62.5938\n",
"Q24.0781 62.5938 24.9219 61.8281\n",
"Q25.7812 61.0781 25.7812 59.8125\n",
"Q25.7812 59.5156 25.75 59.3438\n",
"Q25.7344 59.1875 25.6875 58.9844\n",
"L21.6875 43.1094\n",
"L31.9844 43.1094\n",
"Q33.0156 43.1094 33.0156 41.7969\n",
"Q32.9531 41.5469 32.8125 40.9531\n",
"Q32.6719 40.375 32.4219 39.9844\n",
"Q32.1719 39.5938 31.6875 39.5938\n",
"L20.7969 39.5938\n",
"L13.625 10.6875\n",
"Q12.8906 7.85938 12.8906 5.8125\n",
"Q12.8906 1.51562 15.8281 1.51562\n",
"Q20.2188 1.51562 23.6094 5.64062\n",
"Q27 9.76562 28.8125 14.7031\n",
"Q29.2031 15.2812 29.5938 15.2812\n",
"L30.8125 15.2812\n",
"Q31.2031 15.2812 31.4375 15.0156\n",
"Q31.6875 14.75 31.6875 14.4062\n",
"Q31.6875 14.2031 31.5938 14.1094\n",
"Q29.3906 8.0625 25.1875 3.46875\n",
"Q21 -1.125 15.5781 -1.125\n",
"Q11.625 -1.125 8.90625 1.45312\n",
"Q6.20312 4.04688 6.20312 8.10938\" id=\"Cmmi10-74\"/>\n",
" <path d=\"\n",
"M9.42188 54.6875\n",
"L18.4062 54.6875\n",
"L18.4062 0\n",
"L9.42188 0\n",
"z\n",
"\n",
"M9.42188 75.9844\n",
"L18.4062 75.9844\n",
"L18.4062 64.5938\n",
"L9.42188 64.5938\n",
"z\n",
"\" id=\"DejaVuSans-69\"/>\n",
" <path d=\"\n",
"M18.3125 70.2188\n",
"L18.3125 54.6875\n",
"L36.8125 54.6875\n",
"L36.8125 47.7031\n",
"L18.3125 47.7031\n",
"L18.3125 18.0156\n",
"Q18.3125 11.3281 20.1406 9.42188\n",
"Q21.9688 7.51562 27.5938 7.51562\n",
"L36.8125 7.51562\n",
"L36.8125 0\n",
"L27.5938 0\n",
"Q17.1875 0 13.2344 3.875\n",
"Q9.28125 7.76562 9.28125 18.0156\n",
"L9.28125 47.7031\n",
"L2.6875 47.7031\n",
"L2.6875 54.6875\n",
"L9.28125 54.6875\n",
"L9.28125 70.2188\n",
"z\n",
"\" id=\"DejaVuSans-74\"/>\n",
" <path d=\"\n",
"M56.2031 29.5938\n",
"L56.2031 25.2031\n",
"L14.8906 25.2031\n",
"Q15.4844 15.9219 20.4844 11.0625\n",
"Q25.4844 6.20312 34.4219 6.20312\n",
"Q39.5938 6.20312 44.4531 7.46875\n",
"Q49.3125 8.73438 54.1094 11.2812\n",
"L54.1094 2.78125\n",
"Q49.2656 0.734375 44.1875 -0.34375\n",
"Q39.1094 -1.42188 33.8906 -1.42188\n",
"Q20.7969 -1.42188 13.1562 6.1875\n",
"Q5.51562 13.8125 5.51562 26.8125\n",
"Q5.51562 40.2344 12.7656 48.1094\n",
"Q20.0156 56 32.3281 56\n",
"Q43.3594 56 49.7812 48.8906\n",
"Q56.2031 41.7969 56.2031 29.5938\n",
"M47.2188 32.2344\n",
"Q47.125 39.5938 43.0938 43.9844\n",
"Q39.0625 48.3906 32.4219 48.3906\n",
"Q24.9062 48.3906 20.3906 44.1406\n",
"Q15.875 39.8906 15.1875 32.1719\n",
"z\n",
"\" id=\"DejaVuSans-65\"/>\n",
" <path d=\"\n",
"M18.1094 8.20312\n",
"L18.1094 -20.7969\n",
"L9.07812 -20.7969\n",
"L9.07812 54.6875\n",
"L18.1094 54.6875\n",
"L18.1094 46.3906\n",
"Q20.9531 51.2656 25.2656 53.625\n",
"Q29.5938 56 35.5938 56\n",
"Q45.5625 56 51.7812 48.0938\n",
"Q58.0156 40.1875 58.0156 27.2969\n",
"Q58.0156 14.4062 51.7812 6.48438\n",
"Q45.5625 -1.42188 35.5938 -1.42188\n",
"Q29.5938 -1.42188 25.2656 0.953125\n",
"Q20.9531 3.32812 18.1094 8.20312\n",
"M48.6875 27.2969\n",
"Q48.6875 37.2031 44.6094 42.8438\n",
"Q40.5312 48.4844 33.4062 48.4844\n",
"Q26.2656 48.4844 22.1875 42.8438\n",
"Q18.1094 37.2031 18.1094 27.2969\n",
"Q18.1094 17.3906 22.1875 11.75\n",
"Q26.2656 6.10938 33.4062 6.10938\n",
"Q40.5312 6.10938 44.6094 11.75\n",
"Q48.6875 17.3906 48.6875 27.2969\" id=\"DejaVuSans-70\"/>\n",
" <path d=\"\n",
"M44.2812 53.0781\n",
"L44.2812 44.5781\n",
"Q40.4844 46.5312 36.375 47.5\n",
"Q32.2812 48.4844 27.875 48.4844\n",
"Q21.1875 48.4844 17.8438 46.4375\n",
"Q14.5 44.3906 14.5 40.2812\n",
"Q14.5 37.1562 16.8906 35.375\n",
"Q19.2812 33.5938 26.5156 31.9844\n",
"L29.5938 31.2969\n",
"Q39.1562 29.25 43.1875 25.5156\n",
"Q47.2188 21.7812 47.2188 15.0938\n",
"Q47.2188 7.46875 41.1875 3.01562\n",
"Q35.1562 -1.42188 24.6094 -1.42188\n",
"Q20.2188 -1.42188 15.4531 -0.5625\n",
"Q10.6875 0.296875 5.42188 2\n",
"L5.42188 11.2812\n",
"Q10.4062 8.6875 15.2344 7.39062\n",
"Q20.0625 6.10938 24.8125 6.10938\n",
"Q31.1562 6.10938 34.5625 8.28125\n",
"Q37.9844 10.4531 37.9844 14.4062\n",
"Q37.9844 18.0625 35.5156 20.0156\n",
"Q33.0625 21.9688 24.7031 23.7812\n",
"L21.5781 24.5156\n",
"Q13.2344 26.2656 9.51562 29.9062\n",
"Q5.8125 33.5469 5.8125 39.8906\n",
"Q5.8125 47.6094 11.2812 51.7969\n",
"Q16.75 56 26.8125 56\n",
"Q31.7812 56 36.1719 55.2656\n",
"Q40.5781 54.5469 44.2812 53.0781\" id=\"DejaVuSans-73\"/>\n",
" <path d=\"\n",
"M41.1094 46.2969\n",
"Q39.5938 47.1719 37.8125 47.5781\n",
"Q36.0312 48 33.8906 48\n",
"Q26.2656 48 22.1875 43.0469\n",
"Q18.1094 38.0938 18.1094 28.8125\n",
"L18.1094 0\n",
"L9.07812 0\n",
"L9.07812 54.6875\n",
"L18.1094 54.6875\n",
"L18.1094 46.1875\n",
"Q20.9531 51.1719 25.4844 53.5781\n",
"Q30.0312 56 36.5312 56\n",
"Q37.4531 56 38.5781 55.875\n",
"Q39.7031 55.7656 41.0625 55.5156\n",
"z\n",
"\" id=\"DejaVuSans-72\"/>\n",
" </defs>\n",
" <g transform=\"translate(209.80875 397.452875)scale(0.12 -0.12)\">\n",
" <use transform=\"translate(0.0 21.015625)\" xlink:href=\"#DejaVuSans-41\"/>\n",
" <use transform=\"translate(68.408203125 21.015625)\" xlink:href=\"#DejaVuSans-73\"/>\n",
" <use transform=\"translate(120.5078125 21.015625)\" xlink:href=\"#DejaVuSans-73\"/>\n",
" <use transform=\"translate(172.607421875 21.015625)\" xlink:href=\"#DejaVuSans-65\"/>\n",
" <use transform=\"translate(234.130859375 21.015625)\" xlink:href=\"#DejaVuSans-74\"/>\n",
" <use transform=\"translate(273.33984375 21.015625)\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use transform=\"translate(305.126953125 21.015625)\" xlink:href=\"#DejaVuSans-70\"/>\n",
" <use transform=\"translate(368.603515625 21.015625)\" xlink:href=\"#DejaVuSans-72\"/>\n",
" <use transform=\"translate(409.716796875 21.015625)\" xlink:href=\"#DejaVuSans-69\"/>\n",
" <use transform=\"translate(437.5 21.015625)\" xlink:href=\"#DejaVuSans-63\"/>\n",
" <use transform=\"translate(492.48046875 21.015625)\" xlink:href=\"#DejaVuSans-65\"/>\n",
" <use transform=\"translate(554.00390625 21.015625)\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use transform=\"translate(585.791015625 21.015625)\" xlink:href=\"#DejaVuSans-61\"/>\n",
" <use transform=\"translate(647.0703125 21.015625)\" xlink:href=\"#DejaVuSans-74\"/>\n",
" <use transform=\"translate(686.279296875 21.015625)\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use transform=\"translate(718.06640625 21.015625)\" xlink:href=\"#Cmmi10-74\"/>\n",
" <use transform=\"translate(771.708984375 21.015625)\" xlink:href=\"#Cmr10-3d\"/>\n",
" <use transform=\"translate(855.767578125 21.015625)\" xlink:href=\"#Cmr10-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"matplotlib.axis_2\">\n",
" <g id=\"ytick_1\">\n",
" <g id=\"line2d_20\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L4 0\" id=\"me8a85f7bf6\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_21\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L-4 0\" id=\"m1a32005dea\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_11\">\n",
" <!-- 0 -->\n",
" <g transform=\"translate(30.921875 372.1038125)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_2\">\n",
" <g id=\"line2d_22\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"310.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_23\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"310.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_12\">\n",
" <!-- 2 -->\n",
" <g transform=\"translate(31.415 314.589125)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-32\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_3\">\n",
" <g id=\"line2d_24\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"252.536\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_25\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"252.536\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_13\">\n",
" <!-- 4 -->\n",
" <g transform=\"translate(30.59375 256.910375)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-34\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_4\">\n",
" <g id=\"line2d_26\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"194.936\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_27\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"194.936\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_14\">\n",
" <!-- 6 -->\n",
" <defs>\n",
" <path d=\"\n",
"M33.0156 40.375\n",
"Q26.375 40.375 22.4844 35.8281\n",
"Q18.6094 31.2969 18.6094 23.3906\n",
"Q18.6094 15.5312 22.4844 10.9531\n",
"Q26.375 6.39062 33.0156 6.39062\n",
"Q39.6562 6.39062 43.5312 10.9531\n",
"Q47.4062 15.5312 47.4062 23.3906\n",
"Q47.4062 31.2969 43.5312 35.8281\n",
"Q39.6562 40.375 33.0156 40.375\n",
"M52.5938 71.2969\n",
"L52.5938 62.3125\n",
"Q48.875 64.0625 45.0938 64.9844\n",
"Q41.3125 65.9219 37.5938 65.9219\n",
"Q27.8281 65.9219 22.6719 59.3281\n",
"Q17.5312 52.7344 16.7969 39.4062\n",
"Q19.6719 43.6562 24.0156 45.9219\n",
"Q28.375 48.1875 33.5938 48.1875\n",
"Q44.5781 48.1875 50.9531 41.5156\n",
"Q57.3281 34.8594 57.3281 23.3906\n",
"Q57.3281 12.1562 50.6875 5.35938\n",
"Q44.0469 -1.42188 33.0156 -1.42188\n",
"Q20.3594 -1.42188 13.6719 8.26562\n",
"Q6.98438 17.9688 6.98438 36.375\n",
"Q6.98438 53.6562 15.1875 63.9375\n",
"Q23.3906 74.2188 37.2031 74.2188\n",
"Q40.9219 74.2188 44.7031 73.4844\n",
"Q48.4844 72.75 52.5938 71.2969\" id=\"DejaVuSans-36\"/>\n",
" </defs>\n",
" <g transform=\"translate(30.9275 199.3038125)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-36\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_5\">\n",
" <g id=\"line2d_28\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"137.336\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_29\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"137.336\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_15\">\n",
" <!-- 8 -->\n",
" <defs>\n",
" <path d=\"\n",
"M31.7812 34.625\n",
"Q24.75 34.625 20.7188 30.8594\n",
"Q16.7031 27.0938 16.7031 20.5156\n",
"Q16.7031 13.9219 20.7188 10.1562\n",
"Q24.75 6.39062 31.7812 6.39062\n",
"Q38.8125 6.39062 42.8594 10.1719\n",
"Q46.9219 13.9688 46.9219 20.5156\n",
"Q46.9219 27.0938 42.8906 30.8594\n",
"Q38.875 34.625 31.7812 34.625\n",
"M21.9219 38.8125\n",
"Q15.5781 40.375 12.0312 44.7188\n",
"Q8.5 49.0781 8.5 55.3281\n",
"Q8.5 64.0625 14.7188 69.1406\n",
"Q20.9531 74.2188 31.7812 74.2188\n",
"Q42.6719 74.2188 48.875 69.1406\n",
"Q55.0781 64.0625 55.0781 55.3281\n",
"Q55.0781 49.0781 51.5312 44.7188\n",
"Q48 40.375 41.7031 38.8125\n",
"Q48.8281 37.1562 52.7969 32.3125\n",
"Q56.7812 27.4844 56.7812 20.5156\n",
"Q56.7812 9.90625 50.3125 4.23438\n",
"Q43.8438 -1.42188 31.7812 -1.42188\n",
"Q19.7344 -1.42188 13.25 4.23438\n",
"Q6.78125 9.90625 6.78125 20.5156\n",
"Q6.78125 27.4844 10.7812 32.3125\n",
"Q14.7969 37.1562 21.9219 38.8125\n",
"M18.3125 54.3906\n",
"Q18.3125 48.7344 21.8438 45.5625\n",
"Q25.3906 42.3906 31.7812 42.3906\n",
"Q38.1406 42.3906 41.7188 45.5625\n",
"Q45.3125 48.7344 45.3125 54.3906\n",
"Q45.3125 60.0625 41.7188 63.2344\n",
"Q38.1406 66.4062 31.7812 66.4062\n",
"Q25.3906 66.4062 21.8438 63.2344\n",
"Q18.3125 60.0625 18.3125 54.3906\" id=\"DejaVuSans-38\"/>\n",
" </defs>\n",
" <g transform=\"translate(30.96875 141.7038125)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-38\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_6\">\n",
" <g id=\"line2d_30\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"79.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_31\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"79.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_16\">\n",
" <!-- 10 -->\n",
" <g transform=\"translate(23.81375 84.1038125)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_7\">\n",
" <g id=\"line2d_32\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_33\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_17\">\n",
" <!-- 12 -->\n",
" <g transform=\"translate(24.21875 26.589125)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-32\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_18\">\n",
" <!-- Option price -->\n",
" <defs>\n",
" <path d=\"\n",
"M30.6094 48.3906\n",
"Q23.3906 48.3906 19.1875 42.75\n",
"Q14.9844 37.1094 14.9844 27.2969\n",
"Q14.9844 17.4844 19.1562 11.8438\n",
"Q23.3438 6.20312 30.6094 6.20312\n",
"Q37.7969 6.20312 41.9844 11.8594\n",
"Q46.1875 17.5312 46.1875 27.2969\n",
"Q46.1875 37.0156 41.9844 42.7031\n",
"Q37.7969 48.3906 30.6094 48.3906\n",
"M30.6094 56\n",
"Q42.3281 56 49.0156 48.375\n",
"Q55.7188 40.7656 55.7188 27.2969\n",
"Q55.7188 13.875 49.0156 6.21875\n",
"Q42.3281 -1.42188 30.6094 -1.42188\n",
"Q18.8438 -1.42188 12.1719 6.21875\n",
"Q5.51562 13.875 5.51562 27.2969\n",
"Q5.51562 40.7656 12.1719 48.375\n",
"Q18.8438 56 30.6094 56\" id=\"DejaVuSans-6f\"/>\n",
" <path d=\"\n",
"M39.4062 66.2188\n",
"Q28.6562 66.2188 22.3281 58.2031\n",
"Q16.0156 50.2031 16.0156 36.375\n",
"Q16.0156 22.6094 22.3281 14.5938\n",
"Q28.6562 6.59375 39.4062 6.59375\n",
"Q50.1406 6.59375 56.4219 14.5938\n",
"Q62.7031 22.6094 62.7031 36.375\n",
"Q62.7031 50.2031 56.4219 58.2031\n",
"Q50.1406 66.2188 39.4062 66.2188\n",
"M39.4062 74.2188\n",
"Q54.7344 74.2188 63.9062 63.9375\n",
"Q73.0938 53.6562 73.0938 36.375\n",
"Q73.0938 19.1406 63.9062 8.85938\n",
"Q54.7344 -1.42188 39.4062 -1.42188\n",
"Q24.0312 -1.42188 14.8125 8.82812\n",
"Q5.60938 19.0938 5.60938 36.375\n",
"Q5.60938 53.6562 14.8125 63.9375\n",
"Q24.0312 74.2188 39.4062 74.2188\" id=\"DejaVuSans-4f\"/>\n",
" <path d=\"\n",
"M54.8906 33.0156\n",
"L54.8906 0\n",
"L45.9062 0\n",
"L45.9062 32.7188\n",
"Q45.9062 40.4844 42.875 44.3281\n",
"Q39.8438 48.1875 33.7969 48.1875\n",
"Q26.5156 48.1875 22.3125 43.5469\n",
"Q18.1094 38.9219 18.1094 30.9062\n",
"L18.1094 0\n",
"L9.07812 0\n",
"L9.07812 54.6875\n",
"L18.1094 54.6875\n",
"L18.1094 46.1875\n",
"Q21.3438 51.125 25.7031 53.5625\n",
"Q30.0781 56 35.7969 56\n",
"Q45.2188 56 50.0469 50.1719\n",
"Q54.8906 44.3438 54.8906 33.0156\" id=\"DejaVuSans-6e\"/>\n",
" </defs>\n",
" <g transform=\"translate(18.81375 228.986)rotate(-90.0)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-4f\"/>\n",
" <use x=\"78.7109375\" xlink:href=\"#DejaVuSans-70\"/>\n",
" <use x=\"142.1875\" xlink:href=\"#DejaVuSans-74\"/>\n",
" <use x=\"181.396484375\" xlink:href=\"#DejaVuSans-69\"/>\n",
" <use x=\"209.1796875\" xlink:href=\"#DejaVuSans-6f\"/>\n",
" <use x=\"270.361328125\" xlink:href=\"#DejaVuSans-6e\"/>\n",
" <use x=\"333.740234375\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use x=\"365.52734375\" xlink:href=\"#DejaVuSans-70\"/>\n",
" <use x=\"429.00390625\" xlink:href=\"#DejaVuSans-72\"/>\n",
" <use x=\"470.1171875\" xlink:href=\"#DejaVuSans-69\"/>\n",
" <use x=\"497.900390625\" xlink:href=\"#DejaVuSans-63\"/>\n",
" <use x=\"552.880859375\" xlink:href=\"#DejaVuSans-65\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"patch_3\">\n",
" <path d=\"\n",
"M40.9688 22.136\n",
"L487.369 22.136\" style=\"fill:none;stroke:#000000;\"/>\n",
" </g>\n",
" <g id=\"patch_4\">\n",
" <path d=\"\n",
"M487.369 367.736\n",
"L487.369 22.136\" style=\"fill:none;stroke:#000000;\"/>\n",
" </g>\n",
" <g id=\"patch_5\">\n",
" <path d=\"\n",
"M40.9688 367.736\n",
"L487.369 367.736\" style=\"fill:none;stroke:#000000;\"/>\n",
" </g>\n",
" <g id=\"patch_6\">\n",
" <path d=\"\n",
"M40.9688 367.736\n",
"L40.9688 22.136\" style=\"fill:none;stroke:#000000;\"/>\n",
" </g>\n",
" <g id=\"text_19\">\n",
" <!-- $\\sigma=0.25, r=0.1, T=0.25, K=10$ -->\n",
" <defs>\n",
" <path d=\"\n",
"M4.98438 0\n",
"L4.98438 2.6875\n",
"Q4.98438 2.9375 5.17188 3.21875\n",
"L20.7031 20.4062\n",
"Q24.2188 24.2188 26.4062 26.7969\n",
"Q28.6094 29.3906 30.75 32.7656\n",
"Q32.9062 36.1406 34.1562 39.625\n",
"Q35.4062 43.1094 35.4062 47.0156\n",
"Q35.4062 51.125 33.8906 54.8594\n",
"Q32.375 58.5938 29.375 60.8438\n",
"Q26.375 63.0938 22.125 63.0938\n",
"Q17.7812 63.0938 14.3125 60.4688\n",
"Q10.8438 57.8594 9.42188 53.7188\n",
"Q9.8125 53.8125 10.5 53.8125\n",
"Q12.75 53.8125 14.3281 52.2969\n",
"Q15.9219 50.7812 15.9219 48.3906\n",
"Q15.9219 46.0938 14.3281 44.5\n",
"Q12.75 42.9219 10.5 42.9219\n",
"Q8.15625 42.9219 6.5625 44.5469\n",
"Q4.98438 46.1875 4.98438 48.3906\n",
"Q4.98438 52.1562 6.39062 55.4375\n",
"Q7.8125 58.7344 10.4688 61.2969\n",
"Q13.1406 63.875 16.4844 65.2344\n",
"Q19.8281 66.6094 23.5781 66.6094\n",
"Q29.2969 66.6094 34.2188 64.1875\n",
"Q39.1562 61.7656 42.0312 57.3438\n",
"Q44.9219 52.9375 44.9219 47.0156\n",
"Q44.9219 42.6719 43.0156 38.7656\n",
"Q41.1094 34.8594 38.125 31.6562\n",
"Q35.1562 28.4688 30.5156 24.4062\n",
"Q25.875 20.3594 24.4219 19\n",
"L13.0938 8.10938\n",
"L22.7031 8.10938\n",
"Q29.7812 8.10938 34.5469 8.21875\n",
"Q39.3125 8.34375 39.5938 8.59375\n",
"Q40.7656 9.85938 42 17.8281\n",
"L44.9219 17.8281\n",
"L42.0938 0\n",
"z\n",
"\" id=\"Cmr10-32\"/>\n",
" <path d=\"\n",
"M9.28125 0\n",
"L9.28125 3.51562\n",
"Q21.7812 3.51562 21.7812 6.6875\n",
"L21.7812 59.1875\n",
"Q16.6094 56.6875 8.6875 56.6875\n",
"L8.6875 60.2031\n",
"Q20.9531 60.2031 27.2031 66.6094\n",
"L28.6094 66.6094\n",
"Q28.9531 66.6094 29.2656 66.3281\n",
"Q29.5938 66.0625 29.5938 65.7188\n",
"L29.5938 6.6875\n",
"Q29.5938 3.51562 42.0938 3.51562\n",
"L42.0938 0\n",
"z\n",
"\" id=\"Cmr10-31\"/>\n",
" <path d=\"\n",
"M4.6875 0\n",
"Q3.71875 0 3.71875 1.3125\n",
"Q3.76562 1.5625 3.90625 2.17188\n",
"Q4.04688 2.78125 4.3125 3.14062\n",
"Q4.59375 3.51562 4.98438 3.51562\n",
"Q11.0781 3.51562 13.4844 4.20312\n",
"Q14.7969 4.64062 15.375 6.89062\n",
"L29.1094 61.8125\n",
"Q29.2969 62.7969 29.2969 63.1875\n",
"Q29.2969 64.2656 28.0781 64.4062\n",
"Q26.2188 64.7969 20.9062 64.7969\n",
"Q19.9219 64.7969 19.9219 66.1094\n",
"Q20.2656 67.3906 20.4531 67.8438\n",
"Q20.6562 68.3125 21.5781 68.3125\n",
"L48.4844 68.3125\n",
"Q49.5156 68.3125 49.5156 67\n",
"Q49.4688 66.75 49.3125 66.1562\n",
"Q49.1719 65.5781 48.9219 65.1875\n",
"Q48.6875 64.7969 48.1875 64.7969\n",
"Q42.0938 64.7969 39.7031 64.1094\n",
"Q38.375 63.625 37.7969 61.375\n",
"L29.6875 29\n",
"L68.8906 59.2812\n",
"Q69 59.4688 70.1406 60.6094\n",
"Q71.2969 61.7656 71.2969 62.8906\n",
"Q71.2969 64.7969 67.9219 64.7969\n",
"Q66.8906 64.7969 66.8906 66.1094\n",
"Q67.0938 66.8906 67.2031 67.3281\n",
"Q67.3281 67.7812 67.6406 68.0469\n",
"Q67.9688 68.3125 68.6094 68.3125\n",
"L87.9844 68.3125\n",
"Q88.5312 68.3125 88.7656 67.9219\n",
"Q89.0156 67.5312 89.0156 67\n",
"Q88.9688 66.75 88.7969 66.1094\n",
"Q88.625 65.4844 88.3594 65.1406\n",
"Q88.0938 64.7969 87.5938 64.7969\n",
"Q80.2812 64.7969 71.5781 58.0156\n",
"Q71.5312 57.9531 71.4375 57.9219\n",
"Q71.3438 57.9062 71.2344 57.875\n",
"Q71.1406 57.8594 71.0938 57.8125\n",
"L50.4844 41.7969\n",
"L65.4844 6.6875\n",
"Q66.8438 4.5 68.4062 4\n",
"Q69.9688 3.51562 73.1875 3.51562\n",
"Q74.2188 3.51562 74.2188 2.20312\n",
"Q73.9219 1.03125 73.625 0.515625\n",
"Q73.3438 0 72.5156 0\n",
"L49.3125 0\n",
"Q48.3906 0 48.3906 1.3125\n",
"Q48.5312 2.34375 48.7188 2.92188\n",
"Q48.9219 3.51562 49.7031 3.51562\n",
"Q52.25 3.51562 54.0312 4.03125\n",
"Q55.8125 4.54688 55.8125 6.39062\n",
"Q55.8125 7.07812 55.7188 7.42188\n",
"L43.3125 36.2812\n",
"L28.7188 25\n",
"L24.125 6.5\n",
"Q23.875 5.28125 23.875 5.07812\n",
"Q23.875 4.04688 25.0938 3.90625\n",
"Q27 3.51562 32.3281 3.51562\n",
"Q33.2969 3.51562 33.2969 2.20312\n",
"Q32.9531 0.78125 32.75 0.390625\n",
"Q32.5625 0 31.5938 0\n",
"z\n",
"\" id=\"Cmmi10-4b\"/>\n",
" <path d=\"\n",
"M8.6875 11.375\n",
"Q9.71875 8.45312 11.8438 6.04688\n",
"Q13.9688 3.65625 16.875 2.3125\n",
"Q19.7812 0.984375 22.9062 0.984375\n",
"Q30.125 0.984375 32.8594 6.59375\n",
"Q35.5938 12.2031 35.5938 20.2188\n",
"Q35.5938 23.6875 35.4688 26.0469\n",
"Q35.3594 28.4219 34.8125 30.6094\n",
"Q33.8906 34.125 31.5625 36.7656\n",
"Q29.25 39.4062 25.875 39.4062\n",
"Q22.5156 39.4062 20.0938 38.375\n",
"Q17.6719 37.3594 16.1562 35.9844\n",
"Q14.6562 34.625 13.4844 33.1094\n",
"Q12.3125 31.5938 12.0156 31.5\n",
"L10.8906 31.5\n",
"Q10.6406 31.5 10.2656 31.8125\n",
"Q9.90625 32.125 9.90625 32.4219\n",
"L9.90625 65.8281\n",
"Q9.90625 66.0625 10.2188 66.3281\n",
"Q10.5469 66.6094 10.8906 66.6094\n",
"L11.1875 66.6094\n",
"Q17.9219 63.375 25.4844 63.375\n",
"Q32.9062 63.375 39.7969 66.6094\n",
"L40.0938 66.6094\n",
"Q40.4375 66.6094 40.7188 66.3594\n",
"Q41.0156 66.1094 41.0156 65.8281\n",
"L41.0156 64.8906\n",
"Q41.0156 64.4062 40.8281 64.4062\n",
"Q37.4062 59.8594 32.25 57.3125\n",
"Q27.0938 54.7812 21.5781 54.7812\n",
"Q17.5781 54.7812 13.375 55.9062\n",
"L13.375 37.0156\n",
"Q16.7031 39.7031 19.3125 40.8438\n",
"Q21.9219 42 25.9844 42\n",
"Q31.5 42 35.8594 38.8125\n",
"Q40.2344 35.6406 42.5781 30.5312\n",
"Q44.9219 25.4375 44.9219 20.125\n",
"Q44.9219 14.1094 41.9688 8.98438\n",
"Q39.0156 3.85938 33.9375 0.828125\n",
"Q28.8594 -2.20312 22.9062 -2.20312\n",
"Q17.9688 -2.20312 13.8438 0.328125\n",
"Q9.71875 2.875 7.34375 7.17188\n",
"Q4.98438 11.4688 4.98438 16.3125\n",
"Q4.98438 18.5625 6.4375 19.9688\n",
"Q7.90625 21.3906 10.1094 21.3906\n",
"Q12.3125 21.3906 13.7969 19.9375\n",
"Q15.2812 18.5 15.2812 16.3125\n",
"Q15.2812 14.1562 13.7969 12.6719\n",
"Q12.3125 11.1875 10.1094 11.1875\n",
"Q9.76562 11.1875 9.32812 11.25\n",
"Q8.89062 11.3281 8.6875 11.375\" id=\"Cmr10-35\"/>\n",
" <path d=\"\n",
"M18.7031 -1.125\n",
"Q14.2656 -1.125 10.8125 1\n",
"Q7.375 3.125 5.48438 6.73438\n",
"Q3.60938 10.3594 3.60938 14.7031\n",
"Q3.60938 19.3438 5.70312 24.4688\n",
"Q7.8125 29.5938 11.4531 33.8438\n",
"Q15.0938 38.0938 19.6719 40.5938\n",
"Q24.2656 43.1094 29.1094 43.1094\n",
"L54.2969 43.1094\n",
"Q55.3281 43.1094 56.0469 42.4219\n",
"Q56.7812 41.75 56.7812 40.5781\n",
"Q56.7812 39.1094 55.7344 38.0156\n",
"Q54.6875 36.9219 53.2188 36.9219\n",
"L41.0156 36.9219\n",
"Q43.8906 32.625 43.8906 26.5156\n",
"Q43.8906 21.4844 41.9375 16.5938\n",
"Q39.9844 11.7188 36.5156 7.6875\n",
"Q33.0625 3.65625 28.4375 1.26562\n",
"Q23.8281 -1.125 18.7031 -1.125\n",
"M18.7969 1.51562\n",
"Q24.2656 1.51562 28.4844 5.78125\n",
"Q32.7188 10.0625 34.9531 16.2344\n",
"Q37.2031 22.4062 37.2031 27.6875\n",
"Q37.2031 31.9844 34.8281 34.4531\n",
"Q32.4688 36.9219 28.2188 36.9219\n",
"Q22.4062 36.9219 18.3281 33.0156\n",
"Q14.2656 29.1094 12.2344 23.1875\n",
"Q10.2031 17.2812 10.2031 11.8125\n",
"Q10.2031 7.51562 12.4688 4.51562\n",
"Q14.75 1.51562 18.7969 1.51562\" id=\"Cmmi10-be\"/>\n",
" <path d=\"\n",
"M4.59375 1.3125\n",
"Q4.64062 1.5625 4.8125 2.1875\n",
"Q4.98438 2.82812 5.25 3.17188\n",
"Q5.51562 3.51562 6 3.51562\n",
"Q14.5938 3.51562 17.3906 4\n",
"Q20.0625 4.6875 20.6094 6.89062\n",
"L34.2812 61.8125\n",
"Q34.7188 63.0312 34.7188 64.0156\n",
"Q34.7188 64.7969 31.2031 64.7969\n",
"L25.3906 64.7969\n",
"Q18.7031 64.7969 15.0625 62.7344\n",
"Q11.4219 60.6875 9.71875 57.3125\n",
"Q8.01562 53.9531 5.32812 46.2969\n",
"Q4.98438 45.4062 4.29688 45.4062\n",
"L3.42188 45.4062\n",
"Q2.39062 45.4062 2.39062 46.6875\n",
"L9.51562 67.3906\n",
"Q9.71875 68.3125 10.5 68.3125\n",
"L69.5781 68.3125\n",
"Q70.6094 68.3125 70.6094 67\n",
"L67.2812 46.2969\n",
"Q67.2812 46 66.9375 45.7031\n",
"Q66.6094 45.4062 66.3125 45.4062\n",
"L65.375 45.4062\n",
"Q64.4062 45.4062 64.4062 46.6875\n",
"Q65.4844 53.7656 65.4844 56.6875\n",
"Q65.4844 60.2031 64.0156 62\n",
"Q62.5469 63.8125 60.2031 64.2969\n",
"Q57.8594 64.7969 54.1094 64.7969\n",
"L48.1875 64.7969\n",
"Q45.5156 64.7969 44.5781 64.2969\n",
"Q43.6562 63.8125 43.0156 61.375\n",
"L29.2969 6.5\n",
"Q29.25 6.29688 29.2188 6.09375\n",
"Q29.2031 5.90625 29.1094 5.60938\n",
"Q29.1094 4.34375 30.6094 4\n",
"Q33.2031 3.51562 41.7031 3.51562\n",
"Q42.6719 3.51562 42.6719 2.20312\n",
"Q42.3281 0.78125 42.125 0.390625\n",
"Q41.9375 0 41.0156 0\n",
"L5.60938 0\n",
"Q4.59375 0 4.59375 1.3125\" id=\"Cmmi10-54\"/>\n",
" <path d=\"\n",
"M7.71875 1.70312\n",
"Q7.71875 2.29688 7.8125 2.59375\n",
"L15.2812 32.4219\n",
"Q16.0156 35.2031 16.0156 37.3125\n",
"Q16.0156 41.6094 13.0938 41.6094\n",
"Q9.96875 41.6094 8.45312 37.8594\n",
"Q6.9375 34.125 5.51562 28.4219\n",
"Q5.51562 28.125 5.21875 27.9531\n",
"Q4.9375 27.7812 4.6875 27.7812\n",
"L3.51562 27.7812\n",
"Q3.17188 27.7812 2.92188 28.1406\n",
"Q2.6875 28.5156 2.6875 28.8125\n",
"Q3.76562 33.1562 4.76562 36.1719\n",
"Q5.76562 39.2031 7.89062 41.6875\n",
"Q10.0156 44.1875 13.1875 44.1875\n",
"Q16.6562 44.1875 19.2656 42.1875\n",
"Q21.875 40.1875 22.5156 36.9219\n",
"Q25.0469 40.2344 28.2969 42.2031\n",
"Q31.5469 44.1875 35.4062 44.1875\n",
"Q38.5781 44.1875 40.9844 42.3281\n",
"Q43.4062 40.4844 43.4062 37.3125\n",
"Q43.4062 34.7656 41.8125 32.875\n",
"Q40.2344 31 37.5938 31\n",
"Q35.9844 31 34.8906 32\n",
"Q33.7969 33.0156 33.7969 34.625\n",
"Q33.7969 36.8125 35.4062 38.5469\n",
"Q37.0156 40.2812 39.1094 40.2812\n",
"Q37.5 41.6094 35.2031 41.6094\n",
"Q30.9062 41.6094 27.7344 38.5469\n",
"Q24.5625 35.5 22.0156 30.8125\n",
"L14.8906 2.20312\n",
"Q14.5469 0.828125 13.3438 -0.140625\n",
"Q12.1562 -1.125 10.6875 -1.125\n",
"Q9.46875 -1.125 8.59375 -0.34375\n",
"Q7.71875 0.4375 7.71875 1.70312\" id=\"Cmmi10-72\"/>\n",
" <path d=\"\n",
"M9.90625 -18.0156\n",
"Q9.90625 -17.5781 10.2969 -17.1875\n",
"Q13.9219 -13.7188 15.9219 -9.17188\n",
"Q17.9219 -4.64062 17.9219 0.390625\n",
"L17.9219 1.60938\n",
"Q16.3125 0 13.9219 0\n",
"Q11.625 0 10.0156 1.60938\n",
"Q8.40625 3.21875 8.40625 5.51562\n",
"Q8.40625 7.85938 10.0156 9.42188\n",
"Q11.625 10.9844 13.9219 10.9844\n",
"Q17.4844 10.9844 19 7.6875\n",
"Q20.5156 4.39062 20.5156 0.390625\n",
"Q20.5156 -5.17188 18.2812 -10.1719\n",
"Q16.0625 -15.1875 12.0156 -19.1875\n",
"Q11.625 -19.3906 11.375 -19.3906\n",
"Q10.8906 -19.3906 10.3906 -18.9375\n",
"Q9.90625 -18.5 9.90625 -18.0156\" id=\"Cmmi10-3b\"/>\n",
" <path d=\"\n",
"M8.40625 5.51562\n",
"Q8.40625 7.76562 10.0625 9.375\n",
"Q11.7188 10.9844 13.9219 10.9844\n",
"Q15.2812 10.9844 16.5938 10.25\n",
"Q17.9219 9.51562 18.6562 8.20312\n",
"Q19.3906 6.89062 19.3906 5.51562\n",
"Q19.3906 3.32812 17.7656 1.65625\n",
"Q16.1562 0 13.9219 0\n",
"Q11.7188 0 10.0625 1.65625\n",
"Q8.40625 3.32812 8.40625 5.51562\" id=\"Cmmi10-3a\"/>\n",
" </defs>\n",
" <g transform=\"translate(168.62475 20.016)scale(0.144 -0.144)\">\n",
" <use transform=\"translate(0.0 20.6875)\" xlink:href=\"#Cmmi10-be\"/>\n",
" <use transform=\"translate(74.638671875 20.6875)\" xlink:href=\"#Cmr10-3d\"/>\n",
" <use transform=\"translate(158.697265625 20.6875)\" xlink:href=\"#Cmr10-30\"/>\n",
" <use transform=\"translate(208.697265625 20.6875)\" xlink:href=\"#Cmmi10-3a\"/>\n",
" <use transform=\"translate(237.240234375 20.6875)\" xlink:href=\"#Cmr10-32\"/>\n",
" <use transform=\"translate(287.240234375 20.6875)\" xlink:href=\"#Cmr10-35\"/>\n",
" <use transform=\"translate(337.240234375 20.6875)\" xlink:href=\"#Cmmi10-3b\"/>\n",
" <use transform=\"translate(366.908203125 20.6875)\" xlink:href=\"#Cmmi10-72\"/>\n",
" <use transform=\"translate(429.583984375 20.6875)\" xlink:href=\"#Cmr10-3d\"/>\n",
" <use transform=\"translate(513.642578125 20.6875)\" xlink:href=\"#Cmr10-30\"/>\n",
" <use transform=\"translate(563.642578125 20.6875)\" xlink:href=\"#Cmmi10-3a\"/>\n",
" <use transform=\"translate(592.185546875 20.6875)\" xlink:href=\"#Cmr10-31\"/>\n",
" <use transform=\"translate(642.185546875 20.6875)\" xlink:href=\"#Cmmi10-3b\"/>\n",
" <use transform=\"translate(671.853515625 20.6875)\" xlink:href=\"#Cmmi10-54\"/>\n",
" <use transform=\"translate(747.810546875 20.6875)\" xlink:href=\"#Cmr10-3d\"/>\n",
" <use transform=\"translate(831.869140625 20.6875)\" xlink:href=\"#Cmr10-30\"/>\n",
" <use transform=\"translate(881.869140625 20.6875)\" xlink:href=\"#Cmmi10-3a\"/>\n",
" <use transform=\"translate(910.412109375 20.6875)\" xlink:href=\"#Cmr10-32\"/>\n",
" <use transform=\"translate(960.412109375 20.6875)\" xlink:href=\"#Cmr10-35\"/>\n",
" <use transform=\"translate(1010.41210938 20.6875)\" xlink:href=\"#Cmmi10-3b\"/>\n",
" <use transform=\"translate(1040.08007812 20.6875)\" xlink:href=\"#Cmmi10-4b\"/>\n",
" <use transform=\"translate(1142.55078125 20.6875)\" xlink:href=\"#Cmr10-3d\"/>\n",
" <use transform=\"translate(1226.609375 20.6875)\" xlink:href=\"#Cmr10-31\"/>\n",
" <use transform=\"translate(1276.609375 20.6875)\" xlink:href=\"#Cmr10-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <defs>\n",
" <clipPath id=\"p338691d578\">\n",
" <rect height=\"345.6\" width=\"446.4\" x=\"40.96875\" y=\"22.136\"/>\n",
" </clipPath>\n",
" </defs>\n",
"</svg>\n"
],
"text": [
"Figure(PyObject <matplotlib.figure.Figure object at 0x5715850>)"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 2,
"text": [
"PyObject <matplotlib.text.Text object at 0x90b2390>"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This curve has the correct properties for an put option price curve. The value of the put option is monotonically decreasing with $s$, the boudary conditions are correct, and the overall shape is correct. We can also see that the solver responds correctly to increasing the volatility (which should increase the value of the curve everywhere except at the boundaries."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(solver(1000, 40, 1000, 0.25, 0.50, 0.1, 10.0)...)\n",
"xlabel(\"Asset price at \\$t=0\\$\")\n",
"ylabel(\"Option price\")\n",
"title(\"\\$\\\\sigma=0.50, r=0.1, T=0.25, K=10\\$\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAArcAAAI2CAYAAABKcaAKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAIABJREFUeJzs3Xd4VGX+/vH7JKGXBEKRDmIHRCnSa6ihSRGIgCCJroKLuO7PRVAgiCyLuLIKrLqIoLBRQWwoKFVAYUECiIggSpOyEJqQ0ELO74/zhSUkJDNhZp4p79d1cYHnzMy552TYva+Hz5xj2bZtCwAAAAgCYaYDAAAAAJ5CuQUAAEDQoNwCAAAgaFBuAQAAEDQotwAAAAgalFsAAAAEDcotAAAAggblFgAAAEGDcgsAAICgQbkFAABA0KDcAgAAIGhQbgHkaMeOHerZs6f+9Kc/6emnn9bAgQN15MgRl59/++23a+7cuTpw4IBOnjyppUuXqm3bttqxY4dHj2OKJ3KnpaXp7rvvdus5W7duVVhYmKKiotSkSRN17NhRLVu2VFhYmAoWLKi2bdte2RYZGamwsDCdPHnSrWPk5kbf+/r169WrVy/FxsaqVq1aSkhI0MGDB7M8ztXPUG66d++u2rVrKywsTAUKFFDjxo31hz/8IdNjpk2bpgIFCigsLEwVK1bUs88+69Yx8iK3n3+g/t0AjLEB4DpOnTplV6xY0Z47d+6VbRMmTLBr1aplX7hwwaXXsCwr06/8+fPb06dP9/hxTPBE7vXr19v16tWzw8LC3Dr2yJEj7ccff9w+f/78lW3btm2zLcuyExISMj129+7ddqlSpdx6/dzc6HtPTk62u3TpYp85c8a2bdv+/fff7aZNm9plypSx9+zZk+mxrnyGXPXNN9/YlmXZzzzzTLb7jx49ateuXdv+8MMP8/T67srt5x+ofzcAkyi3AK5r1KhRdtmyZe1Lly5d2Xb8+HE7X7589uuvv+7Sa1SpUsV+5JFH7K5du9p//vOf7Z9++skrxzHhRnJv377d7tSpkz1o0CC7YcOGbpfbTp062RkZGZm2TZ8+3bYsK1MRuqxbt25uvX5ubvRn1q1bN/vQoUOZtiUnJ9uWZdl9+/bNtN2Vz5CrJkyYYFuWZS9evDjLvk2bNtlPPPGEffz48Ty/vqtc/fkH6t8NwCTKLYDruvXWW+2uXbtm2V6rVi07JibGpddo2bKlT45jgqdyDxw40LYsy+XHb9q0yZ48eXKW7X379rUty7L379+faXtGRoYdHx/v8uu74kbfe9GiRe0aNWpkWnm2bduOioqyS5cunWmbK58hV3Xo0MHOly+fffr06Uzb586da0+YMMFjx3FHTj//QP27AZjEzC2AbJ0+fVq7du1S5cqVs+wrV66cNm7cGFDH8TSTuQ8cOKB+/fpl2b5q1SpVrVpVFStWzLT97NmziomJ8djxPfHeK1WqpIMHDyo9PT3T9gIFCujcuXMey3q1S5cu6ZtvvlHt2rVVtGhRSVJ6errGjBmjIkWK+GS+1h2B+ncDMC3CdAAArvn+++/1/PPPa+XKlTp9+nSW/R9//LG6du3qsePt3btXklS8ePEs+4oUKaLff/9d6enpiojI+X9GLly4oL/97W86cuSIwsPDtXv3bk2cOFHVq1f32HE+/PBDrVy5Uvv371dSUpKSkpK0c+dO7d+/X8OGDVODBg1cft+u8tT5yYtOnTpl2bZr1y4dOnRIAwcOzLKvcOHCiouL89jxPfHe169fr/Pnz6tw4cJXth08eFBHjhxRmzZtMj02t8+QqzZt2qQzZ86oRYsWkqQjR46od+/eGjVqlNq2bevWa/mCyc8YEMj4GwEEgM8++0x9+vTRoEGDNHv2bO3cuVOjR4/W4MGD1atXL+XLl0+NGjXK9JzHH39cmzdvdus4kyZNUrNmzSRJv//+uyQpf/78WR5XpEgR2batkydPqlSpUjm+5uHDh/Xggw+qUqVKkqS5c+eqWbNm2rx5s8qUKXPDxzl//rzWr1+v1157Tbfeeqt69eqlkSNH6v7779e9996r6OjobMutv5wfT1m1apUkqXnz5rk+1h/ee9GiRa+snl726quvKiIiQhMmTMi0PbfPkKuuPkcbNmzQc889p1WrVqlRo0ZuldsbPX+u8rfPGBAoKLeAn9u5c6fi4uL0j3/8Q4888siV7du3b9f27dvVunXrbJ/3z3/+84aOGx4eLkmyLCvLvosXL0pSln9Szs6uXbsyvUZcXJweffRRTZgwQVOmTLnh46xevVqNGzfW+fPn9dtvv6lfv35q0qSJ9u/fr5IlS6pXr17ZPs9fzo+nuFNu/fG9//LLL5o2bZrGjh2revXqZdqX22fIVatWrZJlWdq1a5d+/fVXffLJJ6pcubLeeustJSYmZlsis3Oj589V/vYZAwIFM7eAn3v22WdVq1atTMVWkkqXLq3Dhw977bilS5e+7r7U1FRZlpVl5S071/4fc1hYmEqVKqVPPvnEI8eJjIxUq1attG7dOp0/f14PPPCAJGemc9OmTS6Vvbzw1PnxlFWrVql8+fJu/1N9Xnj6vZ8/f179+vXTU089pZEjR2bZn9tnyBW2bWvNmjWKiopSrVq1NHz4cBUsWFDx8fFKSUnR+++/7/Jr+Yq/fcaAQEG5BfzYyZMn9dlnn2U7R7lz505VqVLFa8cuW7asLMvSiRMnsuxLTU1VVFRUrv/H2rRp02zLZUZGhv773/965Dj169dX8eLFtWLFCpUuXVo1atTI7a15hCfOj6f89ttv2rNnj9eK/LU8+d5t29bgwYPVu3dvjRs3Lst+Vz5Drti2bZuOHz+uBx98MNMIwuOPP66wsDBNnz7d5dfyFX/6jAGBhLEEwI/t2LFD6enpuu+++zJtT01N1YoVKzRp0qTrPvfRRx/Vpk2b3DreK6+8oqZNm0pyZvruvfde7du3L8vjdu3apXvuuSfX19uyZYtuu+22LNuPHj2qatWqeew4krRixQq3yp0/nB9PcWckQfKv9z569Gg1btxYQ4cOvbJtzpw56t+/vyTXPkOuuHyOrp17rVy5sjp37qxPP/1UycnJqlOnTq6vdaPnz1X+9BkDAorBy5AByMWOHTtsy7LsHTt2ZNr+0ksv2XfccUeWa4R62ujRo+0KFSpk2rZr1y7bsqwsd4jauXOnffbs2UzbHnjgAfvYsWOZtm3atMm2LMseP358no7z008/2efOncu0LS0tzS5QoIA9depU997gDbrR83PZwIEDc7yJQ3bv+Wp/+MMfbMuy7B9//NGN9DfGE+/97bfftl999dUs26++Jq+rnyHbzvk89enTxw4LC7MPHjyYZd9XX31lW5ZlDx48ONvneltOP393zjMAB+UW8HNNmjSxp02bduW/V65caVetWtUnRebQoUN2VFSU/e67717Z9uSTT9o1a9a0L168eGXb119/bVuWZbdv3z7T8zds2GD36tXLTktLs23buZnAgAED7CZNmmS6dairx1m2bJltWZb9wAMPZDrO0qVLbcuy7B9++MEzb9xFN3p+LuvTp49tWdaV83S1673nyy5dumTfcsstdnR09A2+G/fc6HtftmyZXaFCBbt///52v379rvzq06dPpjuUufoZyuk8Xbp0yb7pppvs6tWrZ/teMjIy7DJlytiFCxe2Dx8+nLcTcgNy+vm7ep4B/A9jCYCfW7BggYYNG6Yff/zxyjUt169fn+OXTTzlpptu0sqVKzVq1CglJyfr9OnTOnHihBYvXpzp2po33XSTypQpo1tuuSXT8+vVq6cnn3xSAwcOVKFChfT777/r7rvv1owZM5QvXz63j1OuXDmVKlUqy8XrDx06pPvuu89n87bu5s7u/Bw9elQDBgzQgQMHtG3bNlmWpSpVqqhmzZpKSEjQgw8+KCn795yRkaHu3bsrNTVV+/bt0y+//KKwsDA1atRIkZGRGjhwoEeva+vp9y5JvXr10qlTpzR37twrXxizbVuWZem555678jhXP0PZnafdu3fr0Ucf1b59+3TkyBEVLFhQrVq1Uq9eva6MQWzevFl/+MMflJKSIkmqU6eO+vXrl+PIjye4+vN39TwD+B/Ltm3bZIAzZ85o3Lhx2rx5szZt2qRjx45pzJgxGjNmzJXHZGRk6JVXXtGiRYv0448/6tSpU6pSpYq6deumESNGKDIy0uA7AOBrY8eO1dixY03H8KlQfM95wXkCYPxqCSkpKfrXv/6lixcvqnv37pKyXvYlLS1NY8eOVbVq1fTqq69q0aJFeuSRR/Tmm2+qSZMmXrtVIwD/dP78edMRfC4U33NecJ4AGP83japVq165zMmxY8c0Y8aMLI8pXLiw9u3bpxIlSlzZ1rx5c1WuXFkPPPCAPvzww2zvsw4g+KxevVr33nuv6Rg+FYrvOS84TwAkP1i5vdr1JiTCwsIyFdvL6tevL8m5xiOA4Hfp0iV9/PHH6t27t+koPhOK7zkvOE8ALvOrcuuu5cuXS5LPv0QCwIzw8HC9/PLLpmP4VCi+57zgPAG4zPhYQl4dOHBAI0aMUP369dW5c+cs+1NSUvTll1+qatWqKlSokIGEAAAAyMnZs2e1Z88etW/fXqVKlfLIawZkuT1+/LhiY2NlWdZ17wf+5ZdfXrnDDQAAAPzXnDlzPPb9qYArtydOnFDbtm116NAhLV++XFWrVs32cZdvyzhnzhzdeeedPkwY2IYPH64pU6aYjhFwOG/u45zlDefNfZyzvOG8uY9z5r7t27erf//+bt1OOzcBVW5PnDihNm3aaO/evVq2bJlq1qx53ccWLFhQknTnnXe6dK9wOKKiojhfecB5cx/nLG84b+7jnOUN5819nLO8u9zbPCFgyu3lYrtnzx4tWbJEtWvXNh0JAAAAfsYvyu2iRYuUmpqq06dPS5K2bdum+fPnS5I6deokSWrfvr02b96sKVOm6MKFC1q3bt2V55cpU0Y333yz74MDAADAr/hFuR0yZIj27t0rybk72bx58zRv3jxZlqXdu3crIyND3333nSzL0pNPPpnl+YMGDdLMmTN9HRsAAAB+xi/K7e7du3N9TEZGhg+SIC4uznSEgMR5cx/nLG84b+7jnOUN5819nDP/YNnXuy1YgEtOTlbdunW1ceNGhrsBAAD8kDf6WkDfoQwAAAC4GuUWAAAAQYNyCwAAgKBBuQUAAEDQoNwCAAAgaFBuAQAAEDQotwAAAAgalFsAAAAEDcotAAAAggblFgAAAEGDcgsAAICgQbkFAABA0KDcAgAAIGhQbgEAABA0KLcAAAAIGpRbAAAABA3KLQAAAIIG5RYAAABBg3ILAACAoEG5BQAAQNAI+nJ7/rzpBAAAAPCVoC+3bdpIx46ZTgEAAABfCPpym5YmrVhhOgUAAAB8IejLrSQtW2Y6AQAAAHyBcgsAAICgERLl9uefpf37TacAAACAt4VEubUsafly0ykAAADgbSFRbu+5h9EEAACAUBD05TY8XIqJccqtbZtOAwAAAG8K+nIbFuaU24MHpZ07TacBAACANwV9uQ0Pl5o2lSIiGE0AAAAIdkFfbsPCpKJFpYYNKbcAAADBLiTKreSMJqxYIV26ZDYPAAAAvCfoy214uPN7TIx04oS0ZYvZPAAAAPCeoC+3l1duGzSQChdmNAEAACCYBX25vbxymz+/1KwZ5RYAACCYBX25DbvqHcbESKtXSxcumMsDAAAA7wn6cnt55VaSWreW0tKk//zHXB4AAAB4T0iV23vukUqUYDQBAAAgWAV9ub16LCE8XGrVinILAAAQrEKq3ErO3O26dVJqqpk8AAAA8J6gL7dXjyVIztxterrzxTIAAAAEl6Avt9eu3N5+u1S+PKMJAAAAwSjoy+21K7eW5YwmUG4BAACCT9CX22tXbiWn3G7eLB075vs8AAAA8J6gL7fXrtxKztytbUsrV/o8DgAAALwoJMttpUrSrbcymgAAABBsgr7cZjeWIDF3CwAAEIyCvtxmt3IrOaMJO3dKv/3m2zwAAADwnqAvt9dbuW3Vyvl9+XLfZQEAAIB3hWy5LVVKuuceRhMAAACCSdCX2+uNJUjO3O3y5c6VEwAAABD4gr7cXm/lVnLmbn/7Tfr5Z9/lAQAAgPcEfbnNaeW2eXMpIoLRBAAAgGAR0uW2aFGpQQPKLQAAQLAI+nKb01iC5MzdrlghZWT4Jg8AAAC8J+jLbU4rt5Izd3v8uLRli2/yAAAAwHuCvtzmtnLbsKFUqBCjCQAAAMEg6Mttbiu3BQpIzZpRbgEAAIJB0Jfb3FZuJWfudvVq6cIF7+cBAACA91Bu5czdpqZK69d7Pw8AAAC8J+jLbURE7o+5914pKorRBAAAgEAX9OXWlZXb8HCpVSvnVrwAAAAIXJTb/9O6tbR2rTOeAAAAgMAU9OU2t6slXBYTI128KK1Z4908AAAA8J6gL7eurtzecYdUrhxztwAAAIHMaLk9c+aMnnnmGbVr106lS5dWWFiYEhMTs31scnKy2rRpo2LFiqlEiRLq2bOndu/enesxXF25tSxn9Za5WwAAgMBltNympKToX//6ly5evKju3btLkizLyvK4n376SS1btlR6errmzZunmTNnaufOnWrWrJlSUlJyPIarK7eSM3ebnOzcjhcAAACBx4ULZXlP1apVdeLECUnSsWPHNGPGjGwfN3r0aBUqVEgLFy5U0aJFJUl169bVrbfeqsmTJ2vixInXPYarK7eSs3Jr29LKlVKPHq4/DwAAAP7Bb2ZubdvOdnt6eroWLlyonj17Xim2klS5cmW1atVKH330UY6v6065rVxZuuUW5m4BAAACld+U2+v55ZdfdO7cOd19991Z9tWqVUu7du3ShRzum+vOWILE3C0AAEAg8/tye+zYMUlSyZIls+wrWbKkbNu+MtqQHXdWbiVn7vann6QDB9x7HgAAAMwzOnPrC59+Oly//hqVaVtcXJzi4uKyfXyrVs7vy5dLAwZ4Ox0AAEBoSEpKUlJSUqZtJ0+e9Phx/L7cRkdHS5KOZ3MJg+PHj8uyLJUoUeK6z3/jjSlq27aOy8crXVqqXZtyCwAA4EnZLS4mJyerbt26Hj2O348lVK9eXYUKFdL333+fZd/WrVt16623Kn/+/Nd9/v91Y7e0bu18qew633EDAACAn/L7chsREaEuXbpowYIFOnPmzJXt+/bt04oVK9TDC9fsiomR9u+Xdu3y+EsDAADAi4yPJSxatEipqak6ffq0JGnbtm2aP3++JKlTp04qVKiQEhMTVb9+fXXu3FkjRozQ2bNnNXr0aJUpU0ZPP/20xzM1by5FRDirt7fe6vGXBwAAgJcYL7dDhgzR3r17JTl3J5s3b57mzZsny7K0e/duVa5cWbfffrtWrlypv/zlL+rVq5ciIiIUExOjyZMnX5nJ9aRixaT77nPmbh97zOMvDwAAAC8xXm53797t0uPq1KmjJUuWeDnN/7RuLf3zn1JGhvvXygUAAIAZ1LbriImRjh2TsvkeGwAAAPwU5fY6GjWSChXiVrwAAACBhHJ7HQUKSE2bciteAACAQEK5zUHr1tKqVdLFi6aTAAAAwBWU2xzExEhnzkjr15tOAgAAAFdQbnNQp44UGcloAgAAQKCg3OYgPFxq2ZIvlQEAAAQKym0uYmKktWultDTTSQAAAJAbym0uYmKkCxekNWtMJwEAAEBuKLe5uPNO6aabmLsFAAAIBJTbXFiWc0kw5m4BAAD8H+XWBTEx0saN0okTppMAAAAgJ5RbF8TESLYtrVxpOgkAAAByQrl1QZUqUvXqzN0CAAD4O8qti5i7BQAA8H+UWxfFxEjbt0sHD5pOAgAAgOuh3LqoVSvn9xUrzOYAAADA9VFuXVSmjFSrFqMJAAAA/oxy64aYGKfc2rbpJAAAAMgO5dYNMTHSvn3SL7+YTgIAAIDsUG7d0Ly5FB7OJcEAAAD8FeXWDcWLS/XrM3cLAADgryi3boqJcVZuMzJMJwEAAMC1KLduiomRUlKkrVtNJwEAAMC1KLduatRIKliQuVsAAAB/RLl1U8GCUpMmzN0CAAD4I8ptHsTESF9/LV28aDoJAAAArka5zYOYGOnMGWnDBtNJAAAAcDXKbR7UqSNFRjJ3CwAA4G8ot3kQESG1aMHcLQAAgL+h3OZRTIz07bdSWprpJAAAALiMcptHMTHShQtOwQUAAIB/oNzm0V13SWXLMpoAAADgTyi3eWRZUuvWlFsAAAB/Qrm9ATEx0saN0smTppMAAABAotzekJgYKSPDuaEDAAAAzKPc3oCqVaVq1RhNAAAA8BeU2xsUE0O5BQAA8BeU2xsUEyP9+KN06JDpJAAAAKDc3qBWrZzfV6wwmwMAAACU2xtWtqxUsyajCQAAAP6AcusBl+dubdt0EgAAgNBGufWAmBhp715p927TSQAAAEIb5dYDmjeXwsIYTQAAADCNcusBkZFS/fqUWwAAANMotx7Spo1TbjMyTCcBAAAIXZRbD2nXTkpJkTZvNp0EAAAgdFFuPaRhQ6loUemrr0wnAQAACF2UWw/Jn19q2ZJyCwAAYBLl1oPatZO++UZKTTWdBAAAIDRRbj2oXTvpwgVp1SrTSQAAAEIT5daDbrtNqlSJ0QQAAABTKLceZFnO6i3lFgAAwAzKrYe1ayf9+KN04IDpJAAAAKGHcuthMTHOCu6SJaaTAAAAhB7KrYdFR0t16zKaAAAAYALl1gvatZOWLuVWvAAAAL5GufWCtm2lo0elLVtMJwEAAAgtlFsvaNRIKlKE0QQAAABfo9x6QYEC3IoXAADABMqtl7RtK61ZI6WlmU4CAAAQOii3XsKteAEAAHyPcusld9whVazIaAIAAIAvUW69xLKc0QRu5gAAAOA7lFsvatdO+uEH6eBB00kAAABCA+XWi9q04Va8AAAAvkS59aJSpaR772XuFgAAwFcCptx+99136tatm8qXL68iRYrozjvv1AsvvKCzZ8+ajpajdu2clVtuxQsAAOB9AVFut27dqqZNm2r//v169dVX9fnnn6tv374aN26c4uLiTMfLUYcOzq14k5NNJwEAAAh+EaYDuOK9997ThQsXNH/+fN18882SpJYtW+rQoUN68803derUKUVGRhpOmb3GjaXixaVFi6R69UynAQAACG4BsXJbsGBBScpSYCMjIxUeHq78+fObiOWSfPmcL5YtWmQ6CQAAQPALiHL78MMPq3Tp0nr88ce1e/dunT59WgsXLtSbb76poUOHqlChQqYj5qhjR+k//5GOHzedBAAAILgFRLmtWLGiVq5cqU2bNql69eqKjIxU165dNWjQIE2ZMsV0vFx16OB8oYyrJgAAAHhXQMzc7tixQ23atFH16tU1adIklS5dWuvWrdP48eN1+vRpzZgx47rPHT58uKKiojJti4uL8+kX0SpWlO6+2xlN6NvXZ4cFAADwG0lJSUpKSsq07eTJkx4/jmXbtu3xV/Wwnj176ttvv9Wvv/6aaQRh1qxZGjx4sFauXKnmzZtnek5ycrLq1q2rjRs3qk6dOr6OnMWIEdLMmdLhw1JYQKyXAwAAeJc3+lpA1Kxt27bprrvuyjJbW+//Lj+wbds2E7Hc0rEjlwQDAADwtoAot5UqVdIPP/yg1NTUTNvXrl0ryZnJ9XdXXxIMAAAA3hEQ5fapp55SSkqK2rZtq3nz5mn58uWaMGGCnn76adWoUUMdO3Y0HTFXXBIMAADA+wKi3MbGxmrlypWKjIzU8OHD1aVLF7377rt67LHHtGrVKkVEBMT34hQbyyXBAAAAvCkwWqGkZs2aaVGAL3tefUkwrpoAAADgeQGxchssKlRwLgn2xRemkwAAAAQnyq2PdewoLV7srOACAADAsyi3PsYlwQAAALyHcutjXBIMAADAeyi3PpYvn9S2LXO3AAAA3kC5NeDyJcGOHjWdBAAAILhQbg3o1Mn5ndVbAAAAz6LcGlC2rHTffdJnn5lOAgAAEFwot4Z07Sp9+aV0/rzpJAAAAMGDcmtIly7SmTPSypWmkwAAAAQPyq0hNWtKVaowmgAAAOBJlFtDLMsZTfjsM8m2TacBAAAIDpRbg7p0kfbtk77/3nQSAACA4EC5NahFC6lYMUYTAAAAPIVya1D+/FL79pRbAAAAT6HcGta1q7R+vXT4sOkkAAAAgY9ya1hsrBQWJi1caDoJAABA4KPcGhYdLTVuzGgCAACAJ1Bu/UDXrtKSJdLZs6aTAAAABDbKrR/o0sUptkuXmk4CAAAQ2Ci3fuCOO5xfH31kOgkAAEBgo9z6iR49pE8+kdLTTScBAAAIXJRbP9Gjh3T8uLRqlekkAAAAgStP5Xbx4sUaMWKEHnnkEe3bt0+StH79eh05csSj4UJJnTpS5crSggWmkwAAAAQut8ptWlqa2rRpo9jYWL300kuaOXOmUlJSJEkvv/yyJk2a5JWQocCynNXbBQukjAzTaQAAAAKTW+V21KhR2rhxo+bPn69Tp07Jtu0r+9q2baslS5Z4PGAo6dFDOnRI+s9/TCcBAAAITG6V23nz5mncuHHq0aOHChYsmGlf5cqVr4woIG8aN5bKlGE0AQAAIK/cKrdHjx5VzZo1s3+hsDCdO3fOI6FCVXi4dP/9Trm9alEcAAAALnKr3JYvX17ff/99tvu2bt2qatWqeSRUKOvRQ/r1V+k6pxkAAAA5cKvc9uzZUxMmTFBycrIsy7qyfc+ePXrllVfUq1cvjwcMNa1aSZGRjCYAAADkhVvldvTo0Spfvrzuu+8+1atXT5I0ePBg1axZU6VLl9aIESO8EjKU5M/v3I6XcgsAAOA+t8pt8eLF9c0332j8+PEqUqSIqlevrsKFC2vkyJFavXq1Chcu7K2cIaVHD+mHH6SdO00nAQAACCwR7j6hcOHCGjFiBKu0XtS+vVSokLN6y2kGAABwnVsrt0eOHNGOHTuy3bdjxw4dPXrUI6FCXeHCUmysNG+e6SQAAACBxa1yO3ToUE2ePDnbfX//+981bNgwj4SC1KePlJws7dplOgkAAEDgcKvcfvvtt2rXrl22+9q3b6/Vq1d7JBSkTp2kIkWk9983nQQAACBwuFVuU1JSVKpUqWz3RUVFMZbgQYVNlaS9AAAgAElEQVQLO1dNoNwCAAC4zq1yW6ZMmevexOGHH35QdHS0R0LB0aePtHWrtH276SQAAACBwa1y27FjR02YMCHLl8p27typCRMmKDY21qPhQl2HDlLx4qzeAgAAuMqtcjtmzBiFh4erdu3a6tixox555BF16NBBtWrVUnh4uBITE72VMyQVLCh16+aUW9s2nQYAAMD/uVVuK1SooA0bNqhfv37asmWLZs+era1bt2rAgAHasGGDKlSo4K2cIatPH+mnn5zxBAAAAOTM7Zs4VKhQQW+99ZY3siAbbdtKJUpI770n3X236TQAAAD+za2VW/he/vzO7XgZTQAAAMhdriu348aNU0JCgsqXL6/ExERZlpXj40ePHu2xcHD06SO99Za0caNUr57pNAAAAP4r13I7duxYdejQ4Uq5zQ3l1vNatZLKlJHmzqXcAgAA5CTXsYSMjAzdd999V/6c2y94XkSEFBcnJSVJ6emm0wAAAPgvl2duz507pzfffFPbuaOAEQMGSP/9r7RsmekkAAAA/svlclugQAH98Y9/1JEjR7yZB9dRp450xx3Su++aTgIAAOC/XC63lmXp5ptv1uHDh72ZB9dhWc7q7UcfSWfOmE4DAADgn9y6FNiTTz6piRMn6tSpU97Kgxw8+KCUluYUXAAAAGTl1k0ctm3bppSUFFWrVk2tW7dWuXLlslwa7NVXX/VoQPxP1apS8+bSnDnOKi4AAAAyc6vcTps27cqfFyxYkO1jKLfe1b+/9Nhj0qFDUrlyptMAAAD4F7fGErgUmHkPPOBcGiwpyXQSAAAA/8PtdwNMVJTUpQtXTQAAAMiOW2MJl3377bdauXKljh07pujoaLVs2VKNGzf2dDZcx4AB0v33S99/L919t+k0AAAA/sOtcnv27Fn16dNHCxcuzLIvNjZW8+bNU6FChTwWDtmLjXVux/v229Irr5hOAwAA4D/cGkt45plntHjxYr344ovavXu30tLS9Ouvv2r8+PH66quv9P/+3//zVk5cJV8+6aGHnNGECxdMpwEAAPAfbpXb999/X6NGjdKzzz6rKlWqqGDBgqpatapGjhypUaNG6f333/dWTlzj4YelY8ekTz81nQQAAMB/uFVu09LS1LRp02z3NW7cWGlpaR4JhdzddZfUsKE0c6bpJAAAAP7DrXLboEEDbdiwIdt93333nRo0aOCRUHDN4MHSl19Kv/1mOgkAAIB/cKvcvvbaa3r99dc1depUnThxQpJ0/Phxvfbaa3rzzTf12muveSUkstenj1SwoPTOO6aTAAAA+Ae3rpbQoEEDXbx4UcOGDdOwYcMUERGh9PR0SVL+/PnVsGFDWZYl27ZlWZZ+//13r4SGo3hx56YOM2dKzz4rXXMnZAAAgJDjVrnt2bOny4+1aFo+MXiwNHu2tHq11Ly56TQAAABmuVVuZ82a5aUYyKtmzaRbbnFWbym3AAAg1HH73QBnWc5lwebNk5gCAQAAoY5yGwQGDpTOnZO4zDAAAAh1lNsgUKGC1KGD9NZbppMAAACYFVDlds2aNYqNjVXJkiVVuHBh3XbbbRo/frzpWH4hPl76z3+kH34wnQQAAMCcgCm3//73v9WyZUuVKFFC7777rhYtWqS//OUvpmP5jc6dpdKlWb0FAAChza2rJZhy4MABPfroo3rsscc0derUK9tbtGhhMJV/yZ9feughadYsaeJEqUAB04kAAAB8L0/l9siRI9q7d6/Onj2bZV9zL1yPasaMGUpLS2OlNhfx8dLLL0uffurc3AEAACDUuFVuDx06pP79+2vFihXZ7rcsS5cuXfJIsKutWrVK0dHR+vHHH9WlSxdt27ZNJUuWVI8ePTRp0iQVK1bM48cMRHfeKTVuLM2YQbkFAAChya1y+8QTT2jz5s2aNGmSatWqpQI++rfvAwcOKDU1Vb1799bIkSPVqFEjrV+/XmPGjNEPP/yg1atX+yRHIIiPlxISpL17pSpVTKcBAADwLbfK7ddff62XXnpJgwcP9laebGVkZOjcuXMaO3asnnnmGUnO+EP+/Pk1fPhwLV++XK1bt872ucOHD1dUVFSmbXFxcYqLi/N6bhN695aefNKZvR0zxnQaAAAAR1JSkpKSkjJtO3nypMeP41a5tSxLlStX9niI3ERHR2vXrl1q3759pu0dOnSQJG3atOm65XbKlCmqU6eO1zP6i6JFpb59ndvxPvecFB5uOhEAAED2i4vJycmqW7euR4/j1qXAevXqpYULF3o0gCvuueeeHPdbluWjJIEhPl7at09atsx0EgAAAN9ya+W2T58+SkhI0KVLl9S1a1dFR0dneYw3Vkl79uypN954Q1988YVq1659Zfvnn38uSWrQoIHHjxnIGjSQatRwrnnbrp3pNAAAAL7jVrm9/E//06ZN07Rp07Ls99bVEtq0aaPOnTtr3LhxysjIUIMGDfTdd99p3Lhx6tKli5o0aeLxYwYyy3JWb0eMkFJSpFKlTCcCAADwDbfK7cyZM72VI1cffPCBEhMT9eabbyoxMVEVKlTQn/70J43hW1PZGjBA+stfpDlzpOHDTacBAADwDcu2bdt0CG+4PKC8cePGkPpC2dV695a2b5e+/95ZzQUAAPAn3uhrbn2h7Go7d+7U2rVr9fPPP3skCDwvPl764QdpwwbTSQAAAHzD7XL7wQcfqHLlyrrjjjvUpEkT3X777apSpYrmzZvnjXy4AW3aSJUqOXcsAwAACAVuldsvvvhCcXFxioqK0t/+9je98847mjhxoiIjIxUXF6cvvvjCWzmRB+Hh0uDB0nvvSampptMAAAB4n1szt02aNFGxYsX0xRdfKCzsf704IyNDsbGxOn36tL755huvBHUXM7eOvXulatWcmzoMGmQ6DQAAwP8Yn7ndvHmzhgwZkqnYSlJYWJiGDBmizZs3eyQUPKdKFWc8gdEEAAAQCtwqt+Hh4bpw4UK2+y5evJil9MI/JCRI33wj/fST6SQAAADe5VYbrV+/viZNmqS0tLRM28+dO6fJkydzpzA/1a2bFB3tjCYAAAAEM7du4pCYmKjWrVurevXq6tWrl8qVK6eDBw9qwYIFOnbsmJYvX+6tnLgBBQpI/ftLs2dLL74o5ctnOhEAAIB3uLVy27RpUy1ZskRVq1bV9OnT9dxzz+n1119XtWrVtGTJEm6D68fi46UjR6SFC00nAQAA8B63Vm4lqUWLFlq7dq1SU1N14sQJlShRQkWKFPFGNnhQrVrSffdJb70lde9uOg0AAIB35PkbYEWKFFHFihUptgEkPl5atEg6cMB0EgAAAO/IdeX2nXfeUadOnRQdHa3Zs2fLsqwcH//QQw95LBw8q29f6amnpFmzpFGjTKcBAADwvFzL7aBBg7Ru3TpFR0fr4YcfzvUFKbf+q3hxqXdv56oJzz4rceU2AAAQbHItt7/++qvKly9/5c8IbPHxzsrtypVS69am0wAAAHhWruW2atWq2f4ZgalJE+n2250vllFuAQBAsHHrH6ZvvvlmbdmyJdt9W7du1c033+yRUPAey3JWbz/8UDpxwnQaAAAAz3Kr3O7Zs0fnz5/Pdt+5c+e0Z88eT2SClz30kHTpkjR3rukkAAAAnuWxrxT9+uuvKlasmKdeDl5UtqzUubMzmgAAABBMcp25nT17tmbNmnXlv4cMGaLixYtnekxaWpq2bNmiFi1aeDwgvCMhwSm4yclSnTqm0wAAAHhGruU2NTVVR48evfLfJ0+e1Llz5zI9pkCBAurbt68SExM9nxBe0b69VL68NGOGNH266TQAAACekWu5HTJkiIYMGSLJuVrC/Pnzdc8993g9GLwrIkIaNEiaNk16+WWpUCHTiQAAAG6c218oo9gGj8GDpVOnnCsnAAAABINcV26vlZ6erg8++EArV67UsWPHFB0drZYtW6p3796KiHD75WBQ9epSq1bOaEL//qbTAAAA3Di32mhKSorat2+vTZs2KSIiQiVLltSxY8c0Y8YMTZ48WV999ZVKlSrlrazwgvh4p9ju2iXdcovpNAAAADfGrbGEp556Sjt37tTcuXOVlpamw4cP6+zZs5ozZ45+/vlnDR8+3Fs54SU9ekhRUdLMmaaTAAAA3Di3yu1nn32mF154QXFxcVdGECIiIvTggw/qhRde0GeffeaVkPCeQoWkfv2kWbOk9HTTaQAAAG6MW+XWtm3VrFkz2301atSQbdseCQXfio+XDh2SFi0ynQQAAODGuFVuY2JitHTp0mz3LV26VK1atfJIKPjWvfc6N3LgjmUAACDQufWFstGjR6t79+5KT09Xv379dNNNN+nQoUOaO3euPvroIy1YsEDHjx+/8viSJUt6PDC8Iz5eGjbMWcEtV850GgAAgLyxbDdmCcLCXF/otSxLly5dylMoT0hOTlbdunW1ceNG1eH+srk6edIptWPHSn/5i+k0AAAgFHijr7m9cusqy7LcDgNzoqKkXr2c0YRnnpH48QEAgEDkVrkdO3asl2LAH8THS3PmSKtXS82bm04DAADgPre+UCY5V0xISUlRSkoKV0cIMi1aOHct44tlAAAgULlcbteuXauuXbuqWLFiKlOmjMqUKaPixYurW7duWrdunTczwkcsy1m9nTdPOnXKdBoAAAD3uVRup02bpmbNmmnRokWqUaOGevfurd69e+uuu+7S559/rmbNmmnatGnezgofGDhQOn9eSkoynQQAAMB9uc7crlu3Tk8++aRiY2M1ffp0VaxYMdP+/fv3a8iQIRo+fLjq1aunBg0aeC0svK98eSk21hlNeOwx02kAAADck+vK7csvv6z77rtPH330UZZiK0mVKlXSxx9/rPr162vy5MleCQnfSkiQvvtO2rLFdBIAAAD35Fpu16xZo6FDhyo8PPy6jwkPD9fQoUO1evVqj4aDGbGxUtmyfLEMAAAEnlzL7fHjx1WlSpVcX6hy5co6ceKER0LBrHz5nNnbOXOkc+dMpwEAAHBdruW2ZMmS2rt3b64vtH//fm63G0Ti46UTJ6SPPzadBAAAwHW5ltumTZtq+vTpOV7TNiMjQ1OnTlWzZs08Gg7m3Hab1KyZNGOG6SQAAACuy7XcPv3001q3bp3uv/9+HTx4MMv+AwcOqHv37lq/fr2efvppr4SEGfHx0rJl0u7dppMAAAC4JtdLgTVs2FBTpkzR8OHDtWjRItWrV0/VqlWTJO3evVsbNmyQbduaMmUKlwELMr16ScOGSW+/LY0bZzoNAABA7nItt5L0xz/+UXXq1NFf//pXrVix4sodyQoXLqwOHTpoxIgRatKkiVeDwveKFJHi4pxyO2aMlMMFMwAAAPyCS+VWkpo0aaKFCxfq0qVLSklJkSSVKlUqx0uEIfDFx0tvvCF99ZXUsaPpNAAAADlz6fa7VwsPD1fZsmVVtmxZim0IqFdPqlWLa94CAIDA4Ha5RWixLOeOZZ98Ih05YjoNAABAzii3yFW/flJYmPTuu6aTAAAA5Ixyi1xFR0vduzujCTlc7hgAAMA4yi1ckpAgbd8urV1rOgkAAMD1UW7hktatpapV+WIZAADwb5RbuCQsTHr4Yen996XTp02nAQAAyB7lFi57+GEpLU364APTSQAAALJHuYXLKlWS2reXZswwnQQAACB7lFu4JT5eWrdO+vFH00kAAACyotzCLV27SqVK8cUyAADgnyi3cEv+/NJDD0nvvCNduGA6DQAAQGaUW7gtPl5KSZE+/dR0EgAAgMwot3DbXXdJjRoxmgAAAPwP5RZ5Eh8vffmltG+f6SQAAAD/Q7lFnvTuLRUuLM2aZToJAADA/1BukSfFikl9+0ozZ0oZGabTAAAAOCi3yLP4eGnvXmnZMtNJAAAAHJRb5FnDhtKdd/LFMgAA4D8ot8gzy5ISEqSPPpKOHTOdBgAAgHKLGzRggGTb0pw5ppMAAABQbnGDSpd2bsn71ltOyQUAADApYMvtjBkzFBYWpmLFipmOEvISEqStW6XvvjOdBAAAhLqALLcHDhzQn//8Z5UvX16WZZmOE/LatpUqVZJmzDCdBAAAhLqALLePPfaYWrVqpbZt28rm38KNCw+XBg2SkpKk1FTTaQAAQCgLuHI7Z84crV69WtOmTaPY+pHBg6UzZ6T5800nAQAAoSygyu1///tfDR8+XBMnTlT58uVNx8FVqlaVYmIYTQAAAGYFVLkdOnSo7rrrLj322GOmoyAb8fHSmjXSjh2mkwAAgFAVYTqAq+bPn6+FCxdqy5Ytbj1v+PDhioqKyrQtLi5OcXFxnowHSfffL5UoIc2cKf3tb6bTAAAAf5KUlKSkpKRM206ePOnx4wREuT1z5oyeeOIJDRs2TGXLlr1yIi5cuCBJOnXqlCIiIlSkSJEsz50yZYrq1Knj07yhqmBB56YOs2ZJ48dL+fKZTgQAAPxFdouLycnJqlu3rkePExBjCSkpKTpy5IgmT56skiVLXvn13nvvKTU1VSVKlNCAAQNMx4Sc0YQjR6TPPzedBAAAhKKAWLktV66cVqxYkematrZta+LEifr666+1ePFilSpVymBCXHb33VK9es4dy+6/33QaAAAQagKi3BYoUEAtWrTIsv3tt99WeHi4mjdvbiAVrichQRoyRDpwQKpQwXQaAAAQSgJiLOF6LMviDmV+qG9fqUABafZs00kAAECoCehy+/bbb+v33383HQPXiIyUHnjAuWpCRobpNAAAIJQEdLmF/0pIkH75Rfr6a9NJAABAKKHcwiuaNpVuu835YhkAAICvUG7hFZYlDR4sffihdOKE6TQAACBUUG7hNQMHShcvSv/+t+kkAAAgVFBu4TU33SR17sxoAgAA8B3KLbwqPl7atElKTjadBAAAhALKLbyqY0epXDlWbwEAgG9QbuFVERHSoEHS3LnS2bOm0wAAgGBHuYXXDR4snTolLVhgOgkAAAh2lFt43S23SC1bSjNmmE4CAACCHeUWPhEfL61c6dy1DAAAwFsot/CJnj2lyEhp5kzTSQAAQDCj3MInChWS+vWT3n5bSk83nQYAAAQryi18Jj5eOnRIWrzYdBIAABCsKLfwmTp1pHvu4Zq3AADAeyi38KmEBOmzz6TDh00nAQAAwYhyC5968EHnxg7vvGM6CQAACEaUW/hUiRLOlRPeekuybdNpAABAsKHcwufi46WdO6U1a0wnAQAAwYZyC59r2VK6+Wa+WAYAADyPcgufCwuTBg+W5s2TTp0ynQYAAAQTyi2MGDRIOndOeu8900kAAEAwodzCiAoVpI4dGU0AAACeRbmFMfHx0oYN0vffm04CAACCBeUWxnTuLJUpw+otAADwHMotjMmXTxo4UJozRzp/3nQaAAAQDCi3MGrwYOn4cenjj00nAQAAwYByC6PuuENq0kSaMcN0EgAAEAwotzAuIUFaulTas8d0EgAAEOgotzDugQekYsWkt982nQQAAAQ6yi2MK1JE6tvXKbeXLplOAwAAAhnlFn4hIUHav19assR0EgAAEMgot/AL9etLNWtyzVsAAHBjKLfwC5bl3LHsk0+ko0dNpwEAAIGKcgu/0b+/U3Lffdd0EgAAEKgot/AbpUpJ99/vjCbYtuk0AAAgEFFu4Vfi46Uff5T+8x/TSQAAQCCi3MKvtGkjVanCHcsAAEDeUG7hV8LCpIcflt5/XzpzxnQaAAAQaCi38DsPPyylpkoffGA6CQAACDSUW/idypWldu0YTQAAAO6j3MIvxcdLa9dK27ebTgIAAAIJ5RZ+qWtXKTqaO5YBAAD3UG7hlwoUkB56SJo9W7pwwXQaAAAQKCi38Fvx8VJKivTZZ6aTAACAQEG5hd+qUUNq0IDRBAAA4DrKLfxafLy0eLG0f7/pJAAAIBBQbuHX+vaVCheWZs0ynQQAAAQCyi38WrFiUu/e0syZUkaG6TQAAMDfUW7h9+LjpT17pOXLTScBAAD+jnILv9e4sXTHHXyxDAAA5I5yC79nWc7q7YIF0rFjptMAAAB/RrlFQHjoIWfmdu5c00kAAIA/o9wiIJQp49yS9623JNs2nQYAAPgryi0CRny89P330saNppMAAAB/RblFwGjfXqpQQZoxw3QSAADgryi3CBjh4dLDD0tJSVJamuk0AADAH1FuEVAeflj6/Xdp/nzTSQAAgD+i3CKg3Hyz1Lo1owkAACB7lFsEnIQEafVqaedO00kAAIC/odwi4HTvLpUoIc2caToJAADwN5RbBJyCBaV+/aRZs6SLF02nAQAA/oRyi4CUkCD997/SF1+YTgIAAPwJ5RYBqXZtqW5d545lAAAAl1FuEbDi46XPP5cOHjSdBAAA+AvKLQJWXJxUoIA0e7bpJAAAwF9QbhGwoqKkXr2c0QTbNp0GAAD4g4Apt8uWLdPAgQN12223qUiRIqpYsaLuv/9+JScnm44Gg+LjpV9+kb7+2nQSAADgDwKm3L7xxhvat2+fnnrqKS1atEj/+Mc/dOTIETVs2FArVqwwHQ+GNG8u3XILXywDAACOCNMBXDV16lSVKVMm07YOHTrolltu0YQJE9SqVStDyWCSZTmrt4mJ0muvOaMKAAAgdAXMyu21xVaSihQpojvvvFO//fabgUTwFwMHOjdz+Pe/TScBAACmBUy5zc6pU6eUnJysGjVqmI4Cg8qVkzp1YjQBAAAEeLkdOnSozp49q1GjRpmOAsPi46XkZGnTJtNJAACASQEzc3ut559/Xv/+9781depU3Xvvvdd93PDhwxV1zSBmXFyc4uLivB0RPhQbK910k7N6O3Wq6TQAAOBaSUlJSkpKyrTt5MmTHj+OZduBd4XQxMREJSYmasKECRoxYkS2j0lOTlbdunW1ceNG1alTx8cJYcKIEdIbbzh3LCtUyHQaAACQG2/0tYAbS7hcbBMTE69bbBGa4uOlkyeljz4ynQQAAJgSUOX2hRdeUGJiop5//nk9//zzpuPAz9x6q3Pd23/9y3QSAABgSsDM3L788ssaM2aMOnTooNjYWK1bty7T/oYNGxpKBn/y+ONSXJz0/ffS3XebTgMAAHwtYMrtwoULZVmWFi9erMWLF2faZ1mWLl26ZCgZ/EnPnlKFCtI//sGlwQAACEUBM5awYsUKXbp0SRkZGVl+UWxxWb580hNPSHPnSkeOmE4DAAB8LWDKLeCqRx6RwsKcKycAAIDQQrlF0ImOlh56SJo+XTp/3nQaAADgS5RbBKVhw6TDh6UPPjCdBAAA+BLlFkHprruk9u2lV16RAu82JQAAIK8otwhaf/6ztGmT9NVXppMAAABfodwiaMXESA0aSOPHm04CAAB8hXKLoGVZ0qhR0po10qpVptMAAABfoNwiqHXuLNWuzeotAAChgnKLoHZ59XbJEmn9etNpAACAt1FuEfR69JBuv1168UXTSQAAgLdRbhH0wsOd1dtPP5U2bDCdBgAAeBPlFiHhwQeda9+OHGk6CQAA8CbKLUJCeLgzlrB0qfMLAAAEJ8otQka3bs51b599lruWAQAQrCi3CBmWJU2cKH33nbRggek0AADAGyi3CCktW0rt2ztfMEtPN50GAAB4GuUWIeevf5V27pT++U/TSQAAgKdRbhFy7r1XSkiQRo+Wjh41nQYAAHgS5RYh6cUXnS+VPfec6SQAAMCTKLcISaVLS+PGSf/6l5ScbDoNAADwFMotQtaQIc6NHf74Ry4NBgBAsKDcImRFREivvip9+6309tum0wAAAE+g3CKktW4tPfSQ9PTT0qFDptMAAIAbRblFyPv736V8+ZzxBAAAENgotwh50dHSa69JH34offSR6TQAAOBGUG4BSb17S126OF8yO3HCdBoAAJBXlFtAkmVJ06dLZ886BZerJwAAEJgot8D/qVjRuSXve+9Jc+eaTgMAAPKCcgtcJS5O6t9fGjpU2r3bdBoAAOAuyi1wjalTpZIlpQEDpPR002kAAIA7KLfANSIjpTlzpLVrpbFjTacBAADuoNwC2WjSRBo/XnrxRenTT02nAQAArqLcAtcxYoR0//3OeMLPP5tOAwAAXEG5Ba7DsqRZs6SbbpJ69JBSU00nAgAAuaHcAjmIjJQWLHCunDBwoJSRYToRAADICeUWyEWNGs51bxcscEYVAACA/6LcAi7o1k165RXppZekN94wnQYAAFxPhOkAQKAYNkzatcu5wUPlylLHjqYTAQCAa7FyC7jIsqQpU6ROnaSePaXVq00nAgAA16LcAm4ID5fee09q1MgpuRs2mE4EAACuRrkF3FSokPTJJ1LNmlKHDtLWraYTAQCAyyi3QB4ULSp98YVUpYrUurW0ebPpRAAAQKLcAnkWFSUtWSJVrSq1aiWtW2c6EQAAoNwCNyA6Wlq2zBlRaNNGWrHCdCIAAEIb5Ra4QcWLS4sXS40bOzO4771nOhEAAKGLcgt4QJEi0sKFUp8+Ulyc9Ne/SrZtOhUAAKGHmzgAHpI/vzR7tnTzzdLIkc4NH6ZPlwoUMJ0MAIDQwcot4EGWJY0d65TcOXOk5s2lfftMpwIAIHRQbgEveOgh6ZtvpMOHpbp1paVLTScCACA0UG4BL6lXT9q4UapTR2rfXho3TkpPN50KAIDgRrkFvKhUKedmD88/LyUmSs2aObO4AADAOyi3gJeFhztzuGvWSCkpUu3a0uuvczUFAAC8gXIL+EijRtKmTc487uOPSzEx0k8/mU4FAEBwodwCPlS0qPTPf0pfffX/27v7qKjq/A/g7xkQeRBHBgQNRA3E0HCBlnwIFczEVtcEFg0I8aHcjCxXS2k9JKSyZpJbqWctDCoRfEhOmamtLmhZaSmamLZqirn04xl0EFTg+/vjHkaH4WEg4s4M79c59zBz7517P/fjR8/Hy3e+V5pFYcQIachCTY3ckREREZkHNrdEMnjsMSA/H3jlFWDtWunxvbt2cagCERHRb8Xmlkgm1tbSl8x++AEYOhSIiAAeeUSaQoyIiIg6hs0tkfsBP3cAABg4SURBVMyGDpVmVDh4EKitBQIDgSeeAL7/Xu7IiIiITA+bWyIj8eijUkP70UfAuXNAQADw+OO8k0tERNQebG6JjIhSCTz1lNTcZmYC165Jd3KDgoBPPgHq6+WOkIiIyLixuSUyQhYWwJNPAqdPA9nZwK1bwPTpgIcH8Prr0ny5REREpI/NLZERUyqlpvabb4DvvgOCg4EVKwA3NyA6GjhwgHdziYiI7sXmlshE/PGPQFqaNFThtdekB0JMngy4uwNLl0qzLnAqMSIi6u7Y3BKZGCcnqZk9e1a6mxsWBrz/vvRYXy8vadu33wINDXJHSkRE1PXY3BKZKIVCupv7zjtAYSGwb580bCE9XXrUr5sb8OyzwO7dQGWl3NESERF1DTa3RGbAykoaovDuu8CvvwJHjgAzZwI5OUB4OODoCIwZI43XPXKEj/slIiLzxeaWyMxYWABjxwLr1wM//QRcvgz861+Aq6t0l3f8eEClku7uvvSSNBtDcbHcURMREXUOS7kDIKLf16BBwDPPSEt9PXDmjPRgiK++AnbsAFJSpP3c3QE/P93FzU0a/kBERGQqTObOrUajwaJFi+Dq6gobGxv4+flh+/btcodldjIzM+UOwSSZSt4sLABfXyAuTnpIxNWr0pKVJQ1jqK6W7u4+8YTU7Do7AxMmAM89B7z9NvDFF9L+nfFlNVPJmbFh3tqPOesY5q39mDPjYDLNbVhYGD788EMkJiZi//79CAgIQGRkJAupkzGfHWPKeRswQGps164F/v1voKREamA/+QR4/nmgb1/pLu/SpUBICDBwIGBvD/j7AxERwMsvAxs3Anv3SjM4VFcbdl5TzpmcmLf2Y846hnlrP+bMOJjEsITPP/8cBw8eRGZmJmbOnAkAGD9+PAoKCvDyyy9j5syZUCpNpk8nMmoKhdTwDhgATJt2d319PVBQAJw/f3f5+Wdpvt2rV4E7d+7u27ev9Pn+/VteOFUZERH9Hkyiuc3Ozoa9vT0iIiJ01s+ZMwdRUVE4duwYRo8eLVN0RN2DhQVw//3S8qc/6W6rr5dmabhy5e5y9aq0Li8P+PxzoKhI/2lqDg7STA5qtfTz3uXedSoV0Lu3dMe4d2+gVy/p6W1ERERNmURzm5+fD29vb727sz4+PgCAs2fPsrklkpGFhfTlMzc3IDCw+X3q64HSUqnh/b//A155BYiMBMrKgPJy6ecvvwCnT0uvy8qA27dbPqednW7D2/jTzg6wsZEWW9u7r1ta1/jeyqr5pUcP6fr4xToiItNgEs1tWVkZPD099dar1Wrt9qZqa2sBAOfOnft9gzMzlZWVOHnypNxhmBzmrX2cnQF7+0pMnNhyzoSQ5uOtqgI0GuDmTWk8772vmy6lpVKDfOuWtNTWSkvj+9aa5bb06HF3sbTU/dn42tJSaoSVSmlpfG1hofv63p9KpfS55j7T9LMKBXDmTCWef/4kFIq764C7r1tbGu8PdPSzTfdv1FLj39I+Xf3ZgoJKvPfeyTY/21nnNAcKBXDtWiU++sg8/l3rqj+fa9cqsXXr758zc6q3y5elPq2mEydgN4nmtiMuX74MAHjqqadkjsT0PPTQQ3KHYJKYt/YzpZzduaM7rlhOGzeaTt6Mxfz5zFlHzJrFvLVXTAxz1hFXrlzBI4880inHMonm1tHRsdm7s+Xl5drtTYWEhGDr1q0YNGgQbGxsfvcYiYiIiKh9amtrcfnyZYSEhHTaMU2iuR0xYgQyMzPR0NCgM+72zJkzAIAHH3xQ7zNOTk6Ijo7ushiJiIiIqP3GjBnTqcczie8bh4aGQqPRYNeuXTrr09PT4erqipEjR8oUGREREREZE5O4czt58mQ89thjWLBgAa5fvw4PDw9kZmbiiy++QEZGBhTmNLKaiIiIiDpMIYQQcgdhiOrqaixfvhw7duxAeXk5vL298corr2DGjBlyh0ZERERERsIkhiUAgJ2dHf75z3+isLAQtbW1yMvLa7ax1Wg0WLRoEVxdXWFjYwM/Pz9s375dhohNR25uLpRKZbPL8ePH5Q5PdhqNBkuXLsWkSZPQt29fKJVKJCUlNbvvyZMnMXHiRNjb28PBwQHh4eHamTu6G0PzNnv27GZrb9iwYTJELa9Dhw4hNjYWXl5esLOzg5ubG6ZPn97sNHOstbsMzRtr7a5Tp05hypQpGDhwIGxtbeHo6IgxY8YgIyNDb1/W2l2G5o211rrU1FQolUrY29vrbeuMejOJYQntERYWhu+//x6vv/46vLy8kJGRgcjISDQ0NCAyMlLu8IzaP/7xDwQHB+usGz58uEzRGI/S0lK899578PX1RWhoKFJTU5sdCnP+/HkEBQXB398fO3fuRE1NDV599VWMHTsWp06dgpOTkwzRy8fQvAGAjY0NcnJy9NZ1N5s3b0ZJSQn+9re/Yfjw4SgpKUFKSgpGjRqFAwcOaP9+stZ0GZo3gLXWqKqqCu7u7oiOjoarqys0Gg0yMjIQExODK1euYPny5QBYa00ZmjeAtdaS//3vf3jppZdw33334fr16zrbOq3ehBnZu3evUCgUIisrS2f9pEmThKurq6ivr5cpMuOWk5MjFAqF+Pjjj+UOxeiVlpYKhUIhkpKS9LZFREQIZ2dncePGDe26goICYWVlJZYtW9aVYRqd1vIWGxsr7O3tZYjK+BQVFemt02g0ol+/fmLixInadaw1XYbmjbXWtlGjRgl3d3fte9aaYZrmjbXWsqlTp4rp06eL2bNni169euls66x6M5lhCYbIzs6Gvb09IiIidNbPmTMHhYWFOHbsmEyRmQZhGsOvZdVSjurq6vDZZ58hPDwcvXr10q53d3dHcHAwsrOzuypEo9RWbbH2JM7Oznrr7Ozs4O3tjWvXrgFgrTXHkLw1Yq21ztHREZaW0i91WWuGuzdvjVhr+rZu3Yovv/wSGzdu1MtPZ9abWTW3+fn58Pb21pkLFwB8fHwAAGfPnpUjLJMRFxeHHj16QKVSYfLkyTh69KjcIZmMS5cuoba2FiNGjNDb5uPjg4sXL+L2b3n2q5mrqalB//79YWlpiQEDBmDhwoWoqKiQOyyjUFVVhZMnT2qHCLHWDNM0b41Ya7qEEKirq0NJSQk2bdqEAwcO4KWXXgLAWmtNa3lrxFrTVVRUhEWLFmHNmjW477779LZ3Zr2Z1ZjbsrIyeHp66q1Xq9Xa7aSvT58+WLRoEYKCguDo6IgLFy7gjTfeQFBQEPbu3YtJkybJHaLRa6ytxlq7l1qthhACFRUVcHFx6erQjJ6vry/8/Py0D2PJzc3F+vXrcejQIXz33Xews7OTOUJ5xcXFoaamRjuWj7VmmKZ5A1hrzVmwYAHeffddAICFhQXWrVuHBQsWAGCttaa1vAGstebExcVh2LBhePbZZ5vd3pn1ZlbNLXWMr68vfH19te8feeQRhIaGwsfHB8uWLWNzS7+rRYsW6bx/9NFH4efnh7/85S9ITU3Fiy++KFNk8ktISMC2bduwYcMG+Pn5yR2OyWgpb6w1fcuXL8f8+fNRXFyMTz/9FIsXL0ZtbS2WLVsmd2hGra28sdZ07dq1C5999hlOnz7dJeczq+bW0dGx2buz5eXl2u1kGJVKhSlTpmDz5s24desWevbsKXdIRq2xthpr7V7l5eVQKBRwcHDo6rBMVmhoKOzs7Lr1OPmkpCSsXr0aycnJeO6557TrWWutaylvLenutTZgwAAMGDAAgPTAJED6z8G8efNYa61oKW9z585F3759m/1Md601jUaD559/Hi+88AJcXFxQWVkJANohBlVVVbC0tOzUejOrMbcjRozAuXPn0NDQoLP+zJkzAKD99QC1D58A1zYPDw/Y2Njghx9+0Nt25swZDBkyBFZWVjJEZpqEEHp/j7uTpKQk7RIfH6+zjbXWstby1pLuXmtNBQQEoK6uDj///DNrrR0a89bafKzdtdZKS0tRXFyMdevWQa1Wa5esrCxUV1fDwcEBMTEx8PT07LR6M6vmNjQ0FBqNBrt27dJZn56eDldXV4wcOVKmyExPRUUF9uzZAz8/P/7jZQBLS0v8+c9/xu7du6HRaLTrr169ipycHISFhckYnenZtWsXampqMHr0aLlD6XIrV65EUlISEhISkJCQoLedtda8tvLWku5ca83JycmBhYUFPDw8WGvtcG/eWtJda61///7IyclBbm6udsnJyUFISAisra2Rm5uLVatWwcLCotPqzWQev2uokJAQ7UMcPDw8kJmZidTUVO3DHEhfdHQ0Bg8eDH9/f6jValy4cAEpKSm4fPky9u3bhwkTJsgdouz27duH6upq3LhxA/PmzUNERIR2yrkpU6bAxsYGP/30EwICAuDv74/4+Hjt5NOVlZU4depUtxwW01beiouL8dRTTyEqKgr3338/hBA4fPgw3nrrLXh6euLYsWPdatLzlJQUvPzyy5g8eTJWrFihN1XOqFGjAIC11oQheSsoKGCt3WP+/PlQqVQICAiAi4sLSktLsXPnTuzYsQNLly7FmjVrALDWmjIkb6w1w8yePRsff/wxbty4oV3XafXW/ul3jZtGoxEvvvii6N+/v+jZs6fw9fUV27dvlzsso7ZmzRrh5+cn+vTpIywtLYWzs7MIDw8X33//vdyhGY1BgwYJhUIhFAqFUCqVOq8LCgq0+504cUJMnDhR2NnZCZVKJcLCwsTPP/8sY+TyaitvFRUVIiwsTAwePFjY2tqKnj17iqFDh4r4+Hhx/fp1ucPvckFBQTp5undRKpU6+7LW7jIkb6w1XWlpaWLcuHGib9++okePHsLBwUEEBweLjIwMvX1Za3cZkjfWmmFmz57d7IMuOqPezO7OLRERERF1X2Y15paIiIiIujc2t0RERERkNtjcEhEREZHZYHNLRERERGaDzS0RERERmQ02t0RERERkNtjcEhEREZHZYHNLRERERGaDzS0RGZ133nkHSqUSPj4+cocCAPj666+RlJSEqqqqLjtneno6lEolrl692mXnNFRH87F7926Ul5d3ejzJyclYsmQJEhMTERsbi+vXr3f6OYjIdLC5JSKjs2XLFtjY2ODs2bM4fvy43OHI0txOnToV3377Lfr169dl5zRUR/Jx8+ZNREZGorCwsFNj2bhxI44cOYKUlBQkJibC29sbs2bN6tRzEJFpYXNLREblxIkT+OGHH7By5UrY2tpiy5Ytcoek1RVPK7958yYAwMnJCQ8//DCsrKx+93N2VHvycfz4cdjZ2eHBBx/s1Bhef/11xMbGat/HxMTg008/xYULFzr1PERkOtjcEpFR2bJlC6ysrDB37lxMnz4dWVlZqKmp0dmnpKQE8+fPh7u7O6ytreHs7IzAwEAcOnSoXftcuHABUVFRcHFxgbW1NYYNG4ZNmzbpnCsxMRFLly4FAAwePBhKpRJKpRJHjhxpNv7ExEQolUqcOnUKYWFhUKlU6NOnD2JiYlBaWtrsvnl5eQgPD4darYanpyeA5oclnD9/HpGRkejXrx+sra0xcOBAxMbG4vbt2zrHNeS6mnPx4kXMmTMHXl5esLOzg5ubG6ZNm4b8/PwO56PR0aNHMXr06DZjaI///ve/uHbtGoYPH65d5+rqCpVKhdzc3E49FxGZDku5AyAialRTU4Nt27bh8ccfR58+fRAdHY1t27Zh586dOr9qjomJQV5eHpKTkzF06FBUVFTgxIkTOuM529rnxx9/xJgxYzBo0CC8+eab6NevH/bv348XXngBpaWlePXVVwEAzzzzDCoqKvDOO+8gOzsb/fv3BwB4e3u3ei2hoaGYOXMmnnvuOeTn5yMhIQE//vgjjh07BktL3X96w8LCEBUVhbi4OFRXVzd7vNOnTyMwMBDOzs5YuXIlhgwZgsLCQuzZswe3b9/W3uE19LqaU1hYCEdHRyQnJ8PFxQUVFRVIT0/HyJEjkZeXBy8vr3bn44MPPsDBgwdx4MABeHh4ICYmBnPnzkVwcHCr+TPEpUuXAAC9e/fWWW9vb2+UY5WJqIsIIiIj8dFHHwmFQiF27twphBDizp07wtnZWYwbN05nP3t7e7F48eJWj9XWPiEhIcLd3V3cuHFDZ/3ChQuFjY2NqKio0K574403hEKhEAUFBW1ew4oVK4RCoRBLlizRWb9t2zahUChERkaG3r6JiYl6x0lLS9M554QJE4RarRalpaWtnr8919WWuro6cfv2beHl5aWTy/bko5FarRZfffWVwfsbIiMjQygUClFcXKyz3tvbW8TFxXXquYjIdPDOLREZjS1btkClUmHatGkAAEtLS8ycORMbNmzAxYsXtb+yf/jhh5GWlga1Wo1HH30UDz30EHr06KFzrNb2qa2txaFDhxAXFwdra2vU1dVpP/f4449jw4YN+PbbbzF58uQOX0t0dLTO+4iICMTGxiI3NxdRUVE628LDw1s91s2bN3H48GE888wzcHR0bHG/33pddXV1WLt2LbZu3YpLly7hzp072m3nz59vNcbW5OfnQ6PRICAgoNntDQ0NCA8PR21tbZvHUqlUyMrKAgBYWFjo/Gx0584dnWsnou6FzS0RGYVLly7h8OHDePLJJ1FTU6P9YtWUKVOwYcMGvP/++0hOTgYAbN++HatWrUJqaioSEhLQq1cvhIaGYu3atXBxcWlzn7q6OtTX1+Ptt9/G22+/rReLQqFAWVnZb7qeprMcWFpaQq1WN3vcxl/tt6SiogINDQ1wc3Nrdb+ysrLfdF2LFy/Gpk2bEB8fj/Hjx8PBwQEKhQJPP/203rjn9vjqq6/g7+/f4pfjlEolsrOz233cvn37ApCa43tVV1dDpVK1P1AiMgtsbonIKLz//vsAgKysLO2duXt98MEHWLVqFZRKJRwdHbF+/XqsX78e165dwyeffIL4+HgUFxdj3759ANDqPrt374aFhQVmzZqFuLi4ZuMZNGjQb7qeX3/9VadpraurQ1lZWbN3XhUKRavHUqvVsLCwwC+//NLqfg4ODr/purZu3YrY2FisWrVKZ31JSQkcHBxaPXdrvvzyS4wZM6bDn2/J4MGDAQBFRUVwcnICIDW6lZWVuP/++zv9fERkGtjcEpHs6uvrkZ6eDk9PT6Smpupt37NnD1JSUvD5559j6tSpOtvc3NwQFxeHgwcP4ptvvmn2+E33sbGxQXBwME6ePAkfHx+9IQ1N9ezZE8DdaboMkZGRAX9/f+37HTt2oL6+HkFBQQYfo5GNjQ3Gjx+PnTt3YvXq1S0OTbC1tW3XdTWlVCr17q7u3bsXhYWF8PLy0q5rbz6+/vprrFu3DgCwbds2jB07FgMGDNBu7+iwhMGDB8PT0xPnz5/Xzpjw008/oba2FhMmTDAoNiIyP2xuiUh2+/fvx6+//oq1a9di3LhxetuHDx+uHZowbtw4BAcHIyoqCkOHDoW9vT2+++47HDhwQDt2taqqChMmTGh1n7feeguBgYEYO3YsFixYgIEDB+LGjRu4ePEi9uzZg//85z/a848YMUL7mVmzZqFHjx544IEH0KtXrxavKTs7G5aWlpg4cSLOnj2LhIQE+Pr6YsaMGR3K0ZtvvonAwECMHDkS8fHx8PDwQFFREfbs2YPNmzdrY2nPdTU1depUpKen44EHHoCPjw9OnDiBdevWwc3NTWdO2/bmo6SkBN7e3to4mo457uiwBACIjY3Fhx9+qP1zTUtLwxNPPIEhQ4Z06HhEZAbk/kYbEVFoaKiwtrZudSaAyMhIYWVlJYqKisSCBQvEH/7wB6FSqYStra3w9vYWSUlJoqamRgghxK1bt9rcRwghrly5IubNmyfc3NyElZWVcHZ2FoGBgSI5OVnv/H//+9+Fq6ursLCwEEqlUhw+fLjZOBtnQMjLyxPTpk0T9vb2onfv3iI6OlqUlJTo7JuYmCiUSqUoKyvTO05aWppQKpU6MxKcO3dOzJgxQzg5OYmePXuKgQMHirlz54pbt27pfLY913WvyspK8fTTTwsXFxdhZ2cnxo0bJ44ePSqCgoJEcHBwh/IhhBCrV68Wf/3rX8WKFSuERqNpNYb2unPnjliyZIlYuHChSEhIELNmzRKVlZWdeg4iMi0KIbrgkTtERN1EYmIiXnvtNZSWlkKtVssdDhFRt8MnlBERERGR2WBzS0TUiRQKRZuzHxAR0e+HwxKIiIiIyGzwzi0RERERmQ02t0RERERkNtjcEhEREZHZYHNLRERERGaDzS0RERERmQ02t0RERERkNtjcEhEREZHZYHNLRERERGaDzS0RERERmQ02t0RERERkNtjcEhEREZHZ+H9aDg7e+VXmFAAAAABJRU5ErkJggg==",
"svg": [
"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Created with matplotlib (http://matplotlib.sourceforge.net/) -->\n",
"<svg height=\"404pt\" version=\"1.1\" viewBox=\"0 0 501 404\" width=\"501pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
" <defs>\n",
" <style type=\"text/css\">\n",
"*{stroke-linecap:square;stroke-linejoin:round;}\n",
" </style>\n",
" </defs>\n",
" <g id=\"figure_1\">\n",
" <g id=\"patch_1\">\n",
" <path d=\"\n",
"M0 404.653\n",
"L501.512 404.653\n",
"L501.512 0\n",
"L0 0\n",
"z\n",
"\" style=\"fill:#ffffff;\"/>\n",
" </g>\n",
" <g id=\"axes_1\">\n",
" <g id=\"patch_2\">\n",
" <path d=\"\n",
"M40.9688 367.736\n",
"L487.369 367.736\n",
"L487.369 22.136\n",
"L40.9688 22.136\n",
"z\n",
"\" style=\"fill:#ffffff;\"/>\n",
" </g>\n",
" <g id=\"line2d_1\">\n",
" <path clip-path=\"url(#p338691d578)\" d=\"\n",
"M40.9688 79.736\n",
"L41.4156 43.0694\n",
"L61.5237 120.118\n",
"L66.439 137.959\n",
"L70.4606 151.688\n",
"L74.0354 163.096\n",
"L77.6102 173.701\n",
"L80.7381 182.319\n",
"L86.1003 196.204\n",
"L131.679 313.579\n",
"L133.913 318.585\n",
"L136.147 323.126\n",
"L138.381 327.247\n",
"L141.062 331.692\n",
"L143.744 335.65\n",
"L146.425 339.173\n",
"L149.106 342.309\n",
"L151.787 345.101\n",
"L154.468 347.587\n",
"L157.149 349.8\n",
"L160.277 352.075\n",
"L163.405 354.062\n",
"L166.533 355.796\n",
"L170.107 357.509\n",
"L173.682 358.975\n",
"L177.704 360.373\n",
"L182.172 361.664\n",
"L186.641 362.727\n",
"L191.556 363.681\n",
"L197.365 364.574\n",
"L204.068 365.361\n",
"L211.664 366.015\n",
"L220.601 366.555\n",
"L231.772 366.996\n",
"L246.071 367.326\n",
"L266.626 367.558\n",
"L300.587 367.689\n",
"L387.275 367.734\n",
"L487.369 367.736\n",
"L487.369 367.736\" style=\"fill:none;stroke:#0000ff;\"/>\n",
" </g>\n",
" <g id=\"matplotlib.axis_1\">\n",
" <g id=\"xtick_1\">\n",
" <g id=\"line2d_2\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L0 -4\" id=\"m0012dd4eef\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_3\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L0 4\" id=\"m476344969c\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_1\">\n",
" <!-- 0 -->\n",
" <defs>\n",
" <path d=\"\n",
"M31.7812 66.4062\n",
"Q24.1719 66.4062 20.3281 58.9062\n",
"Q16.5 51.4219 16.5 36.375\n",
"Q16.5 21.3906 20.3281 13.8906\n",
"Q24.1719 6.39062 31.7812 6.39062\n",
"Q39.4531 6.39062 43.2812 13.8906\n",
"Q47.125 21.3906 47.125 36.375\n",
"Q47.125 51.4219 43.2812 58.9062\n",
"Q39.4531 66.4062 31.7812 66.4062\n",
"M31.7812 74.2188\n",
"Q44.0469 74.2188 50.5156 64.5156\n",
"Q56.9844 54.8281 56.9844 36.375\n",
"Q56.9844 17.9688 50.5156 8.26562\n",
"Q44.0469 -1.42188 31.7812 -1.42188\n",
"Q19.5312 -1.42188 13.0625 8.26562\n",
"Q6.59375 17.9688 6.59375 36.375\n",
"Q6.59375 54.8281 13.0625 64.5156\n",
"Q19.5312 74.2188 31.7812 74.2188\" id=\"DejaVuSans-30\"/>\n",
" </defs>\n",
" <g transform=\"translate(37.9453125 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_2\">\n",
" <g id=\"line2d_4\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"96.76875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_5\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"96.76875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_2\">\n",
" <!-- 5 -->\n",
" <defs>\n",
" <path d=\"\n",
"M10.7969 72.9062\n",
"L49.5156 72.9062\n",
"L49.5156 64.5938\n",
"L19.8281 64.5938\n",
"L19.8281 46.7344\n",
"Q21.9688 47.4688 24.1094 47.8281\n",
"Q26.2656 48.1875 28.4219 48.1875\n",
"Q40.625 48.1875 47.75 41.5\n",
"Q54.8906 34.8125 54.8906 23.3906\n",
"Q54.8906 11.625 47.5625 5.09375\n",
"Q40.2344 -1.42188 26.9062 -1.42188\n",
"Q22.3125 -1.42188 17.5469 -0.640625\n",
"Q12.7969 0.140625 7.71875 1.70312\n",
"L7.71875 11.625\n",
"Q12.1094 9.23438 16.7969 8.0625\n",
"Q21.4844 6.89062 26.7031 6.89062\n",
"Q35.1562 6.89062 40.0781 11.3281\n",
"Q45.0156 15.7656 45.0156 23.3906\n",
"Q45.0156 31 40.0781 35.4375\n",
"Q35.1562 39.8906 26.7031 39.8906\n",
"Q22.75 39.8906 18.8125 39.0156\n",
"Q14.8906 38.1406 10.7969 36.2812\n",
"z\n",
"\" id=\"DejaVuSans-35\"/>\n",
" </defs>\n",
" <g transform=\"translate(93.9384375 380.48475)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_3\">\n",
" <g id=\"line2d_6\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"152.56875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_7\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"152.56875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_3\">\n",
" <!-- 10 -->\n",
" <defs>\n",
" <path d=\"\n",
"M12.4062 8.29688\n",
"L28.5156 8.29688\n",
"L28.5156 63.9219\n",
"L10.9844 60.4062\n",
"L10.9844 69.3906\n",
"L28.4219 72.9062\n",
"L38.2812 72.9062\n",
"L38.2812 8.29688\n",
"L54.3906 8.29688\n",
"L54.3906 0\n",
"L12.4062 0\n",
"z\n",
"\" id=\"DejaVuSans-31\"/>\n",
" </defs>\n",
" <g transform=\"translate(145.99125 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_4\">\n",
" <g id=\"line2d_8\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"208.36875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_9\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"208.36875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_4\">\n",
" <!-- 15 -->\n",
" <g transform=\"translate(201.916875 380.48475)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_5\">\n",
" <g id=\"line2d_10\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"264.16875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_11\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"264.16875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_5\">\n",
" <!-- 20 -->\n",
" <defs>\n",
" <path d=\"\n",
"M19.1875 8.29688\n",
"L53.6094 8.29688\n",
"L53.6094 0\n",
"L7.32812 0\n",
"L7.32812 8.29688\n",
"Q12.9375 14.1094 22.625 23.8906\n",
"Q32.3281 33.6875 34.8125 36.5312\n",
"Q39.5469 41.8438 41.4219 45.5312\n",
"Q43.3125 49.2188 43.3125 52.7812\n",
"Q43.3125 58.5938 39.2344 62.25\n",
"Q35.1562 65.9219 28.6094 65.9219\n",
"Q23.9688 65.9219 18.8125 64.3125\n",
"Q13.6719 62.7031 7.8125 59.4219\n",
"L7.8125 69.3906\n",
"Q13.7656 71.7812 18.9375 73\n",
"Q24.125 74.2188 28.4219 74.2188\n",
"Q39.75 74.2188 46.4844 68.5469\n",
"Q53.2188 62.8906 53.2188 53.4219\n",
"Q53.2188 48.9219 51.5312 44.8906\n",
"Q49.8594 40.875 45.4062 35.4062\n",
"Q44.1875 33.9844 37.6406 27.2188\n",
"Q31.1094 20.4531 19.1875 8.29688\" id=\"DejaVuSans-32\"/>\n",
" </defs>\n",
" <g transform=\"translate(257.371875 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-32\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_6\">\n",
" <g id=\"line2d_12\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"319.96875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_13\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"319.96875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_6\">\n",
" <!-- 25 -->\n",
" <g transform=\"translate(313.2975 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-32\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_7\">\n",
" <g id=\"line2d_14\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"375.76875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_15\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"375.76875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_7\">\n",
" <!-- 30 -->\n",
" <defs>\n",
" <path d=\"\n",
"M40.5781 39.3125\n",
"Q47.6562 37.7969 51.625 33\n",
"Q55.6094 28.2188 55.6094 21.1875\n",
"Q55.6094 10.4062 48.1875 4.48438\n",
"Q40.7656 -1.42188 27.0938 -1.42188\n",
"Q22.5156 -1.42188 17.6562 -0.515625\n",
"Q12.7969 0.390625 7.625 2.20312\n",
"L7.625 11.7188\n",
"Q11.7188 9.32812 16.5938 8.10938\n",
"Q21.4844 6.89062 26.8125 6.89062\n",
"Q36.0781 6.89062 40.9375 10.5469\n",
"Q45.7969 14.2031 45.7969 21.1875\n",
"Q45.7969 27.6406 41.2812 31.2656\n",
"Q36.7656 34.9062 28.7188 34.9062\n",
"L20.2188 34.9062\n",
"L20.2188 43.0156\n",
"L29.1094 43.0156\n",
"Q36.375 43.0156 40.2344 45.9219\n",
"Q44.0938 48.8281 44.0938 54.2969\n",
"Q44.0938 59.9062 40.1094 62.9062\n",
"Q36.1406 65.9219 28.7188 65.9219\n",
"Q24.6562 65.9219 20.0156 65.0312\n",
"Q15.375 64.1562 9.8125 62.3125\n",
"L9.8125 71.0938\n",
"Q15.4375 72.6562 20.3438 73.4375\n",
"Q25.25 74.2188 29.5938 74.2188\n",
"Q40.8281 74.2188 47.3594 69.1094\n",
"Q53.9062 64.0156 53.9062 55.3281\n",
"Q53.9062 49.2656 50.4375 45.0938\n",
"Q46.9688 40.9219 40.5781 39.3125\" id=\"DejaVuSans-33\"/>\n",
" </defs>\n",
" <g transform=\"translate(368.9896875 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-33\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_8\">\n",
" <g id=\"line2d_16\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"431.56875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_17\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"431.56875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_8\">\n",
" <!-- 35 -->\n",
" <g transform=\"translate(424.9153125 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-33\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-35\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_9\">\n",
" <g id=\"line2d_18\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m0012dd4eef\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_19\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m476344969c\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_9\">\n",
" <!-- 40 -->\n",
" <defs>\n",
" <path d=\"\n",
"M37.7969 64.3125\n",
"L12.8906 25.3906\n",
"L37.7969 25.3906\n",
"z\n",
"\n",
"M35.2031 72.9062\n",
"L47.6094 72.9062\n",
"L47.6094 25.3906\n",
"L58.0156 25.3906\n",
"L58.0156 17.1875\n",
"L47.6094 17.1875\n",
"L47.6094 0\n",
"L37.7969 0\n",
"L37.7969 17.1875\n",
"L4.89062 17.1875\n",
"L4.89062 26.7031\n",
"z\n",
"\" id=\"DejaVuSans-34\"/>\n",
" </defs>\n",
" <g transform=\"translate(480.425625 380.64225)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-34\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_10\">\n",
" <!-- Asset price at $t=0$ -->\n",
" <defs>\n",
" <path d=\"\n",
"M25 -2.20312\n",
"Q12.75 -2.20312 8.32812 7.875\n",
"Q3.90625 17.9688 3.90625 31.8906\n",
"Q3.90625 40.5781 5.48438 48.2344\n",
"Q7.07812 55.9062 11.7812 61.25\n",
"Q16.5 66.6094 25 66.6094\n",
"Q31.5938 66.6094 35.7812 63.375\n",
"Q39.9844 60.1562 42.1875 55.0469\n",
"Q44.3906 49.9531 45.1875 44.1094\n",
"Q46 38.2812 46 31.8906\n",
"Q46 23.2969 44.4062 15.7969\n",
"Q42.8281 8.29688 38.1875 3.04688\n",
"Q33.5469 -2.20312 25 -2.20312\n",
"M25 0.390625\n",
"Q30.5625 0.390625 33.2969 6.09375\n",
"Q36.0312 11.8125 36.6719 18.75\n",
"Q37.3125 25.6875 37.3125 33.5\n",
"Q37.3125 41.0156 36.6719 47.3594\n",
"Q36.0312 53.7188 33.3125 58.8594\n",
"Q30.6094 64.0156 25 64.0156\n",
"Q19.3438 64.0156 16.6094 58.8281\n",
"Q13.875 53.6562 13.2344 47.3281\n",
"Q12.5938 41.0156 12.5938 33.5\n",
"Q12.5938 27.9375 12.8594 23\n",
"Q13.1406 18.0625 14.3125 12.8125\n",
"Q15.4844 7.5625 18.0938 3.96875\n",
"Q20.7031 0.390625 25 0.390625\" id=\"Cmr10-30\"/>\n",
" <path d=\"\n",
"M7.51562 13.2812\n",
"Q6.6875 13.2812 6.14062 13.9062\n",
"Q5.60938 14.5469 5.60938 15.2812\n",
"Q5.60938 16.1094 6.14062 16.6875\n",
"Q6.6875 17.2812 7.51562 17.2812\n",
"L70.3125 17.2812\n",
"Q71.0469 17.2812 71.5781 16.6875\n",
"Q72.125 16.1094 72.125 15.2812\n",
"Q72.125 14.5469 71.5781 13.9062\n",
"Q71.0469 13.2812 70.3125 13.2812\n",
"z\n",
"\n",
"M7.51562 32.7188\n",
"Q6.6875 32.7188 6.14062 33.2969\n",
"Q5.60938 33.8906 5.60938 34.7188\n",
"Q5.60938 35.4531 6.14062 36.0781\n",
"Q6.6875 36.7188 7.51562 36.7188\n",
"L70.3125 36.7188\n",
"Q71.0469 36.7188 71.5781 36.0781\n",
"Q72.125 35.4531 72.125 34.7188\n",
"Q72.125 33.8906 71.5781 33.2969\n",
"Q71.0469 32.7188 70.3125 32.7188\n",
"z\n",
"\" id=\"Cmr10-3d\"/>\n",
" <path d=\"\n",
"M34.2812 27.4844\n",
"Q23.3906 27.4844 19.1875 25\n",
"Q14.9844 22.5156 14.9844 16.5\n",
"Q14.9844 11.7188 18.1406 8.90625\n",
"Q21.2969 6.10938 26.7031 6.10938\n",
"Q34.1875 6.10938 38.7031 11.4062\n",
"Q43.2188 16.7031 43.2188 25.4844\n",
"L43.2188 27.4844\n",
"z\n",
"\n",
"M52.2031 31.2031\n",
"L52.2031 0\n",
"L43.2188 0\n",
"L43.2188 8.29688\n",
"Q40.1406 3.32812 35.5469 0.953125\n",
"Q30.9531 -1.42188 24.3125 -1.42188\n",
"Q15.9219 -1.42188 10.9531 3.29688\n",
"Q6 8.01562 6 15.9219\n",
"Q6 25.1406 12.1719 29.8281\n",
"Q18.3594 34.5156 30.6094 34.5156\n",
"L43.2188 34.5156\n",
"L43.2188 35.4062\n",
"Q43.2188 41.6094 39.1406 45\n",
"Q35.0625 48.3906 27.6875 48.3906\n",
"Q23 48.3906 18.5469 47.2656\n",
"Q14.1094 46.1406 10.0156 43.8906\n",
"L10.0156 52.2031\n",
"Q14.9375 54.1094 19.5781 55.0469\n",
"Q24.2188 56 28.6094 56\n",
"Q40.4844 56 46.3438 49.8438\n",
"Q52.2031 43.7031 52.2031 31.2031\" id=\"DejaVuSans-61\"/>\n",
" <path d=\"\n",
"M48.7812 52.5938\n",
"L48.7812 44.1875\n",
"Q44.9688 46.2969 41.1406 47.3438\n",
"Q37.3125 48.3906 33.4062 48.3906\n",
"Q24.6562 48.3906 19.8125 42.8438\n",
"Q14.9844 37.3125 14.9844 27.2969\n",
"Q14.9844 17.2812 19.8125 11.7344\n",
"Q24.6562 6.20312 33.4062 6.20312\n",
"Q37.3125 6.20312 41.1406 7.25\n",
"Q44.9688 8.29688 48.7812 10.4062\n",
"L48.7812 2.09375\n",
"Q45.0156 0.34375 40.9844 -0.53125\n",
"Q36.9688 -1.42188 32.4219 -1.42188\n",
"Q20.0625 -1.42188 12.7812 6.34375\n",
"Q5.51562 14.1094 5.51562 27.2969\n",
"Q5.51562 40.6719 12.8594 48.3281\n",
"Q20.2188 56 33.0156 56\n",
"Q37.1562 56 41.1094 55.1406\n",
"Q45.0625 54.2969 48.7812 52.5938\" id=\"DejaVuSans-63\"/>\n",
" <path id=\"DejaVuSans-20\"/>\n",
" <path d=\"\n",
"M34.1875 63.1875\n",
"L20.7969 26.9062\n",
"L47.6094 26.9062\n",
"z\n",
"\n",
"M28.6094 72.9062\n",
"L39.7969 72.9062\n",
"L67.5781 0\n",
"L57.3281 0\n",
"L50.6875 18.7031\n",
"L17.8281 18.7031\n",
"L11.1875 0\n",
"L0.78125 0\n",
"z\n",
"\" id=\"DejaVuSans-41\"/>\n",
" <path d=\"\n",
"M6.20312 8.10938\n",
"Q6.20312 9.57812 6.5 10.8906\n",
"L13.7188 39.5938\n",
"L3.21875 39.5938\n",
"Q2.20312 39.5938 2.20312 40.9219\n",
"Q2.59375 43.1094 3.51562 43.1094\n",
"L14.5938 43.1094\n",
"L18.6094 59.4219\n",
"Q19 60.75 20.1719 61.6719\n",
"Q21.3438 62.5938 22.7969 62.5938\n",
"Q24.0781 62.5938 24.9219 61.8281\n",
"Q25.7812 61.0781 25.7812 59.8125\n",
"Q25.7812 59.5156 25.75 59.3438\n",
"Q25.7344 59.1875 25.6875 58.9844\n",
"L21.6875 43.1094\n",
"L31.9844 43.1094\n",
"Q33.0156 43.1094 33.0156 41.7969\n",
"Q32.9531 41.5469 32.8125 40.9531\n",
"Q32.6719 40.375 32.4219 39.9844\n",
"Q32.1719 39.5938 31.6875 39.5938\n",
"L20.7969 39.5938\n",
"L13.625 10.6875\n",
"Q12.8906 7.85938 12.8906 5.8125\n",
"Q12.8906 1.51562 15.8281 1.51562\n",
"Q20.2188 1.51562 23.6094 5.64062\n",
"Q27 9.76562 28.8125 14.7031\n",
"Q29.2031 15.2812 29.5938 15.2812\n",
"L30.8125 15.2812\n",
"Q31.2031 15.2812 31.4375 15.0156\n",
"Q31.6875 14.75 31.6875 14.4062\n",
"Q31.6875 14.2031 31.5938 14.1094\n",
"Q29.3906 8.0625 25.1875 3.46875\n",
"Q21 -1.125 15.5781 -1.125\n",
"Q11.625 -1.125 8.90625 1.45312\n",
"Q6.20312 4.04688 6.20312 8.10938\" id=\"Cmmi10-74\"/>\n",
" <path d=\"\n",
"M9.42188 54.6875\n",
"L18.4062 54.6875\n",
"L18.4062 0\n",
"L9.42188 0\n",
"z\n",
"\n",
"M9.42188 75.9844\n",
"L18.4062 75.9844\n",
"L18.4062 64.5938\n",
"L9.42188 64.5938\n",
"z\n",
"\" id=\"DejaVuSans-69\"/>\n",
" <path d=\"\n",
"M18.3125 70.2188\n",
"L18.3125 54.6875\n",
"L36.8125 54.6875\n",
"L36.8125 47.7031\n",
"L18.3125 47.7031\n",
"L18.3125 18.0156\n",
"Q18.3125 11.3281 20.1406 9.42188\n",
"Q21.9688 7.51562 27.5938 7.51562\n",
"L36.8125 7.51562\n",
"L36.8125 0\n",
"L27.5938 0\n",
"Q17.1875 0 13.2344 3.875\n",
"Q9.28125 7.76562 9.28125 18.0156\n",
"L9.28125 47.7031\n",
"L2.6875 47.7031\n",
"L2.6875 54.6875\n",
"L9.28125 54.6875\n",
"L9.28125 70.2188\n",
"z\n",
"\" id=\"DejaVuSans-74\"/>\n",
" <path d=\"\n",
"M56.2031 29.5938\n",
"L56.2031 25.2031\n",
"L14.8906 25.2031\n",
"Q15.4844 15.9219 20.4844 11.0625\n",
"Q25.4844 6.20312 34.4219 6.20312\n",
"Q39.5938 6.20312 44.4531 7.46875\n",
"Q49.3125 8.73438 54.1094 11.2812\n",
"L54.1094 2.78125\n",
"Q49.2656 0.734375 44.1875 -0.34375\n",
"Q39.1094 -1.42188 33.8906 -1.42188\n",
"Q20.7969 -1.42188 13.1562 6.1875\n",
"Q5.51562 13.8125 5.51562 26.8125\n",
"Q5.51562 40.2344 12.7656 48.1094\n",
"Q20.0156 56 32.3281 56\n",
"Q43.3594 56 49.7812 48.8906\n",
"Q56.2031 41.7969 56.2031 29.5938\n",
"M47.2188 32.2344\n",
"Q47.125 39.5938 43.0938 43.9844\n",
"Q39.0625 48.3906 32.4219 48.3906\n",
"Q24.9062 48.3906 20.3906 44.1406\n",
"Q15.875 39.8906 15.1875 32.1719\n",
"z\n",
"\" id=\"DejaVuSans-65\"/>\n",
" <path d=\"\n",
"M18.1094 8.20312\n",
"L18.1094 -20.7969\n",
"L9.07812 -20.7969\n",
"L9.07812 54.6875\n",
"L18.1094 54.6875\n",
"L18.1094 46.3906\n",
"Q20.9531 51.2656 25.2656 53.625\n",
"Q29.5938 56 35.5938 56\n",
"Q45.5625 56 51.7812 48.0938\n",
"Q58.0156 40.1875 58.0156 27.2969\n",
"Q58.0156 14.4062 51.7812 6.48438\n",
"Q45.5625 -1.42188 35.5938 -1.42188\n",
"Q29.5938 -1.42188 25.2656 0.953125\n",
"Q20.9531 3.32812 18.1094 8.20312\n",
"M48.6875 27.2969\n",
"Q48.6875 37.2031 44.6094 42.8438\n",
"Q40.5312 48.4844 33.4062 48.4844\n",
"Q26.2656 48.4844 22.1875 42.8438\n",
"Q18.1094 37.2031 18.1094 27.2969\n",
"Q18.1094 17.3906 22.1875 11.75\n",
"Q26.2656 6.10938 33.4062 6.10938\n",
"Q40.5312 6.10938 44.6094 11.75\n",
"Q48.6875 17.3906 48.6875 27.2969\" id=\"DejaVuSans-70\"/>\n",
" <path d=\"\n",
"M44.2812 53.0781\n",
"L44.2812 44.5781\n",
"Q40.4844 46.5312 36.375 47.5\n",
"Q32.2812 48.4844 27.875 48.4844\n",
"Q21.1875 48.4844 17.8438 46.4375\n",
"Q14.5 44.3906 14.5 40.2812\n",
"Q14.5 37.1562 16.8906 35.375\n",
"Q19.2812 33.5938 26.5156 31.9844\n",
"L29.5938 31.2969\n",
"Q39.1562 29.25 43.1875 25.5156\n",
"Q47.2188 21.7812 47.2188 15.0938\n",
"Q47.2188 7.46875 41.1875 3.01562\n",
"Q35.1562 -1.42188 24.6094 -1.42188\n",
"Q20.2188 -1.42188 15.4531 -0.5625\n",
"Q10.6875 0.296875 5.42188 2\n",
"L5.42188 11.2812\n",
"Q10.4062 8.6875 15.2344 7.39062\n",
"Q20.0625 6.10938 24.8125 6.10938\n",
"Q31.1562 6.10938 34.5625 8.28125\n",
"Q37.9844 10.4531 37.9844 14.4062\n",
"Q37.9844 18.0625 35.5156 20.0156\n",
"Q33.0625 21.9688 24.7031 23.7812\n",
"L21.5781 24.5156\n",
"Q13.2344 26.2656 9.51562 29.9062\n",
"Q5.8125 33.5469 5.8125 39.8906\n",
"Q5.8125 47.6094 11.2812 51.7969\n",
"Q16.75 56 26.8125 56\n",
"Q31.7812 56 36.1719 55.2656\n",
"Q40.5781 54.5469 44.2812 53.0781\" id=\"DejaVuSans-73\"/>\n",
" <path d=\"\n",
"M41.1094 46.2969\n",
"Q39.5938 47.1719 37.8125 47.5781\n",
"Q36.0312 48 33.8906 48\n",
"Q26.2656 48 22.1875 43.0469\n",
"Q18.1094 38.0938 18.1094 28.8125\n",
"L18.1094 0\n",
"L9.07812 0\n",
"L9.07812 54.6875\n",
"L18.1094 54.6875\n",
"L18.1094 46.1875\n",
"Q20.9531 51.1719 25.4844 53.5781\n",
"Q30.0312 56 36.5312 56\n",
"Q37.4531 56 38.5781 55.875\n",
"Q39.7031 55.7656 41.0625 55.5156\n",
"z\n",
"\" id=\"DejaVuSans-72\"/>\n",
" </defs>\n",
" <g transform=\"translate(209.80875 397.452875)scale(0.12 -0.12)\">\n",
" <use transform=\"translate(0.0 21.015625)\" xlink:href=\"#DejaVuSans-41\"/>\n",
" <use transform=\"translate(68.408203125 21.015625)\" xlink:href=\"#DejaVuSans-73\"/>\n",
" <use transform=\"translate(120.5078125 21.015625)\" xlink:href=\"#DejaVuSans-73\"/>\n",
" <use transform=\"translate(172.607421875 21.015625)\" xlink:href=\"#DejaVuSans-65\"/>\n",
" <use transform=\"translate(234.130859375 21.015625)\" xlink:href=\"#DejaVuSans-74\"/>\n",
" <use transform=\"translate(273.33984375 21.015625)\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use transform=\"translate(305.126953125 21.015625)\" xlink:href=\"#DejaVuSans-70\"/>\n",
" <use transform=\"translate(368.603515625 21.015625)\" xlink:href=\"#DejaVuSans-72\"/>\n",
" <use transform=\"translate(409.716796875 21.015625)\" xlink:href=\"#DejaVuSans-69\"/>\n",
" <use transform=\"translate(437.5 21.015625)\" xlink:href=\"#DejaVuSans-63\"/>\n",
" <use transform=\"translate(492.48046875 21.015625)\" xlink:href=\"#DejaVuSans-65\"/>\n",
" <use transform=\"translate(554.00390625 21.015625)\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use transform=\"translate(585.791015625 21.015625)\" xlink:href=\"#DejaVuSans-61\"/>\n",
" <use transform=\"translate(647.0703125 21.015625)\" xlink:href=\"#DejaVuSans-74\"/>\n",
" <use transform=\"translate(686.279296875 21.015625)\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use transform=\"translate(718.06640625 21.015625)\" xlink:href=\"#Cmmi10-74\"/>\n",
" <use transform=\"translate(771.708984375 21.015625)\" xlink:href=\"#Cmr10-3d\"/>\n",
" <use transform=\"translate(855.767578125 21.015625)\" xlink:href=\"#Cmr10-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"matplotlib.axis_2\">\n",
" <g id=\"ytick_1\">\n",
" <g id=\"line2d_20\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L4 0\" id=\"me8a85f7bf6\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_21\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L-4 0\" id=\"m1a32005dea\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"367.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_11\">\n",
" <!-- 0 -->\n",
" <g transform=\"translate(30.921875 372.1038125)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_2\">\n",
" <g id=\"line2d_22\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"310.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_23\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"310.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_12\">\n",
" <!-- 2 -->\n",
" <g transform=\"translate(31.415 314.589125)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-32\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_3\">\n",
" <g id=\"line2d_24\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"252.536\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_25\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"252.536\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_13\">\n",
" <!-- 4 -->\n",
" <g transform=\"translate(30.59375 256.910375)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-34\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_4\">\n",
" <g id=\"line2d_26\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"194.936\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_27\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"194.936\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_14\">\n",
" <!-- 6 -->\n",
" <defs>\n",
" <path d=\"\n",
"M33.0156 40.375\n",
"Q26.375 40.375 22.4844 35.8281\n",
"Q18.6094 31.2969 18.6094 23.3906\n",
"Q18.6094 15.5312 22.4844 10.9531\n",
"Q26.375 6.39062 33.0156 6.39062\n",
"Q39.6562 6.39062 43.5312 10.9531\n",
"Q47.4062 15.5312 47.4062 23.3906\n",
"Q47.4062 31.2969 43.5312 35.8281\n",
"Q39.6562 40.375 33.0156 40.375\n",
"M52.5938 71.2969\n",
"L52.5938 62.3125\n",
"Q48.875 64.0625 45.0938 64.9844\n",
"Q41.3125 65.9219 37.5938 65.9219\n",
"Q27.8281 65.9219 22.6719 59.3281\n",
"Q17.5312 52.7344 16.7969 39.4062\n",
"Q19.6719 43.6562 24.0156 45.9219\n",
"Q28.375 48.1875 33.5938 48.1875\n",
"Q44.5781 48.1875 50.9531 41.5156\n",
"Q57.3281 34.8594 57.3281 23.3906\n",
"Q57.3281 12.1562 50.6875 5.35938\n",
"Q44.0469 -1.42188 33.0156 -1.42188\n",
"Q20.3594 -1.42188 13.6719 8.26562\n",
"Q6.98438 17.9688 6.98438 36.375\n",
"Q6.98438 53.6562 15.1875 63.9375\n",
"Q23.3906 74.2188 37.2031 74.2188\n",
"Q40.9219 74.2188 44.7031 73.4844\n",
"Q48.4844 72.75 52.5938 71.2969\" id=\"DejaVuSans-36\"/>\n",
" </defs>\n",
" <g transform=\"translate(30.9275 199.3038125)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-36\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_5\">\n",
" <g id=\"line2d_28\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"137.336\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_29\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"137.336\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_15\">\n",
" <!-- 8 -->\n",
" <defs>\n",
" <path d=\"\n",
"M31.7812 34.625\n",
"Q24.75 34.625 20.7188 30.8594\n",
"Q16.7031 27.0938 16.7031 20.5156\n",
"Q16.7031 13.9219 20.7188 10.1562\n",
"Q24.75 6.39062 31.7812 6.39062\n",
"Q38.8125 6.39062 42.8594 10.1719\n",
"Q46.9219 13.9688 46.9219 20.5156\n",
"Q46.9219 27.0938 42.8906 30.8594\n",
"Q38.875 34.625 31.7812 34.625\n",
"M21.9219 38.8125\n",
"Q15.5781 40.375 12.0312 44.7188\n",
"Q8.5 49.0781 8.5 55.3281\n",
"Q8.5 64.0625 14.7188 69.1406\n",
"Q20.9531 74.2188 31.7812 74.2188\n",
"Q42.6719 74.2188 48.875 69.1406\n",
"Q55.0781 64.0625 55.0781 55.3281\n",
"Q55.0781 49.0781 51.5312 44.7188\n",
"Q48 40.375 41.7031 38.8125\n",
"Q48.8281 37.1562 52.7969 32.3125\n",
"Q56.7812 27.4844 56.7812 20.5156\n",
"Q56.7812 9.90625 50.3125 4.23438\n",
"Q43.8438 -1.42188 31.7812 -1.42188\n",
"Q19.7344 -1.42188 13.25 4.23438\n",
"Q6.78125 9.90625 6.78125 20.5156\n",
"Q6.78125 27.4844 10.7812 32.3125\n",
"Q14.7969 37.1562 21.9219 38.8125\n",
"M18.3125 54.3906\n",
"Q18.3125 48.7344 21.8438 45.5625\n",
"Q25.3906 42.3906 31.7812 42.3906\n",
"Q38.1406 42.3906 41.7188 45.5625\n",
"Q45.3125 48.7344 45.3125 54.3906\n",
"Q45.3125 60.0625 41.7188 63.2344\n",
"Q38.1406 66.4062 31.7812 66.4062\n",
"Q25.3906 66.4062 21.8438 63.2344\n",
"Q18.3125 60.0625 18.3125 54.3906\" id=\"DejaVuSans-38\"/>\n",
" </defs>\n",
" <g transform=\"translate(30.96875 141.7038125)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-38\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_6\">\n",
" <g id=\"line2d_30\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"79.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_31\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"79.736\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_16\">\n",
" <!-- 10 -->\n",
" <g transform=\"translate(23.81375 84.1038125)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_7\">\n",
" <g id=\"line2d_32\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"40.96875\" xlink:href=\"#me8a85f7bf6\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_33\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"487.36875\" xlink:href=\"#m1a32005dea\" y=\"22.136\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_17\">\n",
" <!-- 12 -->\n",
" <g transform=\"translate(24.21875 26.589125)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"63.623046875\" xlink:href=\"#DejaVuSans-32\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_18\">\n",
" <!-- Option price -->\n",
" <defs>\n",
" <path d=\"\n",
"M30.6094 48.3906\n",
"Q23.3906 48.3906 19.1875 42.75\n",
"Q14.9844 37.1094 14.9844 27.2969\n",
"Q14.9844 17.4844 19.1562 11.8438\n",
"Q23.3438 6.20312 30.6094 6.20312\n",
"Q37.7969 6.20312 41.9844 11.8594\n",
"Q46.1875 17.5312 46.1875 27.2969\n",
"Q46.1875 37.0156 41.9844 42.7031\n",
"Q37.7969 48.3906 30.6094 48.3906\n",
"M30.6094 56\n",
"Q42.3281 56 49.0156 48.375\n",
"Q55.7188 40.7656 55.7188 27.2969\n",
"Q55.7188 13.875 49.0156 6.21875\n",
"Q42.3281 -1.42188 30.6094 -1.42188\n",
"Q18.8438 -1.42188 12.1719 6.21875\n",
"Q5.51562 13.875 5.51562 27.2969\n",
"Q5.51562 40.7656 12.1719 48.375\n",
"Q18.8438 56 30.6094 56\" id=\"DejaVuSans-6f\"/>\n",
" <path d=\"\n",
"M39.4062 66.2188\n",
"Q28.6562 66.2188 22.3281 58.2031\n",
"Q16.0156 50.2031 16.0156 36.375\n",
"Q16.0156 22.6094 22.3281 14.5938\n",
"Q28.6562 6.59375 39.4062 6.59375\n",
"Q50.1406 6.59375 56.4219 14.5938\n",
"Q62.7031 22.6094 62.7031 36.375\n",
"Q62.7031 50.2031 56.4219 58.2031\n",
"Q50.1406 66.2188 39.4062 66.2188\n",
"M39.4062 74.2188\n",
"Q54.7344 74.2188 63.9062 63.9375\n",
"Q73.0938 53.6562 73.0938 36.375\n",
"Q73.0938 19.1406 63.9062 8.85938\n",
"Q54.7344 -1.42188 39.4062 -1.42188\n",
"Q24.0312 -1.42188 14.8125 8.82812\n",
"Q5.60938 19.0938 5.60938 36.375\n",
"Q5.60938 53.6562 14.8125 63.9375\n",
"Q24.0312 74.2188 39.4062 74.2188\" id=\"DejaVuSans-4f\"/>\n",
" <path d=\"\n",
"M54.8906 33.0156\n",
"L54.8906 0\n",
"L45.9062 0\n",
"L45.9062 32.7188\n",
"Q45.9062 40.4844 42.875 44.3281\n",
"Q39.8438 48.1875 33.7969 48.1875\n",
"Q26.5156 48.1875 22.3125 43.5469\n",
"Q18.1094 38.9219 18.1094 30.9062\n",
"L18.1094 0\n",
"L9.07812 0\n",
"L9.07812 54.6875\n",
"L18.1094 54.6875\n",
"L18.1094 46.1875\n",
"Q21.3438 51.125 25.7031 53.5625\n",
"Q30.0781 56 35.7969 56\n",
"Q45.2188 56 50.0469 50.1719\n",
"Q54.8906 44.3438 54.8906 33.0156\" id=\"DejaVuSans-6e\"/>\n",
" </defs>\n",
" <g transform=\"translate(18.81375 228.986)rotate(-90.0)scale(0.12 -0.12)\">\n",
" <use xlink:href=\"#DejaVuSans-4f\"/>\n",
" <use x=\"78.7109375\" xlink:href=\"#DejaVuSans-70\"/>\n",
" <use x=\"142.1875\" xlink:href=\"#DejaVuSans-74\"/>\n",
" <use x=\"181.396484375\" xlink:href=\"#DejaVuSans-69\"/>\n",
" <use x=\"209.1796875\" xlink:href=\"#DejaVuSans-6f\"/>\n",
" <use x=\"270.361328125\" xlink:href=\"#DejaVuSans-6e\"/>\n",
" <use x=\"333.740234375\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use x=\"365.52734375\" xlink:href=\"#DejaVuSans-70\"/>\n",
" <use x=\"429.00390625\" xlink:href=\"#DejaVuSans-72\"/>\n",
" <use x=\"470.1171875\" xlink:href=\"#DejaVuSans-69\"/>\n",
" <use x=\"497.900390625\" xlink:href=\"#DejaVuSans-63\"/>\n",
" <use x=\"552.880859375\" xlink:href=\"#DejaVuSans-65\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"patch_3\">\n",
" <path d=\"\n",
"M40.9688 22.136\n",
"L487.369 22.136\" style=\"fill:none;stroke:#000000;\"/>\n",
" </g>\n",
" <g id=\"patch_4\">\n",
" <path d=\"\n",
"M487.369 367.736\n",
"L487.369 22.136\" style=\"fill:none;stroke:#000000;\"/>\n",
" </g>\n",
" <g id=\"patch_5\">\n",
" <path d=\"\n",
"M40.9688 367.736\n",
"L487.369 367.736\" style=\"fill:none;stroke:#000000;\"/>\n",
" </g>\n",
" <g id=\"patch_6\">\n",
" <path d=\"\n",
"M40.9688 367.736\n",
"L40.9688 22.136\" style=\"fill:none;stroke:#000000;\"/>\n",
" </g>\n",
" <g id=\"text_19\">\n",
" <!-- $\\sigma=0.50, r=0.1, T=0.25, K=10$ -->\n",
" <defs>\n",
" <path d=\"\n",
"M4.98438 0\n",
"L4.98438 2.6875\n",
"Q4.98438 2.9375 5.17188 3.21875\n",
"L20.7031 20.4062\n",
"Q24.2188 24.2188 26.4062 26.7969\n",
"Q28.6094 29.3906 30.75 32.7656\n",
"Q32.9062 36.1406 34.1562 39.625\n",
"Q35.4062 43.1094 35.4062 47.0156\n",
"Q35.4062 51.125 33.8906 54.8594\n",
"Q32.375 58.5938 29.375 60.8438\n",
"Q26.375 63.0938 22.125 63.0938\n",
"Q17.7812 63.0938 14.3125 60.4688\n",
"Q10.8438 57.8594 9.42188 53.7188\n",
"Q9.8125 53.8125 10.5 53.8125\n",
"Q12.75 53.8125 14.3281 52.2969\n",
"Q15.9219 50.7812 15.9219 48.3906\n",
"Q15.9219 46.0938 14.3281 44.5\n",
"Q12.75 42.9219 10.5 42.9219\n",
"Q8.15625 42.9219 6.5625 44.5469\n",
"Q4.98438 46.1875 4.98438 48.3906\n",
"Q4.98438 52.1562 6.39062 55.4375\n",
"Q7.8125 58.7344 10.4688 61.2969\n",
"Q13.1406 63.875 16.4844 65.2344\n",
"Q19.8281 66.6094 23.5781 66.6094\n",
"Q29.2969 66.6094 34.2188 64.1875\n",
"Q39.1562 61.7656 42.0312 57.3438\n",
"Q44.9219 52.9375 44.9219 47.0156\n",
"Q44.9219 42.6719 43.0156 38.7656\n",
"Q41.1094 34.8594 38.125 31.6562\n",
"Q35.1562 28.4688 30.5156 24.4062\n",
"Q25.875 20.3594 24.4219 19\n",
"L13.0938 8.10938\n",
"L22.7031 8.10938\n",
"Q29.7812 8.10938 34.5469 8.21875\n",
"Q39.3125 8.34375 39.5938 8.59375\n",
"Q40.7656 9.85938 42 17.8281\n",
"L44.9219 17.8281\n",
"L42.0938 0\n",
"z\n",
"\" id=\"Cmr10-32\"/>\n",
" <path d=\"\n",
"M9.28125 0\n",
"L9.28125 3.51562\n",
"Q21.7812 3.51562 21.7812 6.6875\n",
"L21.7812 59.1875\n",
"Q16.6094 56.6875 8.6875 56.6875\n",
"L8.6875 60.2031\n",
"Q20.9531 60.2031 27.2031 66.6094\n",
"L28.6094 66.6094\n",
"Q28.9531 66.6094 29.2656 66.3281\n",
"Q29.5938 66.0625 29.5938 65.7188\n",
"L29.5938 6.6875\n",
"Q29.5938 3.51562 42.0938 3.51562\n",
"L42.0938 0\n",
"z\n",
"\" id=\"Cmr10-31\"/>\n",
" <path d=\"\n",
"M4.6875 0\n",
"Q3.71875 0 3.71875 1.3125\n",
"Q3.76562 1.5625 3.90625 2.17188\n",
"Q4.04688 2.78125 4.3125 3.14062\n",
"Q4.59375 3.51562 4.98438 3.51562\n",
"Q11.0781 3.51562 13.4844 4.20312\n",
"Q14.7969 4.64062 15.375 6.89062\n",
"L29.1094 61.8125\n",
"Q29.2969 62.7969 29.2969 63.1875\n",
"Q29.2969 64.2656 28.0781 64.4062\n",
"Q26.2188 64.7969 20.9062 64.7969\n",
"Q19.9219 64.7969 19.9219 66.1094\n",
"Q20.2656 67.3906 20.4531 67.8438\n",
"Q20.6562 68.3125 21.5781 68.3125\n",
"L48.4844 68.3125\n",
"Q49.5156 68.3125 49.5156 67\n",
"Q49.4688 66.75 49.3125 66.1562\n",
"Q49.1719 65.5781 48.9219 65.1875\n",
"Q48.6875 64.7969 48.1875 64.7969\n",
"Q42.0938 64.7969 39.7031 64.1094\n",
"Q38.375 63.625 37.7969 61.375\n",
"L29.6875 29\n",
"L68.8906 59.2812\n",
"Q69 59.4688 70.1406 60.6094\n",
"Q71.2969 61.7656 71.2969 62.8906\n",
"Q71.2969 64.7969 67.9219 64.7969\n",
"Q66.8906 64.7969 66.8906 66.1094\n",
"Q67.0938 66.8906 67.2031 67.3281\n",
"Q67.3281 67.7812 67.6406 68.0469\n",
"Q67.9688 68.3125 68.6094 68.3125\n",
"L87.9844 68.3125\n",
"Q88.5312 68.3125 88.7656 67.9219\n",
"Q89.0156 67.5312 89.0156 67\n",
"Q88.9688 66.75 88.7969 66.1094\n",
"Q88.625 65.4844 88.3594 65.1406\n",
"Q88.0938 64.7969 87.5938 64.7969\n",
"Q80.2812 64.7969 71.5781 58.0156\n",
"Q71.5312 57.9531 71.4375 57.9219\n",
"Q71.3438 57.9062 71.2344 57.875\n",
"Q71.1406 57.8594 71.0938 57.8125\n",
"L50.4844 41.7969\n",
"L65.4844 6.6875\n",
"Q66.8438 4.5 68.4062 4\n",
"Q69.9688 3.51562 73.1875 3.51562\n",
"Q74.2188 3.51562 74.2188 2.20312\n",
"Q73.9219 1.03125 73.625 0.515625\n",
"Q73.3438 0 72.5156 0\n",
"L49.3125 0\n",
"Q48.3906 0 48.3906 1.3125\n",
"Q48.5312 2.34375 48.7188 2.92188\n",
"Q48.9219 3.51562 49.7031 3.51562\n",
"Q52.25 3.51562 54.0312 4.03125\n",
"Q55.8125 4.54688 55.8125 6.39062\n",
"Q55.8125 7.07812 55.7188 7.42188\n",
"L43.3125 36.2812\n",
"L28.7188 25\n",
"L24.125 6.5\n",
"Q23.875 5.28125 23.875 5.07812\n",
"Q23.875 4.04688 25.0938 3.90625\n",
"Q27 3.51562 32.3281 3.51562\n",
"Q33.2969 3.51562 33.2969 2.20312\n",
"Q32.9531 0.78125 32.75 0.390625\n",
"Q32.5625 0 31.5938 0\n",
"z\n",
"\" id=\"Cmmi10-4b\"/>\n",
" <path d=\"\n",
"M8.6875 11.375\n",
"Q9.71875 8.45312 11.8438 6.04688\n",
"Q13.9688 3.65625 16.875 2.3125\n",
"Q19.7812 0.984375 22.9062 0.984375\n",
"Q30.125 0.984375 32.8594 6.59375\n",
"Q35.5938 12.2031 35.5938 20.2188\n",
"Q35.5938 23.6875 35.4688 26.0469\n",
"Q35.3594 28.4219 34.8125 30.6094\n",
"Q33.8906 34.125 31.5625 36.7656\n",
"Q29.25 39.4062 25.875 39.4062\n",
"Q22.5156 39.4062 20.0938 38.375\n",
"Q17.6719 37.3594 16.1562 35.9844\n",
"Q14.6562 34.625 13.4844 33.1094\n",
"Q12.3125 31.5938 12.0156 31.5\n",
"L10.8906 31.5\n",
"Q10.6406 31.5 10.2656 31.8125\n",
"Q9.90625 32.125 9.90625 32.4219\n",
"L9.90625 65.8281\n",
"Q9.90625 66.0625 10.2188 66.3281\n",
"Q10.5469 66.6094 10.8906 66.6094\n",
"L11.1875 66.6094\n",
"Q17.9219 63.375 25.4844 63.375\n",
"Q32.9062 63.375 39.7969 66.6094\n",
"L40.0938 66.6094\n",
"Q40.4375 66.6094 40.7188 66.3594\n",
"Q41.0156 66.1094 41.0156 65.8281\n",
"L41.0156 64.8906\n",
"Q41.0156 64.4062 40.8281 64.4062\n",
"Q37.4062 59.8594 32.25 57.3125\n",
"Q27.0938 54.7812 21.5781 54.7812\n",
"Q17.5781 54.7812 13.375 55.9062\n",
"L13.375 37.0156\n",
"Q16.7031 39.7031 19.3125 40.8438\n",
"Q21.9219 42 25.9844 42\n",
"Q31.5 42 35.8594 38.8125\n",
"Q40.2344 35.6406 42.5781 30.5312\n",
"Q44.9219 25.4375 44.9219 20.125\n",
"Q44.9219 14.1094 41.9688 8.98438\n",
"Q39.0156 3.85938 33.9375 0.828125\n",
"Q28.8594 -2.20312 22.9062 -2.20312\n",
"Q17.9688 -2.20312 13.8438 0.328125\n",
"Q9.71875 2.875 7.34375 7.17188\n",
"Q4.98438 11.4688 4.98438 16.3125\n",
"Q4.98438 18.5625 6.4375 19.9688\n",
"Q7.90625 21.3906 10.1094 21.3906\n",
"Q12.3125 21.3906 13.7969 19.9375\n",
"Q15.2812 18.5 15.2812 16.3125\n",
"Q15.2812 14.1562 13.7969 12.6719\n",
"Q12.3125 11.1875 10.1094 11.1875\n",
"Q9.76562 11.1875 9.32812 11.25\n",
"Q8.89062 11.3281 8.6875 11.375\" id=\"Cmr10-35\"/>\n",
" <path d=\"\n",
"M18.7031 -1.125\n",
"Q14.2656 -1.125 10.8125 1\n",
"Q7.375 3.125 5.48438 6.73438\n",
"Q3.60938 10.3594 3.60938 14.7031\n",
"Q3.60938 19.3438 5.70312 24.4688\n",
"Q7.8125 29.5938 11.4531 33.8438\n",
"Q15.0938 38.0938 19.6719 40.5938\n",
"Q24.2656 43.1094 29.1094 43.1094\n",
"L54.2969 43.1094\n",
"Q55.3281 43.1094 56.0469 42.4219\n",
"Q56.7812 41.75 56.7812 40.5781\n",
"Q56.7812 39.1094 55.7344 38.0156\n",
"Q54.6875 36.9219 53.2188 36.9219\n",
"L41.0156 36.9219\n",
"Q43.8906 32.625 43.8906 26.5156\n",
"Q43.8906 21.4844 41.9375 16.5938\n",
"Q39.9844 11.7188 36.5156 7.6875\n",
"Q33.0625 3.65625 28.4375 1.26562\n",
"Q23.8281 -1.125 18.7031 -1.125\n",
"M18.7969 1.51562\n",
"Q24.2656 1.51562 28.4844 5.78125\n",
"Q32.7188 10.0625 34.9531 16.2344\n",
"Q37.2031 22.4062 37.2031 27.6875\n",
"Q37.2031 31.9844 34.8281 34.4531\n",
"Q32.4688 36.9219 28.2188 36.9219\n",
"Q22.4062 36.9219 18.3281 33.0156\n",
"Q14.2656 29.1094 12.2344 23.1875\n",
"Q10.2031 17.2812 10.2031 11.8125\n",
"Q10.2031 7.51562 12.4688 4.51562\n",
"Q14.75 1.51562 18.7969 1.51562\" id=\"Cmmi10-be\"/>\n",
" <path d=\"\n",
"M4.59375 1.3125\n",
"Q4.64062 1.5625 4.8125 2.1875\n",
"Q4.98438 2.82812 5.25 3.17188\n",
"Q5.51562 3.51562 6 3.51562\n",
"Q14.5938 3.51562 17.3906 4\n",
"Q20.0625 4.6875 20.6094 6.89062\n",
"L34.2812 61.8125\n",
"Q34.7188 63.0312 34.7188 64.0156\n",
"Q34.7188 64.7969 31.2031 64.7969\n",
"L25.3906 64.7969\n",
"Q18.7031 64.7969 15.0625 62.7344\n",
"Q11.4219 60.6875 9.71875 57.3125\n",
"Q8.01562 53.9531 5.32812 46.2969\n",
"Q4.98438 45.4062 4.29688 45.4062\n",
"L3.42188 45.4062\n",
"Q2.39062 45.4062 2.39062 46.6875\n",
"L9.51562 67.3906\n",
"Q9.71875 68.3125 10.5 68.3125\n",
"L69.5781 68.3125\n",
"Q70.6094 68.3125 70.6094 67\n",
"L67.2812 46.2969\n",
"Q67.2812 46 66.9375 45.7031\n",
"Q66.6094 45.4062 66.3125 45.4062\n",
"L65.375 45.4062\n",
"Q64.4062 45.4062 64.4062 46.6875\n",
"Q65.4844 53.7656 65.4844 56.6875\n",
"Q65.4844 60.2031 64.0156 62\n",
"Q62.5469 63.8125 60.2031 64.2969\n",
"Q57.8594 64.7969 54.1094 64.7969\n",
"L48.1875 64.7969\n",
"Q45.5156 64.7969 44.5781 64.2969\n",
"Q43.6562 63.8125 43.0156 61.375\n",
"L29.2969 6.5\n",
"Q29.25 6.29688 29.2188 6.09375\n",
"Q29.2031 5.90625 29.1094 5.60938\n",
"Q29.1094 4.34375 30.6094 4\n",
"Q33.2031 3.51562 41.7031 3.51562\n",
"Q42.6719 3.51562 42.6719 2.20312\n",
"Q42.3281 0.78125 42.125 0.390625\n",
"Q41.9375 0 41.0156 0\n",
"L5.60938 0\n",
"Q4.59375 0 4.59375 1.3125\" id=\"Cmmi10-54\"/>\n",
" <path d=\"\n",
"M7.71875 1.70312\n",
"Q7.71875 2.29688 7.8125 2.59375\n",
"L15.2812 32.4219\n",
"Q16.0156 35.2031 16.0156 37.3125\n",
"Q16.0156 41.6094 13.0938 41.6094\n",
"Q9.96875 41.6094 8.45312 37.8594\n",
"Q6.9375 34.125 5.51562 28.4219\n",
"Q5.51562 28.125 5.21875 27.9531\n",
"Q4.9375 27.7812 4.6875 27.7812\n",
"L3.51562 27.7812\n",
"Q3.17188 27.7812 2.92188 28.1406\n",
"Q2.6875 28.5156 2.6875 28.8125\n",
"Q3.76562 33.1562 4.76562 36.1719\n",
"Q5.76562 39.2031 7.89062 41.6875\n",
"Q10.0156 44.1875 13.1875 44.1875\n",
"Q16.6562 44.1875 19.2656 42.1875\n",
"Q21.875 40.1875 22.5156 36.9219\n",
"Q25.0469 40.2344 28.2969 42.2031\n",
"Q31.5469 44.1875 35.4062 44.1875\n",
"Q38.5781 44.1875 40.9844 42.3281\n",
"Q43.4062 40.4844 43.4062 37.3125\n",
"Q43.4062 34.7656 41.8125 32.875\n",
"Q40.2344 31 37.5938 31\n",
"Q35.9844 31 34.8906 32\n",
"Q33.7969 33.0156 33.7969 34.625\n",
"Q33.7969 36.8125 35.4062 38.5469\n",
"Q37.0156 40.2812 39.1094 40.2812\n",
"Q37.5 41.6094 35.2031 41.6094\n",
"Q30.9062 41.6094 27.7344 38.5469\n",
"Q24.5625 35.5 22.0156 30.8125\n",
"L14.8906 2.20312\n",
"Q14.5469 0.828125 13.3438 -0.140625\n",
"Q12.1562 -1.125 10.6875 -1.125\n",
"Q9.46875 -1.125 8.59375 -0.34375\n",
"Q7.71875 0.4375 7.71875 1.70312\" id=\"Cmmi10-72\"/>\n",
" <path d=\"\n",
"M9.90625 -18.0156\n",
"Q9.90625 -17.5781 10.2969 -17.1875\n",
"Q13.9219 -13.7188 15.9219 -9.17188\n",
"Q17.9219 -4.64062 17.9219 0.390625\n",
"L17.9219 1.60938\n",
"Q16.3125 0 13.9219 0\n",
"Q11.625 0 10.0156 1.60938\n",
"Q8.40625 3.21875 8.40625 5.51562\n",
"Q8.40625 7.85938 10.0156 9.42188\n",
"Q11.625 10.9844 13.9219 10.9844\n",
"Q17.4844 10.9844 19 7.6875\n",
"Q20.5156 4.39062 20.5156 0.390625\n",
"Q20.5156 -5.17188 18.2812 -10.1719\n",
"Q16.0625 -15.1875 12.0156 -19.1875\n",
"Q11.625 -19.3906 11.375 -19.3906\n",
"Q10.8906 -19.3906 10.3906 -18.9375\n",
"Q9.90625 -18.5 9.90625 -18.0156\" id=\"Cmmi10-3b\"/>\n",
" <path d=\"\n",
"M8.40625 5.51562\n",
"Q8.40625 7.76562 10.0625 9.375\n",
"Q11.7188 10.9844 13.9219 10.9844\n",
"Q15.2812 10.9844 16.5938 10.25\n",
"Q17.9219 9.51562 18.6562 8.20312\n",
"Q19.3906 6.89062 19.3906 5.51562\n",
"Q19.3906 3.32812 17.7656 1.65625\n",
"Q16.1562 0 13.9219 0\n",
"Q11.7188 0 10.0625 1.65625\n",
"Q8.40625 3.32812 8.40625 5.51562\" id=\"Cmmi10-3a\"/>\n",
" </defs>\n",
" <g transform=\"translate(168.62475 20.016)scale(0.144 -0.144)\">\n",
" <use transform=\"translate(0.0 20.6875)\" xlink:href=\"#Cmmi10-be\"/>\n",
" <use transform=\"translate(74.638671875 20.6875)\" xlink:href=\"#Cmr10-3d\"/>\n",
" <use transform=\"translate(158.697265625 20.6875)\" xlink:href=\"#Cmr10-30\"/>\n",
" <use transform=\"translate(208.697265625 20.6875)\" xlink:href=\"#Cmmi10-3a\"/>\n",
" <use transform=\"translate(237.240234375 20.6875)\" xlink:href=\"#Cmr10-35\"/>\n",
" <use transform=\"translate(287.240234375 20.6875)\" xlink:href=\"#Cmr10-30\"/>\n",
" <use transform=\"translate(337.240234375 20.6875)\" xlink:href=\"#Cmmi10-3b\"/>\n",
" <use transform=\"translate(366.908203125 20.6875)\" xlink:href=\"#Cmmi10-72\"/>\n",
" <use transform=\"translate(429.583984375 20.6875)\" xlink:href=\"#Cmr10-3d\"/>\n",
" <use transform=\"translate(513.642578125 20.6875)\" xlink:href=\"#Cmr10-30\"/>\n",
" <use transform=\"translate(563.642578125 20.6875)\" xlink:href=\"#Cmmi10-3a\"/>\n",
" <use transform=\"translate(592.185546875 20.6875)\" xlink:href=\"#Cmr10-31\"/>\n",
" <use transform=\"translate(642.185546875 20.6875)\" xlink:href=\"#Cmmi10-3b\"/>\n",
" <use transform=\"translate(671.853515625 20.6875)\" xlink:href=\"#Cmmi10-54\"/>\n",
" <use transform=\"translate(747.810546875 20.6875)\" xlink:href=\"#Cmr10-3d\"/>\n",
" <use transform=\"translate(831.869140625 20.6875)\" xlink:href=\"#Cmr10-30\"/>\n",
" <use transform=\"translate(881.869140625 20.6875)\" xlink:href=\"#Cmmi10-3a\"/>\n",
" <use transform=\"translate(910.412109375 20.6875)\" xlink:href=\"#Cmr10-32\"/>\n",
" <use transform=\"translate(960.412109375 20.6875)\" xlink:href=\"#Cmr10-35\"/>\n",
" <use transform=\"translate(1010.41210938 20.6875)\" xlink:href=\"#Cmmi10-3b\"/>\n",
" <use transform=\"translate(1040.08007812 20.6875)\" xlink:href=\"#Cmmi10-4b\"/>\n",
" <use transform=\"translate(1142.55078125 20.6875)\" xlink:href=\"#Cmr10-3d\"/>\n",
" <use transform=\"translate(1226.609375 20.6875)\" xlink:href=\"#Cmr10-31\"/>\n",
" <use transform=\"translate(1276.609375 20.6875)\" xlink:href=\"#Cmr10-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <defs>\n",
" <clipPath id=\"p338691d578\">\n",
" <rect height=\"345.6\" width=\"446.4\" x=\"40.96875\" y=\"22.136\"/>\n",
" </clipPath>\n",
" </defs>\n",
"</svg>\n"
],
"text": [
"Figure(PyObject <matplotlib.figure.Figure object at 0x90ddcd0>)"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": [
"PyObject <matplotlib.text.Text object at 0x90f7f90>"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is obviously the correct response to the volatility increase."
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Numerical Correctness"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Although my scheme produces what appears to be a very reasonable options pricing curve, I have not yet checked that the numerical values are correct. The paper includes the correct numerical values for $\\sigma=0.25, r=0.1, T=0.25, K=10$ which I've confirmed with another source (http://www.math.columbia.edu/~smirnov/options13.html)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# values for my solver\n",
"for i=[226, 251, 276]\n",
" print(\"v($(s[i])) = $(v[i])\\n\")\n",
"end"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stderr",
"text": [
"Got bus address: \"unix:abstract=/tmp/dbus-DjhIDjkEaA,guid=7b5ef275947c15c0916c0bfc00000039\" \n",
"Connected to accessibility bus at: \"unix:abstract=/tmp/dbus-DjhIDjkEaA,guid=7b5ef275947c15c0916c0bfc00000039\" \n",
"Registered DEC: true \n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"v(9.00900900900901) = 1.0279040338939691\n",
"v(10.01001001001001) = 0.44818270648684966\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"v(11.01101101101101) = 0.17638215863754847\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For $s=9$, my implementation gave price 1.0279 and the paper's implementation gave 1.0304.\n",
"\n",
"For $s=10$, my implementation gave price 0.4481 and the paper's implementation gave 0.4024.\n",
"\n",
"For $s=11$, my implementation gave price 0.1763 and the paper's implementation gave 0.1206.\n",
"\n",
"I put in a lot of time trying to debug and correct these values, but at this point I can't see any mistakes in my math or my relatively short implementation (which makes it very easy to read over). I initially found a typo in my code (I did ``x ./ 2 .* h`` rather than ``x ./ (2 .* h)``) and fixing this made my results closer to correct but still not right. Some other things I noticed while debugging is that the boundary condition at $s=0$ appears to be unnecessary with the $v\\ge g$ constraint in the LCP. I also noted that switching from implicit Euler to Crank-Nicolson after a few did not for the Rannacher scheme did not make much of a difference in my results with 1000 space steps and 10000 time steps. I also tried using a first order rather than second order approximation to $v_s$ so that my matrix $A$ would be an M-matrix, which should increase stability, but this did not make a difference as with the set of parameters I was testing at the the second-order matrix $A$ already was an M-matrix. I also verified by hand the value of $A$ for the 5 spatial point case.\n",
"\n",
"The confusing part about my implementation being incorrect is that it is so short there is not much room for bugs to hide. I'm convinced that my error must be in my math, which means the error is either with the formulas I derived for the elements of the matrix $A$ or in the operator splitting method.\n",
"\n",
"Deriving these methods was difficult because the paper omitted much of the relevant algebra and contain several different sign errors that we're repeated throughout the paper. For instance, through the paper it is declared $v_t - Av = \\lambda \\ge 0$, while the rest of the financial literature states this should be $\\le 0$. This also changes the equations for the operator splitting method. The paper has the steps $B\\tilde{v}^n = Cv^{n+1} + f + k\\lambda^{n+1}$ and the equation $v^n - k\\lambda^n = \\tilde{v}^n - k\\lambda^{n+1}$, but my derivation presented above found $B\\tilde{v}^n = Cv^{n+1} - k f - k\\lambda^{n+1}$ and $v^n + k\\lambda^n = \\tilde{v}^n + k\\lambda^{n+1}$. As the boundary condition $f$ doesn't seem to affect the result of the computation at all, the paper's $\\lambda$ is my $-\\lambda$, so I tried running the exact equations of the paper with my matrix $A$ and still got the same results. This indicates that the problem is probably with my matrix $A$ or in the implementation (not in the operator splitting equations themselves).\n",
"\n",
"Additionally, the paper did not state an initial value for $\\lambda$, but I corresponded with one of the authors and he told me that \"In practice, we choose always the initial lambda to be zero\"."
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Convergence"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This algorithm should have second order convergence in both $h$ and $k$ because the Crank-Nicolson (and Rannacher) scheme is second order in $k$, the matrix $A$ used the second order in $h$ spatial derivative approximations, and the operator splitting approximation can be shown to be second order. Although the scheme does not appear to be correct, I can still test convergence by treating the result from a very fine grid as the correct solution and looking at the error between that solution and other solutions on less fine grids."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"@time s, reference = solver(10000, 40, 10000, 0.25, 0.25, 0.1, 10.0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"elapsed time: "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"16.761800169 seconds (5727453920 bytes allocated)\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 5,
"text": [
"([0.0,0.004000400040004,0.008000800080008,0.012001200120012002,0.016001600160016,0.020002000200020003,0.024002400240024004,0.028002800280028002,0.032003200320032,0.036003600360036005 \u2026 39.96399639963996,39.967996799679966,39.97199719971997,39.97599759975998,39.97999799979998,39.98399839983998,39.98799879987999,39.991999199919995,39.995999599959994,40.0],[10.0,10.312961462824983,10.30845660538491,10.303951747971055,10.299446890549193,10.29494203312639,10.29043717570415,10.285932318269438,10.28142746084158,10.276922603412679 \u2026 1.4243414953517944e-18,1.2656549812193786e-18,1.1070825813792524e-18,9.486210620418497e-19,7.902671946865357e-19,6.320177559960549e-19,4.738695277911635e-19,3.1581929696543424e-19,1.5786385542025567e-19,0.0])"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"errs = zeros(3)\n",
"for i = [1, 2, 3]\n",
" _, v = solver(10000, 40, 10 .^ i, 0.25, 0.25, 0.1, 10.0)\n",
" errs[i] = maximum(abs(reference - v))\n",
"end\n",
"\n",
"loglog(1 ./ (10.^[1:3] - 1), errs)\n",
"xlabel(\"\\$k\\$\")\n",
"ylabel(\"\\$L_\\\\infty\\$ norm of error\")\n",
"title(\"Modifying step size with 10000 price grid points\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "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",
"svg": [
"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
"<!-- Created with matplotlib (http://matplotlib.sourceforge.net/) -->\n",
"<svg height=\"407pt\" version=\"1.1\" viewBox=\"0 0 518 407\" width=\"518pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
" <defs>\n",
" <style type=\"text/css\">\n",
"*{stroke-linecap:square;stroke-linejoin:round;}\n",
" </style>\n",
" </defs>\n",
" <g id=\"figure_1\">\n",
" <g id=\"patch_1\">\n",
" <path d=\"\n",
"M0 407.022\n",
"L518.1 407.022\n",
"L518.1 0\n",
"L0 0\n",
"z\n",
"\" style=\"fill:#ffffff;\"/>\n",
" </g>\n",
" <g id=\"axes_1\">\n",
" <g id=\"patch_2\">\n",
" <path d=\"\n",
"M53.52 368.742\n",
"L499.92 368.742\n",
"L499.92 23.1417\n",
"L53.52 23.1417\n",
"z\n",
"\" style=\"fill:#ffffff;\"/>\n",
" </g>\n",
" <g id=\"line2d_1\">\n",
" <path clip-path=\"url(#pb4f25b148f)\" d=\"\n",
"M357.929 74.5414\n",
"L202.969 195.042\n",
"L53.5847 315.47\" style=\"fill:none;stroke:#0000ff;\"/>\n",
" </g>\n",
" <g id=\"matplotlib.axis_1\">\n",
" <g id=\"xtick_1\">\n",
" <g id=\"line2d_2\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L0 -4\" id=\"m0012dd4eef\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#m0012dd4eef\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_3\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L0 4\" id=\"m476344969c\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#m476344969c\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_1\">\n",
" <!-- $\\mathdefault{10^{-3}}$ -->\n",
" <defs>\n",
" <path d=\"\n",
"M12.4062 8.29688\n",
"L28.5156 8.29688\n",
"L28.5156 63.9219\n",
"L10.9844 60.4062\n",
"L10.9844 69.3906\n",
"L28.4219 72.9062\n",
"L38.2812 72.9062\n",
"L38.2812 8.29688\n",
"L54.3906 8.29688\n",
"L54.3906 0\n",
"L12.4062 0\n",
"z\n",
"\" id=\"DejaVuSans-31\"/>\n",
" <path d=\"\n",
"M31.7812 66.4062\n",
"Q24.1719 66.4062 20.3281 58.9062\n",
"Q16.5 51.4219 16.5 36.375\n",
"Q16.5 21.3906 20.3281 13.8906\n",
"Q24.1719 6.39062 31.7812 6.39062\n",
"Q39.4531 6.39062 43.2812 13.8906\n",
"Q47.125 21.3906 47.125 36.375\n",
"Q47.125 51.4219 43.2812 58.9062\n",
"Q39.4531 66.4062 31.7812 66.4062\n",
"M31.7812 74.2188\n",
"Q44.0469 74.2188 50.5156 64.5156\n",
"Q56.9844 54.8281 56.9844 36.375\n",
"Q56.9844 17.9688 50.5156 8.26562\n",
"Q44.0469 -1.42188 31.7812 -1.42188\n",
"Q19.5312 -1.42188 13.0625 8.26562\n",
"Q6.59375 17.9688 6.59375 36.375\n",
"Q6.59375 54.8281 13.0625 64.5156\n",
"Q19.5312 74.2188 31.7812 74.2188\" id=\"DejaVuSans-30\"/>\n",
" <path d=\"\n",
"M40.5781 39.3125\n",
"Q47.6562 37.7969 51.625 33\n",
"Q55.6094 28.2188 55.6094 21.1875\n",
"Q55.6094 10.4062 48.1875 4.48438\n",
"Q40.7656 -1.42188 27.0938 -1.42188\n",
"Q22.5156 -1.42188 17.6562 -0.515625\n",
"Q12.7969 0.390625 7.625 2.20312\n",
"L7.625 11.7188\n",
"Q11.7188 9.32812 16.5938 8.10938\n",
"Q21.4844 6.89062 26.8125 6.89062\n",
"Q36.0781 6.89062 40.9375 10.5469\n",
"Q45.7969 14.2031 45.7969 21.1875\n",
"Q45.7969 27.6406 41.2812 31.2656\n",
"Q36.7656 34.9062 28.7188 34.9062\n",
"L20.2188 34.9062\n",
"L20.2188 43.0156\n",
"L29.1094 43.0156\n",
"Q36.375 43.0156 40.2344 45.9219\n",
"Q44.0938 48.8281 44.0938 54.2969\n",
"Q44.0938 59.9062 40.1094 62.9062\n",
"Q36.1406 65.9219 28.7188 65.9219\n",
"Q24.6562 65.9219 20.0156 65.0312\n",
"Q15.375 64.1562 9.8125 62.3125\n",
"L9.8125 71.0938\n",
"Q15.4375 72.6562 20.3438 73.4375\n",
"Q25.25 74.2188 29.5938 74.2188\n",
"Q40.8281 74.2188 47.3594 69.1094\n",
"Q53.9062 64.0156 53.9062 55.3281\n",
"Q53.9062 49.2656 50.4375 45.0938\n",
"Q46.9688 40.9219 40.5781 39.3125\" id=\"DejaVuSans-33\"/>\n",
" <path d=\"\n",
"M4.89062 31.3906\n",
"L31.2031 31.3906\n",
"L31.2031 23.3906\n",
"L4.89062 23.3906\n",
"z\n",
"\" id=\"DejaVuSans-2d\"/>\n",
" </defs>\n",
" <g transform=\"translate(41.04 386.18175)scale(0.12 -0.12)\">\n",
" <use transform=\"translate(0.0 2.234375)\" xlink:href=\"#DejaVuSans-31\"/>\n",
" <use transform=\"translate(63.623046875 2.234375)\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use transform=\"translate(127.24609375 60.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-2d\"/>\n",
" <use transform=\"translate(152.504882812 60.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-33\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_2\">\n",
" <g id=\"line2d_4\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"202.32\" xlink:href=\"#m0012dd4eef\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_5\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"202.32\" xlink:href=\"#m476344969c\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_2\">\n",
" <!-- $\\mathdefault{10^{-2}}$ -->\n",
" <defs>\n",
" <path d=\"\n",
"M19.1875 8.29688\n",
"L53.6094 8.29688\n",
"L53.6094 0\n",
"L7.32812 0\n",
"L7.32812 8.29688\n",
"Q12.9375 14.1094 22.625 23.8906\n",
"Q32.3281 33.6875 34.8125 36.5312\n",
"Q39.5469 41.8438 41.4219 45.5312\n",
"Q43.3125 49.2188 43.3125 52.7812\n",
"Q43.3125 58.5938 39.2344 62.25\n",
"Q35.1562 65.9219 28.6094 65.9219\n",
"Q23.9688 65.9219 18.8125 64.3125\n",
"Q13.6719 62.7031 7.8125 59.4219\n",
"L7.8125 69.3906\n",
"Q13.7656 71.7812 18.9375 73\n",
"Q24.125 74.2188 28.4219 74.2188\n",
"Q39.75 74.2188 46.4844 68.5469\n",
"Q53.2188 62.8906 53.2188 53.4219\n",
"Q53.2188 48.9219 51.5312 44.8906\n",
"Q49.8594 40.875 45.4062 35.4062\n",
"Q44.1875 33.9844 37.6406 27.2188\n",
"Q31.1094 20.4531 19.1875 8.29688\" id=\"DejaVuSans-32\"/>\n",
" </defs>\n",
" <g transform=\"translate(189.84 386.18175)scale(0.12 -0.12)\">\n",
" <use transform=\"translate(0.0 2.234375)\" xlink:href=\"#DejaVuSans-31\"/>\n",
" <use transform=\"translate(63.623046875 2.234375)\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use transform=\"translate(127.24609375 60.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-2d\"/>\n",
" <use transform=\"translate(152.504882812 60.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-32\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_3\">\n",
" <g id=\"line2d_6\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"351.12\" xlink:href=\"#m0012dd4eef\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_7\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"351.12\" xlink:href=\"#m476344969c\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_3\">\n",
" <!-- $\\mathdefault{10^{-1}}$ -->\n",
" <g transform=\"translate(338.64 386.06175)scale(0.12 -0.12)\">\n",
" <use transform=\"translate(0.0 2.153125)\" xlink:href=\"#DejaVuSans-31\"/>\n",
" <use transform=\"translate(63.623046875 2.153125)\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use transform=\"translate(127.24609375 59.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-2d\"/>\n",
" <use transform=\"translate(152.504882812 59.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-31\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_4\">\n",
" <g id=\"line2d_8\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m0012dd4eef\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_9\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m476344969c\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_4\">\n",
" <!-- $\\mathdefault{10^{0}}$ -->\n",
" <g transform=\"translate(488.94 386.18175)scale(0.12 -0.12)\">\n",
" <use transform=\"translate(0.0 2.234375)\" xlink:href=\"#DejaVuSans-31\"/>\n",
" <use transform=\"translate(63.623046875 2.234375)\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use transform=\"translate(127.24609375 60.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-30\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_5\">\n",
" <g id=\"line2d_10\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L0 -2\" id=\"m69b1a1edd1\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"98.3132633548\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_11\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L0 2\" id=\"m9ad4d917ad\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"98.3132633548\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_6\">\n",
" <g id=\"line2d_12\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"124.515642702\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_13\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"124.515642702\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_7\">\n",
" <g id=\"line2d_14\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"143.10652671\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_15\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"143.10652671\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_8\">\n",
" <g id=\"line2d_16\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"157.526736645\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_17\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"157.526736645\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_9\">\n",
" <g id=\"line2d_18\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"169.308906057\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_19\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"169.308906057\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_10\">\n",
" <g id=\"line2d_20\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"179.270588354\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_21\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"179.270588354\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_11\">\n",
" <g id=\"line2d_22\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"187.899790064\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_23\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"187.899790064\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_12\">\n",
" <g id=\"line2d_24\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"195.511285405\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_25\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"195.511285405\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_13\">\n",
" <g id=\"line2d_26\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"247.113263355\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_27\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"247.113263355\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_14\">\n",
" <g id=\"line2d_28\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"273.315642702\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_29\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"273.315642702\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_15\">\n",
" <g id=\"line2d_30\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"291.90652671\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_31\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"291.90652671\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_16\">\n",
" <g id=\"line2d_32\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"306.326736645\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_33\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"306.326736645\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_17\">\n",
" <g id=\"line2d_34\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"318.108906057\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_35\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"318.108906057\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_18\">\n",
" <g id=\"line2d_36\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"328.070588354\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_37\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"328.070588354\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_19\">\n",
" <g id=\"line2d_38\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"336.699790064\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_39\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"336.699790064\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_20\">\n",
" <g id=\"line2d_40\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"344.311285405\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_41\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"344.311285405\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_21\">\n",
" <g id=\"line2d_42\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"395.913263355\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_43\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"395.913263355\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_22\">\n",
" <g id=\"line2d_44\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"422.115642702\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_45\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"422.115642702\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_23\">\n",
" <g id=\"line2d_46\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"440.70652671\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_47\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"440.70652671\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_24\">\n",
" <g id=\"line2d_48\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"455.126736645\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_49\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"455.126736645\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_25\">\n",
" <g id=\"line2d_50\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"466.908906057\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_51\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"466.908906057\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_26\">\n",
" <g id=\"line2d_52\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"476.870588354\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_53\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"476.870588354\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_27\">\n",
" <g id=\"line2d_54\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"485.499790064\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_55\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"485.499790064\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"xtick_28\">\n",
" <g id=\"line2d_56\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"493.111285405\" xlink:href=\"#m69b1a1edd1\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_57\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"493.111285405\" xlink:href=\"#m9ad4d917ad\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_5\">\n",
" <!-- $k$ -->\n",
" <defs>\n",
" <path d=\"\n",
"M5.32812 1.8125\n",
"Q5.32812 2.39062 5.42188 2.6875\n",
"L19.9219 60.5\n",
"Q20.3125 62.2031 20.4062 63.1875\n",
"Q20.4062 64.7969 13.9219 64.7969\n",
"Q12.8906 64.7969 12.8906 66.1094\n",
"Q12.9375 66.3594 13.1094 66.9844\n",
"Q13.2812 67.625 13.5469 67.9688\n",
"Q13.8125 68.3125 14.3125 68.3125\n",
"L27.7812 69.3906\n",
"L28.0781 69.3906\n",
"Q28.0781 69.2812 28.4219 69.1094\n",
"Q28.7656 68.9531 28.8125 68.8906\n",
"Q29 68.4062 29 68.1094\n",
"L18.5 26.3125\n",
"Q22.125 27.8281 27.6094 33.5156\n",
"Q33.1094 39.2031 36.2031 41.6875\n",
"Q39.3125 44.1875 44 44.1875\n",
"Q46.7812 44.1875 48.7344 42.2812\n",
"Q50.6875 40.375 50.6875 37.5938\n",
"Q50.6875 35.8438 49.9531 34.3438\n",
"Q49.2188 32.8594 47.8906 31.9219\n",
"Q46.5781 31 44.8281 31\n",
"Q43.2188 31 42.1094 32\n",
"Q41.0156 33.0156 41.0156 34.625\n",
"Q41.0156 37.0156 42.7031 38.6406\n",
"Q44.3906 40.2812 46.7812 40.2812\n",
"Q45.7969 41.6094 43.7969 41.6094\n",
"Q40.8281 41.6094 38.0625 39.8906\n",
"Q35.2969 38.1875 32.0938 34.9844\n",
"Q28.9062 31.7812 26.2656 29.125\n",
"Q23.6406 26.4688 21.3906 25.0938\n",
"Q27.2969 24.4219 31.6406 22\n",
"Q35.9844 19.5781 35.9844 14.5938\n",
"Q35.9844 13.5781 35.5938 12.0156\n",
"Q34.7188 8.25 34.7188 6\n",
"Q34.7188 1.51562 37.7969 1.51562\n",
"Q41.4062 1.51562 43.2812 5.46875\n",
"Q45.1719 9.42188 46.3906 14.7031\n",
"Q46.5781 15.2812 47.2188 15.2812\n",
"L48.3906 15.2812\n",
"Q48.7812 15.2812 49.0469 15.0312\n",
"Q49.3125 14.7969 49.3125 14.4062\n",
"Q49.3125 14.3125 49.2188 14.1094\n",
"Q45.4531 -1.125 37.5938 -1.125\n",
"Q34.7656 -1.125 32.5938 0.1875\n",
"Q30.4219 1.51562 29.25 3.78125\n",
"Q28.0781 6.0625 28.0781 8.89062\n",
"Q28.0781 10.5 28.5156 12.2031\n",
"Q28.8125 13.375 28.8125 14.4062\n",
"Q28.8125 18.2656 25.3906 20.2656\n",
"Q21.9688 22.2656 17.5781 22.7031\n",
"L12.5 2.29688\n",
"Q12.1094 0.78125 10.9844 -0.171875\n",
"Q9.85938 -1.125 8.40625 -1.125\n",
"Q7.125 -1.125 6.21875 -0.265625\n",
"Q5.32812 0.59375 5.32812 1.8125\" id=\"Cmmi10-6b\"/>\n",
" </defs>\n",
" <g transform=\"translate(273.54 399.82175)scale(0.12 -0.12)\">\n",
" <use transform=\"translate(0.0 2.609375)\" xlink:href=\"#Cmmi10-6b\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"matplotlib.axis_2\">\n",
" <g id=\"ytick_1\">\n",
" <g id=\"line2d_58\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L4 0\" id=\"me8a85f7bf6\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#me8a85f7bf6\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_59\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L-4 0\" id=\"m1a32005dea\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m1a32005dea\" y=\"368.74175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_6\">\n",
" <!-- $\\mathdefault{10^{-4}}$ -->\n",
" <defs>\n",
" <path d=\"\n",
"M37.7969 64.3125\n",
"L12.8906 25.3906\n",
"L37.7969 25.3906\n",
"z\n",
"\n",
"M35.2031 72.9062\n",
"L47.6094 72.9062\n",
"L47.6094 25.3906\n",
"L58.0156 25.3906\n",
"L58.0156 17.1875\n",
"L47.6094 17.1875\n",
"L47.6094 0\n",
"L37.7969 0\n",
"L37.7969 17.1875\n",
"L4.89062 17.1875\n",
"L4.89062 26.7031\n",
"z\n",
"\" id=\"DejaVuSans-34\"/>\n",
" </defs>\n",
" <g transform=\"translate(24.56 375.40175)scale(0.12 -0.12)\">\n",
" <use transform=\"translate(0.0 2.153125)\" xlink:href=\"#DejaVuSans-31\"/>\n",
" <use transform=\"translate(63.623046875 2.153125)\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use transform=\"translate(127.24609375 59.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-2d\"/>\n",
" <use transform=\"translate(152.504882812 59.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-34\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_2\">\n",
" <g id=\"line2d_60\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#me8a85f7bf6\" y=\"253.54175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_61\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m1a32005dea\" y=\"253.54175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_7\">\n",
" <!-- $\\mathdefault{10^{-3}}$ -->\n",
" <g transform=\"translate(24.56 260.26175)scale(0.12 -0.12)\">\n",
" <use transform=\"translate(0.0 2.234375)\" xlink:href=\"#DejaVuSans-31\"/>\n",
" <use transform=\"translate(63.623046875 2.234375)\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use transform=\"translate(127.24609375 60.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-2d\"/>\n",
" <use transform=\"translate(152.504882812 60.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-33\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_3\">\n",
" <g id=\"line2d_62\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#me8a85f7bf6\" y=\"138.34175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_63\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m1a32005dea\" y=\"138.34175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_8\">\n",
" <!-- $\\mathdefault{10^{-2}}$ -->\n",
" <g transform=\"translate(24.56 145.06175)scale(0.12 -0.12)\">\n",
" <use transform=\"translate(0.0 2.234375)\" xlink:href=\"#DejaVuSans-31\"/>\n",
" <use transform=\"translate(63.623046875 2.234375)\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use transform=\"translate(127.24609375 60.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-2d\"/>\n",
" <use transform=\"translate(152.504882812 60.046875)scale(0.7)\" xlink:href=\"#DejaVuSans-32\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_4\">\n",
" <g id=\"line2d_64\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#me8a85f7bf6\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_65\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m1a32005dea\" y=\"23.14175\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_9\">\n",
" <!-- $\\mathdefault{10^{-1}}$ -->\n",
" <g transform=\"translate(24.56 29.80175)scale(0.12 -0.12)\">\n",
" <use transform=\"translate(0.0 2.153125)\" xlink:href=\"#DejaVuSans-31\"/>\n",
" <use transform=\"translate(63.623046875 2.153125)\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use transform=\"translate(127.24609375 59.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-2d\"/>\n",
" <use transform=\"translate(152.504882812 59.965625)scale(0.7)\" xlink:href=\"#DejaVuSans-31\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_5\">\n",
" <g id=\"line2d_66\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L2 0\" id=\"md1aed85dae\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"334.0630945\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_67\">\n",
" <defs>\n",
" <path d=\"\n",
"M0 0\n",
"L-2 0\" id=\"m544cce01ee\" style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\"/>\n",
" </defs>\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"334.0630945\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_6\">\n",
" <g id=\"line2d_68\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"313.777381456\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_69\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"313.777381456\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_7\">\n",
" <g id=\"line2d_70\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"299.384438999\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_71\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"299.384438999\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_8\">\n",
" <g id=\"line2d_72\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"288.2204055\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_73\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"288.2204055\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_9\">\n",
" <g id=\"line2d_74\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"279.098725956\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_75\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"279.098725956\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_10\">\n",
" <g id=\"line2d_76\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"271.38645579\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_77\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"271.38645579\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_11\">\n",
" <g id=\"line2d_78\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"264.705783499\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_79\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"264.705783499\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_12\">\n",
" <g id=\"line2d_80\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"258.813012913\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_81\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"258.813012913\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_13\">\n",
" <g id=\"line2d_82\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"218.8630945\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_83\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"218.8630945\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_14\">\n",
" <g id=\"line2d_84\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"198.577381456\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_85\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"198.577381456\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_15\">\n",
" <g id=\"line2d_86\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"184.184438999\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_87\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"184.184438999\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_16\">\n",
" <g id=\"line2d_88\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"173.0204055\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_89\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"173.0204055\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_17\">\n",
" <g id=\"line2d_90\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"163.898725956\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_91\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"163.898725956\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_18\">\n",
" <g id=\"line2d_92\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"156.18645579\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_93\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"156.18645579\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_19\">\n",
" <g id=\"line2d_94\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"149.505783499\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_95\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"149.505783499\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_20\">\n",
" <g id=\"line2d_96\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"143.613012913\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_97\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"143.613012913\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_21\">\n",
" <g id=\"line2d_98\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"103.6630945\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_99\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"103.6630945\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_22\">\n",
" <g id=\"line2d_100\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"83.3773814563\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_101\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"83.3773814563\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_23\">\n",
" <g id=\"line2d_102\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"68.984438999\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_103\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"68.984438999\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_24\">\n",
" <g id=\"line2d_104\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"57.8204055005\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_105\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"57.8204055005\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_25\">\n",
" <g id=\"line2d_106\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"48.6987259558\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_107\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"48.6987259558\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_26\">\n",
" <g id=\"line2d_108\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"40.9864557904\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_109\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"40.9864557904\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_27\">\n",
" <g id=\"line2d_110\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"34.3057834985\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_111\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"34.3057834985\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"ytick_28\">\n",
" <g id=\"line2d_112\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"53.52\" xlink:href=\"#md1aed85dae\" y=\"28.4130129126\"/>\n",
" </g>\n",
" </g>\n",
" <g id=\"line2d_113\">\n",
" <g>\n",
" <use style=\"stroke:#000000;stroke-linecap:butt;stroke-width:0.5;\" x=\"499.92\" xlink:href=\"#m544cce01ee\" y=\"28.4130129126\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"text_10\">\n",
" <!-- $L_\\infty$ norm of error -->\n",
" <defs>\n",
" <path d=\"\n",
"M4.6875 0\n",
"Q3.71875 0 3.71875 1.3125\n",
"Q3.76562 1.5625 3.90625 2.17188\n",
"Q4.04688 2.78125 4.3125 3.14062\n",
"Q4.59375 3.51562 4.98438 3.51562\n",
"Q11.0781 3.51562 13.4844 4.20312\n",
"Q14.7969 4.64062 15.375 6.89062\n",
"L29.1094 61.8125\n",
"Q29.2969 62.7969 29.2969 63.1875\n",
"Q29.2969 64.2656 28.0781 64.4062\n",
"Q26.2188 64.7969 20.9062 64.7969\n",
"Q19.9219 64.7969 19.9219 66.1094\n",
"Q20.2656 67.3906 20.4531 67.8438\n",
"Q20.6562 68.3125 21.5781 68.3125\n",
"L51.125 68.3125\n",
"Q52 68.3125 52 67\n",
"Q51.8594 65.9688 51.6562 65.375\n",
"Q51.4688 64.7969 50.6875 64.7969\n",
"Q43.3125 64.7969 40.8281 64.3125\n",
"Q38.375 63.875 37.7969 61.375\n",
"L24.125 6.5\n",
"Q23.6875 5.28125 23.6875 4.29688\n",
"Q23.6875 3.51562 27.0938 3.51562\n",
"L36.375 3.51562\n",
"Q44.2344 3.51562 49.1094 6.64062\n",
"Q54 9.76562 56.3438 13.6875\n",
"Q58.6875 17.625 60.2656 21.8438\n",
"Q61.8594 26.0781 62.5938 26.2188\n",
"L63.4844 26.2188\n",
"Q64.5 26.2188 64.5 24.9062\n",
"L55.6094 0.6875\n",
"Q55.4688 0 54.6875 0\n",
"z\n",
"\" id=\"Cmmi10-4c\"/>\n",
" <path d=\"\n",
"M30.6094 48.3906\n",
"Q23.3906 48.3906 19.1875 42.75\n",
"Q14.9844 37.1094 14.9844 27.2969\n",
"Q14.9844 17.4844 19.1562 11.8438\n",
"Q23.3438 6.20312 30.6094 6.20312\n",
"Q37.7969 6.20312 41.9844 11.8594\n",
"Q46.1875 17.5312 46.1875 27.2969\n",
"Q46.1875 37.0156 41.9844 42.7031\n",
"Q37.7969 48.3906 30.6094 48.3906\n",
"M30.6094 56\n",
"Q42.3281 56 49.0156 48.375\n",
"Q55.7188 40.7656 55.7188 27.2969\n",
"Q55.7188 13.875 49.0156 6.21875\n",
"Q42.3281 -1.42188 30.6094 -1.42188\n",
"Q18.8438 -1.42188 12.1719 6.21875\n",
"Q5.51562 13.875 5.51562 27.2969\n",
"Q5.51562 40.7656 12.1719 48.375\n",
"Q18.8438 56 30.6094 56\" id=\"DejaVuSans-6f\"/>\n",
" <path d=\"\n",
"M24.6094 -1.125\n",
"Q18.9531 -1.125 14.5781 2.1875\n",
"Q10.2031 5.51562 7.90625 10.7812\n",
"Q5.60938 16.0625 5.60938 21.5781\n",
"Q5.60938 25.8281 6.95312 29.875\n",
"Q8.29688 33.9375 10.8281 37.1562\n",
"Q13.375 40.375 16.9688 42.2812\n",
"Q20.5625 44.1875 24.9062 44.1875\n",
"Q29.3906 44.1875 33.5938 42.4688\n",
"Q37.7969 40.7656 41.2812 37.9375\n",
"Q44.7812 35.1094 47.7969 31.3906\n",
"L50.7812 27.3906\n",
"Q53.7656 32.125 57.375 35.8594\n",
"Q60.9844 39.5938 65.5469 41.8906\n",
"Q70.125 44.1875 75.2969 44.1875\n",
"Q79.6406 44.1875 83.2031 42.25\n",
"Q86.7656 40.3281 89.25 37\n",
"Q91.75 33.6875 93.0156 29.6562\n",
"Q94.2812 25.6406 94.2812 21.5781\n",
"Q94.2812 15.9219 91.9062 10.6719\n",
"Q89.5469 5.42188 85.1719 2.14062\n",
"Q80.8125 -1.125 75 -1.125\n",
"Q68.4531 -1.125 62.5625 2.39062\n",
"Q56.6875 5.90625 52.0938 11.7188\n",
"L49.125 15.7188\n",
"Q44.5312 8.25 38.2969 3.5625\n",
"Q32.0781 -1.125 24.6094 -1.125\n",
"M23.5781 2.39062\n",
"Q36.2812 2.39062 46.2969 19.3906\n",
"L41.0156 26.125\n",
"Q36.4219 32.1719 32.4688 35.5938\n",
"Q28.5156 39.0156 23.2969 39.0156\n",
"Q18.8438 39.0156 15.4062 36.5\n",
"Q11.9688 33.9844 10.0781 29.9219\n",
"Q8.20312 25.875 8.20312 21.4844\n",
"Q8.20312 18.1094 9.25 14.7188\n",
"Q10.2969 11.3281 12.2969 8.54688\n",
"Q14.3125 5.76562 17.1562 4.07812\n",
"Q20.0156 2.39062 23.5781 2.39062\n",
"M58.8906 17\n",
"Q63.4844 10.9375 67.4375 7.51562\n",
"Q71.3906 4.10938 76.6094 4.10938\n",
"Q79.9375 4.10938 82.7188 5.5625\n",
"Q85.5 7.03125 87.5156 9.51562\n",
"Q89.5469 12.0156 90.625 15.1406\n",
"Q91.7031 18.2656 91.7031 21.5781\n",
"Q91.7031 26.2188 89.8438 30.6406\n",
"Q87.9844 35.0625 84.4844 37.8906\n",
"Q81 40.7188 76.3125 40.7188\n",
"Q63.625 40.7188 53.6094 23.6875\n",
"z\n",
"\" id=\"Cmsy10-31\"/>\n",
" <path d=\"\n",
"M52 44.1875\n",
"Q55.375 50.25 60.0625 53.125\n",
"Q64.75 56 71.0938 56\n",
"Q79.6406 56 84.2812 50.0156\n",
"Q88.9219 44.0469 88.9219 33.0156\n",
"L88.9219 0\n",
"L79.8906 0\n",
"L79.8906 32.7188\n",
"Q79.8906 40.5781 77.0938 44.375\n",
"Q74.3125 48.1875 68.6094 48.1875\n",
"Q61.625 48.1875 57.5625 43.5469\n",
"Q53.5156 38.9219 53.5156 30.9062\n",
"L53.5156 0\n",
"L44.4844 0\n",
"L44.4844 32.7188\n",
"Q44.4844 40.625 41.7031 44.4062\n",
"Q38.9219 48.1875 33.1094 48.1875\n",
"Q26.2188 48.1875 22.1562 43.5312\n",
"Q18.1094 38.875 18.1094 30.9062\n",
"L18.1094 0\n",
"L9.07812 0\n",
"L9.07812 54.6875\n",
"L18.1094 54.6875\n",
"L18.1094 46.1875\n",
"Q21.1875 51.2188 25.4844 53.6094\n",
"Q29.7812 56 35.6875 56\n",
"Q41.6562 56 45.8281 52.9688\n",
"Q50 49.9531 52 44.1875\" id=\"DejaVuSans-6d\"/>\n",
" <path d=\"\n",
"M54.8906 33.0156\n",
"L54.8906 0\n",
"L45.9062 0\n",
"L45.9062 32.7188\n",
"Q45.9062 40.4844 42.875 44.3281\n",
"Q39.8438 48.1875 33.7969 48.1875\n",
"Q26.5156 48.1875 22.3125 43.5469\n",
"Q18.1094 38.9219 18.1094 30.9062\n",
"L18.1094 0\n",
"L9.07812 0\n",
"L9.07812 54.6875\n",
"L18.1094 54.6875\n",
"L18.1094 46.1875\n",
"Q21.3438 51.125 25.7031 53.5625\n",
"Q30.0781 56 35.7969 56\n",
"Q45.2188 56 50.0469 50.1719\n",
"Q54.8906 44.3438 54.8906 33.0156\" id=\"DejaVuSans-6e\"/>\n",
" <path id=\"DejaVuSans-20\"/>\n",
" <path d=\"\n",
"M37.1094 75.9844\n",
"L37.1094 68.5\n",
"L28.5156 68.5\n",
"Q23.6875 68.5 21.7969 66.5469\n",
"Q19.9219 64.5938 19.9219 59.5156\n",
"L19.9219 54.6875\n",
"L34.7188 54.6875\n",
"L34.7188 47.7031\n",
"L19.9219 47.7031\n",
"L19.9219 0\n",
"L10.8906 0\n",
"L10.8906 47.7031\n",
"L2.29688 47.7031\n",
"L2.29688 54.6875\n",
"L10.8906 54.6875\n",
"L10.8906 58.5\n",
"Q10.8906 67.625 15.1406 71.7969\n",
"Q19.3906 75.9844 28.6094 75.9844\n",
"z\n",
"\" id=\"DejaVuSans-66\"/>\n",
" <path d=\"\n",
"M56.2031 29.5938\n",
"L56.2031 25.2031\n",
"L14.8906 25.2031\n",
"Q15.4844 15.9219 20.4844 11.0625\n",
"Q25.4844 6.20312 34.4219 6.20312\n",
"Q39.5938 6.20312 44.4531 7.46875\n",
"Q49.3125 8.73438 54.1094 11.2812\n",
"L54.1094 2.78125\n",
"Q49.2656 0.734375 44.1875 -0.34375\n",
"Q39.1094 -1.42188 33.8906 -1.42188\n",
"Q20.7969 -1.42188 13.1562 6.1875\n",
"Q5.51562 13.8125 5.51562 26.8125\n",
"Q5.51562 40.2344 12.7656 48.1094\n",
"Q20.0156 56 32.3281 56\n",
"Q43.3594 56 49.7812 48.8906\n",
"Q56.2031 41.7969 56.2031 29.5938\n",
"M47.2188 32.2344\n",
"Q47.125 39.5938 43.0938 43.9844\n",
"Q39.0625 48.3906 32.4219 48.3906\n",
"Q24.9062 48.3906 20.3906 44.1406\n",
"Q15.875 39.8906 15.1875 32.1719\n",
"z\n",
"\" id=\"DejaVuSans-65\"/>\n",
" <path d=\"\n",
"M41.1094 46.2969\n",
"Q39.5938 47.1719 37.8125 47.5781\n",
"Q36.0312 48 33.8906 48\n",
"Q26.2656 48 22.1875 43.0469\n",
"Q18.1094 38.0938 18.1094 28.8125\n",
"L18.1094 0\n",
"L9.07812 0\n",
"L9.07812 54.6875\n",
"L18.1094 54.6875\n",
"L18.1094 46.1875\n",
"Q20.9531 51.1719 25.4844 53.5781\n",
"Q30.0312 56 36.5312 56\n",
"Q37.4531 56 38.5781 55.875\n",
"Q39.7031 55.7656 41.0625 55.5156\n",
"z\n",
"\" id=\"DejaVuSans-72\"/>\n",
" </defs>\n",
" <g transform=\"translate(19.56 248.08175)rotate(-90.0)scale(0.12 -0.12)\">\n",
" <use transform=\"translate(0.0 27.015625)\" xlink:href=\"#Cmmi10-4c\"/>\n",
" <use transform=\"translate(68.017578125 1.50625)scale(0.7)\" xlink:href=\"#Cmsy10-31\"/>\n",
" <use transform=\"translate(168.017578125 27.015625)\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use transform=\"translate(199.8046875 27.015625)\" xlink:href=\"#DejaVuSans-6e\"/>\n",
" <use transform=\"translate(263.18359375 27.015625)\" xlink:href=\"#DejaVuSans-6f\"/>\n",
" <use transform=\"translate(324.365234375 27.015625)\" xlink:href=\"#DejaVuSans-72\"/>\n",
" <use transform=\"translate(365.478515625 27.015625)\" xlink:href=\"#DejaVuSans-6d\"/>\n",
" <use transform=\"translate(462.890625 27.015625)\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use transform=\"translate(494.677734375 27.015625)\" xlink:href=\"#DejaVuSans-6f\"/>\n",
" <use transform=\"translate(555.859375 27.015625)\" xlink:href=\"#DejaVuSans-66\"/>\n",
" <use transform=\"translate(591.064453125 27.015625)\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use transform=\"translate(622.8515625 27.015625)\" xlink:href=\"#DejaVuSans-65\"/>\n",
" <use transform=\"translate(684.375 27.015625)\" xlink:href=\"#DejaVuSans-72\"/>\n",
" <use transform=\"translate(725.48828125 27.015625)\" xlink:href=\"#DejaVuSans-72\"/>\n",
" <use transform=\"translate(766.6015625 27.015625)\" xlink:href=\"#DejaVuSans-6f\"/>\n",
" <use transform=\"translate(827.783203125 27.015625)\" xlink:href=\"#DejaVuSans-72\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <g id=\"patch_3\">\n",
" <path d=\"\n",
"M53.52 23.1417\n",
"L499.92 23.1417\" style=\"fill:none;stroke:#000000;\"/>\n",
" </g>\n",
" <g id=\"patch_4\">\n",
" <path d=\"\n",
"M499.92 368.742\n",
"L499.92 23.1417\" style=\"fill:none;stroke:#000000;\"/>\n",
" </g>\n",
" <g id=\"patch_5\">\n",
" <path d=\"\n",
"M53.52 368.742\n",
"L499.92 368.742\" style=\"fill:none;stroke:#000000;\"/>\n",
" </g>\n",
" <g id=\"patch_6\">\n",
" <path d=\"\n",
"M53.52 368.742\n",
"L53.52 23.1417\" style=\"fill:none;stroke:#000000;\"/>\n",
" </g>\n",
" <g id=\"text_11\">\n",
" <!-- Modifying step size with 10000 price grid points -->\n",
" <defs>\n",
" <path d=\"\n",
"M9.8125 72.9062\n",
"L24.5156 72.9062\n",
"L43.1094 23.2969\n",
"L61.8125 72.9062\n",
"L76.5156 72.9062\n",
"L76.5156 0\n",
"L66.8906 0\n",
"L66.8906 64.0156\n",
"L48.0938 14.0156\n",
"L38.1875 14.0156\n",
"L19.3906 64.0156\n",
"L19.3906 0\n",
"L9.8125 0\n",
"z\n",
"\" id=\"DejaVuSans-4d\"/>\n",
" <path d=\"\n",
"M4.20312 54.6875\n",
"L13.1875 54.6875\n",
"L24.4219 12.0156\n",
"L35.5938 54.6875\n",
"L46.1875 54.6875\n",
"L57.4219 12.0156\n",
"L68.6094 54.6875\n",
"L77.5938 54.6875\n",
"L63.2812 0\n",
"L52.6875 0\n",
"L40.9219 44.8281\n",
"L29.1094 0\n",
"L18.5 0\n",
"z\n",
"\" id=\"DejaVuSans-77\"/>\n",
" <path d=\"\n",
"M18.3125 70.2188\n",
"L18.3125 54.6875\n",
"L36.8125 54.6875\n",
"L36.8125 47.7031\n",
"L18.3125 47.7031\n",
"L18.3125 18.0156\n",
"Q18.3125 11.3281 20.1406 9.42188\n",
"Q21.9688 7.51562 27.5938 7.51562\n",
"L36.8125 7.51562\n",
"L36.8125 0\n",
"L27.5938 0\n",
"Q17.1875 0 13.2344 3.875\n",
"Q9.28125 7.76562 9.28125 18.0156\n",
"L9.28125 47.7031\n",
"L2.6875 47.7031\n",
"L2.6875 54.6875\n",
"L9.28125 54.6875\n",
"L9.28125 70.2188\n",
"z\n",
"\" id=\"DejaVuSans-74\"/>\n",
" <path d=\"\n",
"M5.51562 54.6875\n",
"L48.1875 54.6875\n",
"L48.1875 46.4844\n",
"L14.4062 7.17188\n",
"L48.1875 7.17188\n",
"L48.1875 0\n",
"L4.29688 0\n",
"L4.29688 8.20312\n",
"L38.0938 47.5156\n",
"L5.51562 47.5156\n",
"z\n",
"\" id=\"DejaVuSans-7a\"/>\n",
" <path d=\"\n",
"M48.7812 52.5938\n",
"L48.7812 44.1875\n",
"Q44.9688 46.2969 41.1406 47.3438\n",
"Q37.3125 48.3906 33.4062 48.3906\n",
"Q24.6562 48.3906 19.8125 42.8438\n",
"Q14.9844 37.3125 14.9844 27.2969\n",
"Q14.9844 17.2812 19.8125 11.7344\n",
"Q24.6562 6.20312 33.4062 6.20312\n",
"Q37.3125 6.20312 41.1406 7.25\n",
"Q44.9688 8.29688 48.7812 10.4062\n",
"L48.7812 2.09375\n",
"Q45.0156 0.34375 40.9844 -0.53125\n",
"Q36.9688 -1.42188 32.4219 -1.42188\n",
"Q20.0625 -1.42188 12.7812 6.34375\n",
"Q5.51562 14.1094 5.51562 27.2969\n",
"Q5.51562 40.6719 12.8594 48.3281\n",
"Q20.2188 56 33.0156 56\n",
"Q37.1562 56 41.1094 55.1406\n",
"Q45.0625 54.2969 48.7812 52.5938\" id=\"DejaVuSans-63\"/>\n",
" <path d=\"\n",
"M32.1719 -5.07812\n",
"Q28.375 -14.8438 24.75 -17.8125\n",
"Q21.1406 -20.7969 15.0938 -20.7969\n",
"L7.90625 -20.7969\n",
"L7.90625 -13.2812\n",
"L13.1875 -13.2812\n",
"Q16.8906 -13.2812 18.9375 -11.5156\n",
"Q21 -9.76562 23.4844 -3.21875\n",
"L25.0938 0.875\n",
"L2.98438 54.6875\n",
"L12.5 54.6875\n",
"L29.5938 11.9219\n",
"L46.6875 54.6875\n",
"L56.2031 54.6875\n",
"z\n",
"\" id=\"DejaVuSans-79\"/>\n",
" <path d=\"\n",
"M54.8906 33.0156\n",
"L54.8906 0\n",
"L45.9062 0\n",
"L45.9062 32.7188\n",
"Q45.9062 40.4844 42.875 44.3281\n",
"Q39.8438 48.1875 33.7969 48.1875\n",
"Q26.5156 48.1875 22.3125 43.5469\n",
"Q18.1094 38.9219 18.1094 30.9062\n",
"L18.1094 0\n",
"L9.07812 0\n",
"L9.07812 75.9844\n",
"L18.1094 75.9844\n",
"L18.1094 46.1875\n",
"Q21.3438 51.125 25.7031 53.5625\n",
"Q30.0781 56 35.7969 56\n",
"Q45.2188 56 50.0469 50.1719\n",
"Q54.8906 44.3438 54.8906 33.0156\" id=\"DejaVuSans-68\"/>\n",
" <path d=\"\n",
"M9.42188 54.6875\n",
"L18.4062 54.6875\n",
"L18.4062 0\n",
"L9.42188 0\n",
"z\n",
"\n",
"M9.42188 75.9844\n",
"L18.4062 75.9844\n",
"L18.4062 64.5938\n",
"L9.42188 64.5938\n",
"z\n",
"\" id=\"DejaVuSans-69\"/>\n",
" <path d=\"\n",
"M45.4062 27.9844\n",
"Q45.4062 37.75 41.375 43.1094\n",
"Q37.3594 48.4844 30.0781 48.4844\n",
"Q22.8594 48.4844 18.8281 43.1094\n",
"Q14.7969 37.75 14.7969 27.9844\n",
"Q14.7969 18.2656 18.8281 12.8906\n",
"Q22.8594 7.51562 30.0781 7.51562\n",
"Q37.3594 7.51562 41.375 12.8906\n",
"Q45.4062 18.2656 45.4062 27.9844\n",
"M54.3906 6.78125\n",
"Q54.3906 -7.17188 48.1875 -13.9844\n",
"Q42 -20.7969 29.2031 -20.7969\n",
"Q24.4688 -20.7969 20.2656 -20.0938\n",
"Q16.0625 -19.3906 12.1094 -17.9219\n",
"L12.1094 -9.1875\n",
"Q16.0625 -11.3281 19.9219 -12.3438\n",
"Q23.7812 -13.375 27.7812 -13.375\n",
"Q36.625 -13.375 41.0156 -8.76562\n",
"Q45.4062 -4.15625 45.4062 5.17188\n",
"L45.4062 9.625\n",
"Q42.625 4.78125 38.2812 2.39062\n",
"Q33.9375 0 27.875 0\n",
"Q17.8281 0 11.6719 7.65625\n",
"Q5.51562 15.3281 5.51562 27.9844\n",
"Q5.51562 40.6719 11.6719 48.3281\n",
"Q17.8281 56 27.875 56\n",
"Q33.9375 56 38.2812 53.6094\n",
"Q42.625 51.2188 45.4062 46.3906\n",
"L45.4062 54.6875\n",
"L54.3906 54.6875\n",
"z\n",
"\" id=\"DejaVuSans-67\"/>\n",
" <path d=\"\n",
"M45.4062 46.3906\n",
"L45.4062 75.9844\n",
"L54.3906 75.9844\n",
"L54.3906 0\n",
"L45.4062 0\n",
"L45.4062 8.20312\n",
"Q42.5781 3.32812 38.25 0.953125\n",
"Q33.9375 -1.42188 27.875 -1.42188\n",
"Q17.9688 -1.42188 11.7344 6.48438\n",
"Q5.51562 14.4062 5.51562 27.2969\n",
"Q5.51562 40.1875 11.7344 48.0938\n",
"Q17.9688 56 27.875 56\n",
"Q33.9375 56 38.25 53.625\n",
"Q42.5781 51.2656 45.4062 46.3906\n",
"M14.7969 27.2969\n",
"Q14.7969 17.3906 18.875 11.75\n",
"Q22.9531 6.10938 30.0781 6.10938\n",
"Q37.2031 6.10938 41.2969 11.75\n",
"Q45.4062 17.3906 45.4062 27.2969\n",
"Q45.4062 37.2031 41.2969 42.8438\n",
"Q37.2031 48.4844 30.0781 48.4844\n",
"Q22.9531 48.4844 18.875 42.8438\n",
"Q14.7969 37.2031 14.7969 27.2969\" id=\"DejaVuSans-64\"/>\n",
" <path d=\"\n",
"M18.1094 8.20312\n",
"L18.1094 -20.7969\n",
"L9.07812 -20.7969\n",
"L9.07812 54.6875\n",
"L18.1094 54.6875\n",
"L18.1094 46.3906\n",
"Q20.9531 51.2656 25.2656 53.625\n",
"Q29.5938 56 35.5938 56\n",
"Q45.5625 56 51.7812 48.0938\n",
"Q58.0156 40.1875 58.0156 27.2969\n",
"Q58.0156 14.4062 51.7812 6.48438\n",
"Q45.5625 -1.42188 35.5938 -1.42188\n",
"Q29.5938 -1.42188 25.2656 0.953125\n",
"Q20.9531 3.32812 18.1094 8.20312\n",
"M48.6875 27.2969\n",
"Q48.6875 37.2031 44.6094 42.8438\n",
"Q40.5312 48.4844 33.4062 48.4844\n",
"Q26.2656 48.4844 22.1875 42.8438\n",
"Q18.1094 37.2031 18.1094 27.2969\n",
"Q18.1094 17.3906 22.1875 11.75\n",
"Q26.2656 6.10938 33.4062 6.10938\n",
"Q40.5312 6.10938 44.6094 11.75\n",
"Q48.6875 17.3906 48.6875 27.2969\" id=\"DejaVuSans-70\"/>\n",
" <path d=\"\n",
"M44.2812 53.0781\n",
"L44.2812 44.5781\n",
"Q40.4844 46.5312 36.375 47.5\n",
"Q32.2812 48.4844 27.875 48.4844\n",
"Q21.1875 48.4844 17.8438 46.4375\n",
"Q14.5 44.3906 14.5 40.2812\n",
"Q14.5 37.1562 16.8906 35.375\n",
"Q19.2812 33.5938 26.5156 31.9844\n",
"L29.5938 31.2969\n",
"Q39.1562 29.25 43.1875 25.5156\n",
"Q47.2188 21.7812 47.2188 15.0938\n",
"Q47.2188 7.46875 41.1875 3.01562\n",
"Q35.1562 -1.42188 24.6094 -1.42188\n",
"Q20.2188 -1.42188 15.4531 -0.5625\n",
"Q10.6875 0.296875 5.42188 2\n",
"L5.42188 11.2812\n",
"Q10.4062 8.6875 15.2344 7.39062\n",
"Q20.0625 6.10938 24.8125 6.10938\n",
"Q31.1562 6.10938 34.5625 8.28125\n",
"Q37.9844 10.4531 37.9844 14.4062\n",
"Q37.9844 18.0625 35.5156 20.0156\n",
"Q33.0625 21.9688 24.7031 23.7812\n",
"L21.5781 24.5156\n",
"Q13.2344 26.2656 9.51562 29.9062\n",
"Q5.8125 33.5469 5.8125 39.8906\n",
"Q5.8125 47.6094 11.2812 51.7969\n",
"Q16.75 56 26.8125 56\n",
"Q31.7812 56 36.1719 55.2656\n",
"Q40.5781 54.5469 44.2812 53.0781\" id=\"DejaVuSans-73\"/>\n",
" </defs>\n",
" <g transform=\"translate(104.211375 18.14175)scale(0.144 -0.144)\">\n",
" <use xlink:href=\"#DejaVuSans-4d\"/>\n",
" <use x=\"86.279296875\" xlink:href=\"#DejaVuSans-6f\"/>\n",
" <use x=\"147.4609375\" xlink:href=\"#DejaVuSans-64\"/>\n",
" <use x=\"210.9375\" xlink:href=\"#DejaVuSans-69\"/>\n",
" <use x=\"238.720703125\" xlink:href=\"#DejaVuSans-66\"/>\n",
" <use x=\"272.17578125\" xlink:href=\"#DejaVuSans-79\"/>\n",
" <use x=\"331.35546875\" xlink:href=\"#DejaVuSans-69\"/>\n",
" <use x=\"359.138671875\" xlink:href=\"#DejaVuSans-6e\"/>\n",
" <use x=\"422.517578125\" xlink:href=\"#DejaVuSans-67\"/>\n",
" <use x=\"485.994140625\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use x=\"517.78125\" xlink:href=\"#DejaVuSans-73\"/>\n",
" <use x=\"569.880859375\" xlink:href=\"#DejaVuSans-74\"/>\n",
" <use x=\"609.08984375\" xlink:href=\"#DejaVuSans-65\"/>\n",
" <use x=\"670.61328125\" xlink:href=\"#DejaVuSans-70\"/>\n",
" <use x=\"734.08984375\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use x=\"765.876953125\" xlink:href=\"#DejaVuSans-73\"/>\n",
" <use x=\"817.9765625\" xlink:href=\"#DejaVuSans-69\"/>\n",
" <use x=\"845.759765625\" xlink:href=\"#DejaVuSans-7a\"/>\n",
" <use x=\"898.25\" xlink:href=\"#DejaVuSans-65\"/>\n",
" <use x=\"959.7734375\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use x=\"991.560546875\" xlink:href=\"#DejaVuSans-77\"/>\n",
" <use x=\"1073.34765625\" xlink:href=\"#DejaVuSans-69\"/>\n",
" <use x=\"1101.13085938\" xlink:href=\"#DejaVuSans-74\"/>\n",
" <use x=\"1140.33984375\" xlink:href=\"#DejaVuSans-68\"/>\n",
" <use x=\"1203.71875\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use x=\"1235.50585938\" xlink:href=\"#DejaVuSans-31\"/>\n",
" <use x=\"1299.12890625\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"1362.75195312\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"1426.375\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"1489.99804688\" xlink:href=\"#DejaVuSans-30\"/>\n",
" <use x=\"1553.62109375\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use x=\"1585.40820312\" xlink:href=\"#DejaVuSans-70\"/>\n",
" <use x=\"1648.88476562\" xlink:href=\"#DejaVuSans-72\"/>\n",
" <use x=\"1689.99804688\" xlink:href=\"#DejaVuSans-69\"/>\n",
" <use x=\"1717.78125\" xlink:href=\"#DejaVuSans-63\"/>\n",
" <use x=\"1772.76171875\" xlink:href=\"#DejaVuSans-65\"/>\n",
" <use x=\"1834.28515625\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use x=\"1866.07226562\" xlink:href=\"#DejaVuSans-67\"/>\n",
" <use x=\"1929.54882812\" xlink:href=\"#DejaVuSans-72\"/>\n",
" <use x=\"1970.66210938\" xlink:href=\"#DejaVuSans-69\"/>\n",
" <use x=\"1998.4453125\" xlink:href=\"#DejaVuSans-64\"/>\n",
" <use x=\"2061.921875\" xlink:href=\"#DejaVuSans-20\"/>\n",
" <use x=\"2093.70898438\" xlink:href=\"#DejaVuSans-70\"/>\n",
" <use x=\"2157.18554688\" xlink:href=\"#DejaVuSans-6f\"/>\n",
" <use x=\"2218.3671875\" xlink:href=\"#DejaVuSans-69\"/>\n",
" <use x=\"2246.15039062\" xlink:href=\"#DejaVuSans-6e\"/>\n",
" <use x=\"2309.52929688\" xlink:href=\"#DejaVuSans-74\"/>\n",
" <use x=\"2348.73828125\" xlink:href=\"#DejaVuSans-73\"/>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" </g>\n",
" <defs>\n",
" <clipPath id=\"pb4f25b148f\">\n",
" <rect height=\"345.6\" width=\"446.4\" x=\"53.52\" y=\"23.14175\"/>\n",
" </clipPath>\n",
" </defs>\n",
"</svg>\n"
],
"text": [
"Figure(PyObject <matplotlib.figure.Figure object at 0x921e0d0>)"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 6,
"text": [
"PyObject <matplotlib.text.Text object at 0x9120550>"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It appears the order of convergence with respect to $k$ is $O(k)$, not $O(k^2)$ as the paper said.\n",
"\n",
"I'm short on time and convergence analysis with respect to spatial discretization is more difficult because of varying length solution arrays, so I'm going to leave that out."
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Conclusion and Possible Extensions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Despite not getting the correct numerical result (but getting very close), I found this project to be very educational. I didn't know anything about options or finance before, and now I have a introductory understanding of options pricing. I also didn't realize that PDEs could manifest themselves as optimization problems that are not just least squares (this was a linear complementarity problem). Similarly, I found the concept of a free boundary to be interesting.\n",
"\n",
"From a more practical side, working through all of the algebra of a numerical analysis paper was a valuable undertaking because I now better understand parabolic PDEs and operator splitting. Dealing with the errors in this paper wasn't particularly fun, and I probably could have picked a paper with more correct math and with a better explained implementation.\n",
"\n",
"During the course of this project I found a bug in the programming language I was using (it's called Julia) and I submitted a fix: https://github.com/JuliaLang/julia/commit/f1eea04d1c0b46faa860daefe0ee300a58f79298 .\n",
"\n",
"I decided on the paper for this project relatively late. I knew I wanted to do something with options pricing, but to learn about the problem I had to spend a decent amount of time doing general (not paper specific) reading. My initial project plans involved doing multi-asset options pricing (so multiple spatial dimensions), but I couldn't find a paper to summarize about that that I liked.\n",
"\n",
"The extension to this project that I'd most like to do is allow for pricing multi-asset options using the alternating direction implicit method. This would allow for a fast 2nd order solver for multi-asset option pricing. Another extension to this project (that I actually plan on doing over the next week) is rewriting the code using CUDA (a GPU programming language), which should make the code run much much faster.\n",
"\n",
"I'm still very confused as to (1) why my method doesn't agree with other options pricing methods but is clearly close to correct and (2) why the convergence is first order in $k$ rather than second order, but otherwise I've enjoyed this project."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 7
}
],
"metadata": {}
}
]
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment