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Intermediate Python for Finance Training

This is the Gist for Day 2 of the Intermediate Python for Finance Training in London, 29. November 2017

Agenda

Module 3 — pandas

This module is about data analysis and visualization with pandas for finance.

pandas has become the central data analysis tool in the Python ecosystem. It is powerful, among others, in handling financial time series data, in visualizing such data and implementing algorithms on such data sets.

The goal of this module is to be aware of the capabilities of pandas and to be able to apply pandas to typical financial analytics tasks.

Module 4 — OOP

The final module addresses object-oriented programming (OOP) in Python based on finance examples.

OOP is a powerful programming paradigm with many benefits over simple procedural implementations. Among others, it allows a simplified modeling of real-world and financial object, to avoid redundancies, to simplify code maintenance and re-usability.

The goal of this module is to be aware of basic OOP features in Python and to implement financial algorithms in a re-usable fashion.

Notebooks & Code Files

Below you find the all the notebooks and code files as worked on during this day.

The Python Quants

http://twitter.com/dyjh

[email protected] | http://tpq.io

http://pyalgo.tpq.io | http://certificate.tpq.io

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<img src='http://hilpisch.com/tpq_logo.png' width=\"300px\" align=\"right\">"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Intermediate Python &mdash; Day 2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**NumPy Applied to Finance**"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"rn = np.random.standard_normal((100, 3))"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-1.11, -0.34, 1.66],\n",
" [-0.56, 0.9 , 1.5 ],\n",
" [ 1.06, -0.37, 1.05],\n",
" [ 0.72, 0.32, -0.83],\n",
" [ 1.69, 0.43, -1.27],\n",
" [-1.16, 0.83, 0.25],\n",
" [ 0.36, 1.42, -0.59],\n",
" [-2. , -0.09, -0.41],\n",
" [-1.54, -1.22, -1.72],\n",
" [ 1.04, 0.39, -0.06]])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rn[:10].round(2)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-1.11, -0.34, 1.66],\n",
" [-1.67, 0.57, 3.15],\n",
" [-0.62, 0.19, 4.2 ],\n",
" [ 0.11, 0.51, 3.37],\n",
" [ 1.8 , 0.94, 2.11],\n",
" [ 0.64, 1.77, 2.35],\n",
" [ 1. , 3.18, 1.76],\n",
" [-1. , 3.1 , 1.36],\n",
" [-2.53, 1.88, -0.36],\n",
" [-1.49, 2.27, -0.43]])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rn[:10].cumsum(axis=0).round(2)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"from pylab import plt\n",
"plt.style.use('seaborn')\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"rn[0] = 0.0"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
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ynHbyLSui0WqdhRlG/r+Qa1Z58o8Pyiiu7eaROy7O5b3nZB17TjdQ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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x108edd940>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(rn.cumsum(axis=0));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Valuation of European Option by MCS"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"S0 = 36.\n",
"r = 0.06\n",
"T = 1.0\n",
"sigma = 0.2"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"z = np.random.standard_normal(10000)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 408 µs, sys: 168 µs, total: 576 µs\n",
"Wall time: 488 µs\n"
]
}
],
"source": [
"%time ST = S0 * np.exp((r - sigma ** 2 / 2) * T + sigma * T ** 0.5 * z)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"38.123304399624459"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ST.mean()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"import math"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"38.22611567563295"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"S0 * math.exp(r * T)"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 108 ms, sys: 3.88 ms, total: 112 ms\n",
"Wall time: 111 ms\n"
]
}
],
"source": [
"%%time\n",
"for _ in range(100000):\n",
" _r_ = np.exp(0.05)\n",
" # _r_ = math.exp(0.05)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD3CAYAAAAT+Z8iAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nvSQVzqKXpMJZ9JJUuP8DkJaKJ/becTIAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1115c2d30>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(ST, bins=35)\n",
"plt.axvline(ST.mean(), color='r');"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"K = 40."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"h = np.maximum(K - ST, 0)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.28804124, 0.13481958, 2.46022957, 2.10892485, 0. ,\n",
" 5.7209812 , 0. , 3.34141639, 0. , 9.0315011 ])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"h[:10]"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.9129081652985822"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"P0 = math.exp(-r * T) * h.mean()\n",
"P0"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"M = 50\n",
"I = 100000"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"zt = np.random.standard_normal((M + 1, I)) "
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.00021979864848227772"
]
},
"execution_count": 63,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"zt.mean()"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0002653985608809"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"zt.std()"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [],
"source": [
"zt -= zt.mean() # correcting the first moment"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [],
"source": [
"zt /= zt.std() # correcting the second moment"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.7948014273230606e-18"
]
},
"execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"zt.mean()"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.99999999999999867"
]
},
"execution_count": 69,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"zt.std()"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [],
"source": [
"S = np.zeros_like(zt)"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {},
"outputs": [],
"source": [
"S[0] = S0"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [],
"source": [
"dt = T / M"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 84.9 ms, sys: 1.95 ms, total: 86.9 ms\n",
"Wall time: 86 ms\n"
]
}
],
"source": [
"%%time\n",
"for t in range(1, M + 1):\n",
" S[t] = S[t - 1] * np.exp((r - sigma ** 2 / 2) * dt +\n",
" sigma * dt ** 0.5 * zt[t])"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"38.237366454998757"
]
},
"execution_count": 74,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"S[-1].mean()"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [],
"source": [
"h = np.maximum(K - S[-1], 0)"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.8501412345189339"
]
},
"execution_count": 76,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"P0 = math.exp(-r * T) * h.mean()\n",
"P0"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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oXOjmCMK8sWUZefqVtRiMGk5+1kH10Y5rqkYvVd7JYTrTlm3zds4OX5DBYISV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\npP8JcUJwxAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1116bb198>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10, 6))\n",
"plt.plot(S[:, :10])\n",
"plt.plot(S.mean(axis=1), 'r--', lw=3);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Excursion: OLS Regression"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [],
"source": [
"x = np.linspace(0, 10, 15)"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {},
"outputs": [],
"source": [
"y = 0.5 * x ** 2 - 1.5 * x + 2 + np.random.standard_normal(len(x)) * 1.5"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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zvJIkSb0MFN6Z+RzwG0OuRZLUp4GuNpEkTdaOnmEpSVqf4S1JBTK8JalAhrckFcjwlqQC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\nS1KB/h883itf4JABPwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x12f2619e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x, y, 'r.');"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 11.73833679])"
]
},
"execution_count": 81,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"reg_0 = np.polyfit(x, y, deg=0)\n",
"reg_0"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 3.34120874, -4.96770689])"
]
},
"execution_count": 82,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"reg_1 = np.polyfit(x, y, deg=1)\n",
"reg_1"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.49101668, -1.5689581 , 2.63136083])"
]
},
"execution_count": 83,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"reg_2 = np.polyfit(x, y, deg=2)\n",
"reg_2"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ -4.96770689, -2.58112922, -0.19455155, 2.19202612,\n",
" 4.57860379, 6.96518146, 9.35175913, 11.73833679,\n",
" 14.12491446, 16.51149213, 18.8980698 , 21.28464747,\n",
" 23.67122514, 26.05780281, 28.44438048])"
]
},
"execution_count": 84,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.polyval(reg_1, x)"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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wuwsxGlOw28eQnX0nJlN6WPdVWmpgyJBEPvvMzEkn6fPbsipg0yDNW4hGogds\n/kVR0RQ8nvWhgM1w7PZ7GhSwqcv69fr89m+/GbnsMh9z57qx2cK+GxEl0ryFaARVVZ+HAjZfogds\n/sZJJ03H5cqOyP7eftvM6NGJ1NQYGDPGw913eyXq3sRI8xYigmpq1uJ0TsLl+hCA1NQ/hwI2XUhK\nSsXlqgzr/gIBmD7dypw5CdhsGi++WM0ll8j8dlMkzVuICPB4NuN0TmXPnjcASE7uGwrY/DFi+6yo\ngOHDk/joIzMdOgR58cUaOneW25U1VdK8hQgjn29nKGDzIvsDNhNJSTkvLAGbuqiqkZtvTqKw0Mj5\n5/t59tka0sN77lPEGGneQoSB319GSckTlJU9i6a5sVpPDAVsrgxbwKYuK1eauf32RKqqDIwa5eGB\nB7yYTBHdpYgB0ryFaAA9YPNMKGBTgdncEofjfjIybsBgiOx/r2AQHnvMyowZCSQna8yfX8OVV8rC\nUs2FNG8h6iEY9FJevpiSkkfx+52YTFnk5k4jK+u2sAZs6uJywciRiaxcaaFNmyCLF9fQrZvMbzcn\n0ryFOA6aFqCiYhlO53R8vl9DAZv7QgGbtEapobDQwM03J6GqJvr29fPcc26ysxsQvHG5MKsb8Ctd\nkAvB44c0byGOwf6AzSQ8np8xGKxkZY0IBWzsjVbHxx+bGDYsiYoKA0OHesnP92BuyP9il4vMi/th\n3lSAv1Nnyj9YLQ08TkjzFuIoqqrWUFSUT03NV4CRjIzrsdsfwGpt22g1+P0we7aVRx+1YrHA7Nk1\nXHddw+e3zeoGzJsK9M83FehH4Ked3uDtisiT5i1EHWpqfgwFbP4NQGrqFaGAzUmNWseWLQZGjkzi\nm29MtGgRZNGiGk49NTzz236lC/5OnfcdefuVLmHZrog8ad5CHMTj+SUUsHkTgJSUs3E4JpKc3LhH\npJoGL71kYfz4BKqrDVx1lY9HHnGTUb+bwx+ezUb5B6tlzjsOSfMWIsTn21ErYBMgMfHUUMDm3IgG\nbA7H6TRw992JrFplJj1d49lna+jfP0KXAdpsMlUSh6R5i2ZPD9g8TlnZvFDAphO5uRNITf1Lozdt\n0EM3//hHAiUlRvr29TN7tpuWLWUZV3Egg6ZF/puiuLiy3jvZlb8N1/u7CQabzzev0WhoVuOF6IxZ\nS6gmeNEygpe9AikuKHVgemswhs8uwRCM/HHNwWOuDhqZvbs971XlYiXI8IytDLDtxLj350cwqN9Z\nwWIhXpcIbI7f23nX5pI2pn5L/trtqXUePciRt2h2NJOP4LnvELxyMaSXQ2U6xlfuxPjRVRh8CVGp\naa0nlSmlndgZSKSzxcX47E1Hy568AAAWMklEQVS0t9Tsf0EwiLFol37ZidlMMDcvbhu4CI+YP/IG\nsNtTKS4O79KZsay5jRcaZ8x6wOb1UMBmK0ajjezsO8jOvqPRAja12e2pbN9eyYwZVubMsQIwapSX\ne+7xYrUe+Frzt1+Teen5+74uX/lRXM5Ty/f2cb9XjrxF86VpGpWVK3E6J9cK2NweCtjkRK2un36C\n665LZv16E23bBpk7180ZZxx+7W25pE8cTJq3aNKqqj4LBWz+hx6wuRG7/X6s1jZRqykYhPnzLUyd\nCh6PiRtv9DJ5sufIV+nJJX3iINK8RZNUU/NDKGDzEQCpqX/B4RjX6AGbg23fbmDUqEQ+/dSM3Q4z\nZ9Zw6aXHeAmgXNInapHmLZoUj2cTTue0WgGbfjgcE0hO7hXlyuCNN8zcd18ie/YYuOgiPy++aMZo\nlCVcRf0cU/NWFOUM4BFVVfspinIisBjQgPXASFVVZS1KEVU+3/ZQwGYJ+wM2+dhs50a7NMrL4f77\nE3nrLQvJyRqzZrm54QYfDkcqxcXRrk7Eq6Nea6QoyhhgAZAYemgWME5V1b6AAbgycuUJcWR+fym7\ndo1j06aelJcvxmrtSOvWL9Ghw+qYaNyrV5vo1y+Ft96y0KtXgI8/ruLGG31EIfsjmphjOfLeDPQH\nloS+Pg34T+jzlcBFwFvhL02IugUCLsrKnqakZDbB4B4sllbY7Q+QkfG3iN/B5ljU1MDUqQnMn2/F\nbNZ44AEPd97pbdjyrULUctRvJVVV31AUpV2thwyqqu69brsSOOptTjMzkzGbG3ZTPbs9tUHvjzfN\nbbxwbGMOBj3s2PEcW7dOxedzYrHk0L7947RoMRyTKfGo728Mn62qZshQAxu3WjnpJHjpJQOnnZYA\nHBoAkn/n5iESY67PcUDt+e1UYPfR3lBeXl2P3ezX3C7sb27jhaOPWQ/YvBYK2PyG0WjDbn+A7OyR\nmExplJX5AF/jFXwYO3YYmDzexJsrkgG4I+NF7n3zQpJybIed25Z/5+ahgSGdOp+rT772e0VR+oU+\nvxT4tB7bEOKYaJrGnj3vsXlzb7ZvH47fv4vs7JF06rQWh+OBqCQjD+Z2wxNPWOndO4U3VyTRi6/5\ngjOZs/tmUrduiHZ5oomqz5H3P4D5iqJYgQ3A8vCWJISuquq/oYDNN+wP2DyA1do62qUB+nrb//qX\nmQkTEti61UhOTpDpEyoYseDvWH9RJQkpIuqYmreqqr8CZ4Y+LwDOiWBNopmrqfmeoqJJVFV9DEBa\n2pU4HONISFCiXNl+BQVGxo1LYPVqM2azxrBhXu65x0N6uomKgZ9IElJEnJz7FjFDD9hMYc+etwFI\nSTmX3NwJJCWdFuXK9tuzB2bMSGDhQgt+v4F+/fxMneqhc+dap4IkCSkagTRvEXU+3zY2bnyMXbsW\nAwGSkv6Aw5GPzdYvypXtFwzC0qVmpk7Vb5LQtm2QyZPdXHKJX67ZFlEhzVtEjd9fSknJY5SVzUfT\nPCQkKDgcE0hN/XNU7mBTl6+/NvLgg4n88IOJ5GSNsWM9DB/uJTE2rkwUzZQ0b9HoAoFKSkuforR0\nDsFgJRZLazp0mIzJ9FcMhoblAcKpqMjAlCkJvP66BYD+/X1MmOChRYvmdScYEZukeYtGEwx6KC9f\nSHHxTAKBEkymHPLyHiQzczC5uTnRuf7X5Trk5KLHA889Z2XWLCtVVQa6dw8wbZqHM888/FrbQkSD\nNG8RcZoWYPfupRQXT8fn+x2jMRW7fWwoYBPFtJ3LRebF/fbd4KD8g9X8+8t0xo1LpLDQSFZWkEmT\nPNxwgw9T7PxCIAQgzVtEkH4Hm/dCd7BRMRgSyM6+k5ycuzGbs6NdHmZ1A+ZNBQAUbtK441oLH36d\njMmkMWSIl3vv9ZCREeUihaiDNG8RES7Xf3A686mp+RY9YHMzDsd9WCytol3aPn6lC+UdT+Xhzdfy\nOHfh+9pK3776pX9dusgqxyK2SfMWYVVT810oYPMJAGlpV4UCNp2iXNmBXC5YvDiTZyq+phgTrVv6\nmTSlhssvl0v/RHyQ5i3CwuMpCAVs3gEgJeU8cnMnkpR0apQrO1BpqYH58y0sXGilosKAzaYxZoyH\nkSO9JCVFuzohjp00b9EgXu/vFBc/zO7dLwNBkpJ6kZubT0rK2dEu7QDbtxt45hkrL71kobraQHZ2\nkAce8HLrrV7Sj7qosRCxR5q3qBe/v6RWwMZLQsJJOBwTSU29LKYCNr/8YmDOnASWLzfj8xlo2TLI\nuHEerr/eR3JytKsTov6keYvjogds5oYCNi4slrY4HA+Qnn5tTAVs1q418uSTVt57z4ymGejUKcCd\nd3rp39+P1Rrt6oRoOGne4pgEg+5aAZvSUMBmApmZgzAaD71DTDRoGnzxhYknnrCyerX+rd2zZ4BR\no7xcdpkfY31WrxciRknzFkekaX52736V4uKH8Pm2YTSm4XCMIyvrdkym2FjuNBiEDz808eSTCXzz\njX70f9ZZfkaN8nLOOQG5ekQ0SdK8xWHpAZt3KSqagtdbgMGQSHb2KHJy7oqJgA2A3w/vvGNm9mwr\nGzboTfuSS3yMGuWlVy+5Tls0bdK8xSFcrk9wOidRU/MdYCIz8xbs9vuwWFpGuzRAv+3Y0qUWnnrK\nytatRkwmjQEDfNx5p1fCNaLZkOYt9qmp+TYUsFkNQFpafxyOB2MmYKMHayw8+6wVp9NIQoLGoEFe\nbr/dS9u2stKfaF6keQs8HpWioilUVr4LgM12Pg7HRJKSeh7/xg6zSl9DqaqR114zs2TJ/mDNnXd6\nGDrUR26uNG3RPEnzbsb0gM1D7N79CnrA5vRQwKZv/TZ4mFX66tvAi4oMvPWWmWXLLKxbp89nZ2cH\nGTvWy6BBEqwRQpp3M+T3F1NcPJPy8oWhgM3JoTvYXNqggE3tVfrMmwr0I/DjuJdjVZV+N/Zlyyys\nXm0iGDRgNmtcfLGfa67xceGFfomwCxEizbsZCQT2UFo6h9LSp2oFbMaSnj4wLAEbv9IFf6fO+468\n/UqXY6gJPvvMxIoV8MYbNqqq9B8ep50WYMAAH1de6ScnR6ZGhDiYNO9mIBh0U1a2gJKSmQQCZZhM\ndvLyJpKZeUt4AzY2G+UfrD6mOe+ffjKyfLmFN94ws2uXnp5p00Zj2DAv11zjo2PHgxp2BObShYhn\n0rybMD1g8wrFxQ/XCtiMJytrROQCNjZbnVMlu3YZeOMNfVrk55/1I/30dI2//93L0KFWOneuOnyg\nJoxz6UI0FdK8myBN09iz5x2czil4vZtCAZvR5OT8X6MHbFwueP99vWF/+qkJTTNgsWhceqmPa67x\nc+GFfhISwG63Ulx8+G00dC5diKZImncTomkaVVWfUFQ0Cbf7e/SAzaBQwKZFo9Xh98N//2ti2TIL\nK1eaqa7WD6d79QpwzTU+rrzSR1bWcWyvHnPpQjR10rzDKYrzstXV3+B0TqKq6j8ApKVdHQrYnNgo\n+9+508CaNSY+/9zEqlVmnE59HrtduyADBngZMMBHhw71PPF4HHPpQjQX0rzDJUrzsm73RpzOKVRW\nrgDAZrsgFLDpEdH97tq1v1mvWWOmsHD/kn2ZmRq33KKfeOzVKxiehaGOMJcuRHMkzTtMGnte1uv9\nLRSweRU9YPPHUMDmrIjsr6jIwOefm/jsMxOff25m8+b9zTo1VeOii/z07u3nrLMCdO0axBQ7S3sL\n0STFdPOuqoI5c6y0bw/t2xvp2jVISkq0qzq8iM7L1pqO8SfWUFw8g/Ly5/cFbHJzJ2KzXRLWO9gU\nFRn44gsTa9boH7/8sr8b22waF1zgp08fP336BOjeXZq1EI0tppu3qhqZNWvvdcgpGAwaHTsGOeWU\nIN26BTjllCDduwfIzIxqmbpIzcuGpmPYXsDW4Vls/4uboFaNxdIuFLC5JiwBm+JiQ2gKRJ8KKSjY\nv82UFI3zz/fTu3eAPn38nHJKEHNMf+cI0fTF9H/BP/whyBdfuNi0ycaaNV7WrTOybp2JN9808eab\nln2va9VKb+Ldu+t/nnJKkLw8re651kidWIzAvKxR/ZGdPQvYOgP86WWYg5k4TpgcCtjU735eNTWw\ndasRVTXy+ed6s1bV/c06OVnj3HP1o+q9zdpiOcIGhRCNLqabN0DHjhpnngmXXOIB9LumbN1qYP16\nE2vX6s187VojK1daWLly//tycoL7mvneP9u10zBWx0fgQw/YvIwzZTr+28HkgrZv5pA8+kuMaY6j\nvt/lgi1bjPz6q5EtW4xs2WII/Wlk584D7weWnKzRr5/erHv39tOzpzRrIWJdzDfvgxmN0L69Rvv2\nfq64Qn9M0/Q52nXrjKxda9p3hP7JJ2Y++WT/EG02je7tAvxx0wi6sZ7cTUUkvL2djD4nkZOjYbMR\n9VtmaVoQp3MZv/zy4P6ATdrt5LkvhLvOOOAHze7d1GrOBzbp4uJDb9hoMGi0bKnRt6+fdu2CdOgQ\n5PTTA/TsGZSb8goRZwyaFvlFf4qLKxu0E7s9leLiyuN+X3k5Bxyhr1tn5JdfjGja4Tu01aqRnX3g\nR07O4R4Lkp2tkZ5OWG5qGwiA262xe/enbNv2JC5XAV5vComJA0hOvhW/38727fuPnLdu1Zt0Wdmh\nOzeZNFq31mjfPrjvo127IO3ba7RpEyQxsdaLY2i9kPr+G8czGXPz0JAx2+2pdR5Oxt2R9/HIzIS+\nfQP07RsAfIB+BcvP33ooXFOM09qS0spESksNB3wUFhpZv/7oh+Amk0ZW1oENPiEBPJ69Hwa8XnC7\n9T/3PubxEPpa/9zv37uvy0MfR2axaLRtG+S00/yHNOnWrbVjm/KQ9UKEiGtNunkfTkoKnH52Aqef\n3Sr0iOewr6upgbIyvZmXlBgOafD6Y0ZKSw3s2GFkw4a6m73Fojf1hAT9z8REyMjQMJtrMBq3YjLt\nwmp1k5SUTlpaZzIz7aHLAPX3WK1wwgla6Ag6SMuWWoMvzZP1QoSIb7HfvF0uKPwZHG0a9cgwKQla\nttTniI+Fz6c3e4+HUIPWm25CwqFTK17vVpzO6VRULAU0kpPPxOHIJyXlFADsdiguPvwPlXCR9UKE\niG+x3bz3XuO8qYDMGP/V3mLhqPdT9PudtQI2PhISupKbOyHsAZtjIuuFCBHXYrp5N5Vf7QOBCkpK\nZlNW9jTBYFUoYPNgKGAThjOe9SXrhQgRt+rVvBVFMQJPAz3QJ41vU1X1l3AWBvH/q30wWENZ2XxK\nSh4jECjHbM4lN3cyGRk31ztgI4QQUP8j778Ciaqq/klRlDOBx4Arw1dWSOhXe7vzN8obec67ITTN\nT3n5SxQXP4zfvwOjMR2HYyLZ2cMxGmN0cRYhRFypb/M+C/gXgKqqXyqK0it8JR3EZoP2Z0AcXBuq\naUH27Hk7dAebzRgMSeTk3EV29mjM5uO4+4AQQhxFfZt3GlBR6+uAoihmVVX9h3txZmYyZnPDrm2z\n21Mb9P5I0jSN8vJVFBaOxeX6DoPBTIsWw2nbdjwJCfW7g00sjzdSZMzNg4w5POrbvPcAtasx1tW4\nAcrLq+u5G10sp7Kqq7+iqGgS1dWfAZCePgC7/UESEjqyZw/A8dcdy+ONFBlz8yBjPv731qW+zXsN\ncAXwemjOe109txO33O6fcTonU1n5TwBstovJzZ1AYmL3KFcmhGgO6tu83wIuVBTlc8AADApfSbHN\n6/01FLB5jQMDNr2jXZoQohmpV/NWVTUIDA9zLTFND9g8Snn5olDAplsoYHNx4wdshBDNXkyHdGKB\nHrB5krKyZ2oFbMaRnj4gugEbIUSzJs27DnrA5rlQwGZ3KGAzhYyMmyRgI4SIOmneB9E0X62AzU6M\nxgwcjklkZw/DaEyOdnlCCAFI895HD9i8hdM5tVbA5h/k5IzCZIqFOxwLIcR+zb55a5qGy/VvnM7J\nuN0/AmYyM2/Dbh+DxZIX7fKEEOKwmnXz1gM2+VRXrwEMpKcPxOEYi9XaIdqlCSHEETXL5n1owOaS\nUMCmW5QrE0KIY9OsmrfXuyUUsHkdPWDTm9zcfJKTz4x2aUIIcVyaRfP2+YooKXmU8vLFaJqPxMTu\nOBwTsNkukoCNECIuNenmHQjspqRkNqWlT6Np1Vit7XE4xpOW1l8CNkKIuNYkm3cwWB0K2MwKBWzy\nsNunk5n5dwwGS7TLE0KIBmtSzVsP2CwJBWx2YTJlkJs7maysoRKwEUI0KU2ieesBmzdDAZtCDIZk\ncnLuCQVsMqJdnhBChF1cN289YPNhKGCzFjCTlTWEnJwxWCy50S5PCCEiJm6bd3X1l6GAjb6keHr6\ntaGATftolyaEEBEXd83b7V5PUdFkXK5/AZCaeikOxwQSE7tGuTIhhGg8cdO89YDNNCoqlqEHbPqE\nAjZnRLs0IYRodDHfvH2+XRQU3M+OHc8BfhITT8HhmIjNdoEEbIQQzVZMN2+PZxOFhWcTDFZhtXbA\n4RgnARshhCDGm7fRmEJycl9atLgKs3mABGyEECIkppu3xdKCtm1fx25Ppbi4MtrlCCFEzJD5ByGE\niEPSvIUQIg5J8xZCiDgkzVsIIeKQNG8hhIhD0ryFECIOSfMWQog4JM1bCCHikEHTtGjXIIQQ4jjJ\nkbcQQsQhad5CCBGHpHkLIUQckuYthBBxSJq3EELEIWneQggRh6R5CyFEHIrZmzEoimIEngZ6AB7g\nNlVVf4luVZGlKIoFeB5oByQAU1VVfTeqRTUSRVEcwLfAhaqqbox2PZGmKMoDwF8AK/C0qqoLo1xS\nRIW+t19A/94OAEOa6r+zoihnAI+oqtpPUZQTgcWABqwHRqqqGgzHfmL5yPuvQKKqqn8C7gcei3I9\njeFGoFRV1b7ApcDcKNfTKEL/secBNdGupTEoitIP6A30Ac4BWke1oMZxGWBWVbU3MBmYFuV6IkJR\nlDHAAiAx9NAsYFzo/7QBuDJc+4rl5n0W8C8AVVW/BHpFt5xGsQwYX+trf7QKaWQzgWeBHdEupJFc\nDKwD3gJWAO9Ft5xGUQCYQ79RpwG+KNcTKZuB/rW+Pg34T+jzlcAF4dpRLDfvNKCi1tcBRVFidpon\nHFRVdamqWqkoSiqwHBgX7ZoiTVGUW4BiVVU/iHYtjSgH/WDkGmA48LKiKIbolhRxLvQpk43AfGB2\nVKuJEFVV3+DAH0wGVVX3rkFSCaSHa1+x3Lz3AKm1vjaqqtrkj0QVRWkNfAIsUVX1lWjX0whuBS5U\nFGU10BN4UVGUvOiWFHGlwAeqqnpVVVUBN2CPck2Rdhf6mDujn8d6QVGUxKO8pymoPb+dCuwO14Zj\nuXmvQZ8nQ1GUM9F/zWzSFEXJBVYB96mq+ny062kMqqqerarqOaqq9gN+AG5SVXVXlMuKtM+ASxRF\nMSiK0gJIQW/oTVk5+3+TLgMsgCl65TSa70PnOEA/j/VpuDYcy9MQb6EfkX2OPtE/KMr1NIaxQCYw\nXlGUvXPfl6qq2ixO5DUXqqq+pyjK2cD/0A+gRqqqGohyWZH2OPC8oiifol9hM1ZV1aoo19QY/gHM\nVxTFCmxAnw4NC1kSVggh4lAsT5sIIYSogzRvIYSIQ9K8hRAiDknzFkKIOCTNWwgh4pA0byGEiEPS\nvIUQIg79PzxU+Zi8TYF9AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1119385c0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(x, y, 'r.', label='data')\n",
"plt.plot(x, np.polyval(reg_0, x), 'm', label='0th deg')\n",
"plt.plot(x, np.polyval(reg_1, x), 'y', label='1st deg')\n",
"plt.plot(x, np.polyval(reg_2, x), 'b', label='2nd deg')\n",
"plt.legend(loc=0);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Valuing an American Put Option by MCS"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Least-Squares Monte Carlo Valuation (LSM algorithm)."
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {},
"outputs": [],
"source": [
"h = np.maximum(K - S, 0)"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9988007197120864"
]
},
"execution_count": 87,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = math.exp(-r * dt)\n",
"df"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.4462147850838791"
]
},
"execution_count": 88,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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apCnYhGFO4/kupmtiuXWm6yUGuEzFqqDKKqZjMqIPUzAKtIZb2BLbSjKYJKQE8QHLNecW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\nFG+JRCLZgvx/db74XkFnR28AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x12fe27cc0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"V = h[-1].copy()\n",
"for t in range(M - 1, 0, -1):\n",
" reg = np.polyfit(S[t], df * V, deg=5)\n",
" C = np.polyval(reg, S[t])\n",
" if t == 25:\n",
" plt.plot(S[t], df * V, 'g.', alpha=0.2)\n",
" plt.plot(S[t], h[t], 'b.')\n",
" plt.plot(S[t], C, 'r.')\n",
" V = np.where(h[t] > C, h[t], df * V)\n",
"V0 = df * V.mean()\n",
"V0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<img src='http://hilpisch.com/tpq_logo.png' width=\"300px\" align=\"right\">"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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