yhilpisch · January 12, 2020 13:52
diff --git a/00_cqf_lecture.md b/00_cqf_lecture.md
diff --git a/01_cqf_lecture.ipynb b/01_cqf_lecture.ipynb
 {
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Market-Based Valuation of Equity Options"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A Python-based Journey"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dr Yves J Hilpisch\n",
    "\n",
    "The Python Quants GmbH\n",
    "\n",
    "**CQF Lecture, 06. June 2017, London**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.simplefilter('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## About Me"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src=\"http://hilpisch.com/images/tpq_overview.png\" width=\"60%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src=\"http://hilpisch.com/images/pqp_info.png\" width=\"60%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src=\"http://hilpisch.com/images/python_for_finance.png\" width=300px>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src=\"http://hilpisch.com/images/derivatives_analytics_front.jpg\" width=300px>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src=\"http://hilpisch.com/images/lvvd_cover.png\" width=300px>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "I organize a number of **events** and **training programs**.\n",
    "\n",
    "* For Python Quants Bootcamp (with CQF Institute) &mdash; [http://fpq.io](http://fpq.io)\n",
    "* Open Source in Quant Finance Conference &mdash; [http://osqf.tpq.io](http://osqf.tpq.io)\n",
    "* Python for Quant Finance Meetup Group London &mdash; [http://pqf.tpq.io](http://pqf.tpq.io)\n",
    "* University Certificate in Python for Algorithmic Trading &mdash; [http://training.tpq.io](http://training.tpq.io)\n",
    "\n",
    "More information and further links under [http://tpq.io](http://fpq.io) and [http://hilpisch.com](http://hilpisch.com). Follow me on Twitter [http://twitter.com/dyjh](http://twitter.com/dyjh)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Agenda"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Benchmark Case of Normally Distributed Returns\n",
    "* Market Stylized Facts about Index Prices and Equity Options\n",
    "* Fourier-based Option Pricing\n",
    "* Merton (1976) Jump-Diffusion Model\n",
    "* Monte Carlo Simulation in the Merton (1976) Model\n",
    "* Calibration of the Merton (1976) Model to Market Quotes\n",
    "\n",
    "Go to [http://derivatives-analytics-with-python.com](http://derivatives-analytics-with-python.com) to find links to all the resources and Python codes (eg Quant Platform, Github repository)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Benchmark Case"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let us first set the stage with **standard normally distributed (pseudo-) random numbers** ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "a = np.random.standard_normal(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.026074605659732387"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0100638127574169"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "... and a simulated **geometric Brownian motion** (GBM) path. We make the following assumptions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import pandas as pd\n",
    "# model parameters\n",
    "S0 = 100.0  # initial index level\n",
    "T = 10.0  # time horizon\n",
    "r = 0.05  # risk-less short rate\n",
    "vol = 0.2  # instantaneous volatility\n",
    "\n",
    "# simulation parameters\n",
    "np.random.seed(250000)\n",
    "gbm_dates = pd.DatetimeIndex(start='30-09-2004',\n",
    "                             end='31-08-2015',\n",
    "                             freq='B')\n",
    "M = len(gbm_dates)  # time steps\n",
    "dt = 1 / 252.  # fixed for simplicity\n",
    "df = math.exp(-r * dt)  # discount factor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "This **function** simulates GBM paths given the assumptions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def simulate_gbm():\n",
    "    # stock price paths\n",
    "    rand = np.random.standard_normal((M, I))  # random numbers\n",
    "    S = np.zeros_like(rand)  # stock matrix\n",
    "    S[0] = S0  # initial values\n",
    "    for t in range(1, M):  # stock price paths\n",
    "        S[t] = S[t - 1] * np.exp((r - vol ** 2 / 2) * dt\n",
    "                        + vol * rand[t] * math.sqrt(dt))\n",
    "\n",
    "    gbm = pd.DataFrame(S[:, 0], index=gbm_dates, columns=['index'])\n",
    "    gbm['returns'] = np.log(gbm['index'] / gbm['index'].shift(1))\n",
    "\n",
    "\n",
    "    # Realized Volatility (eg. as defined for variance swaps)\n",
    "    gbm['rea_var'] = 252 * np.cumsum(gbm['returns'] ** 2) / np.arange(len(gbm))\n",
    "    gbm['rea_vol'] = np.sqrt(gbm['rea_var'])\n",
    "    gbm = gbm.dropna()\n",
    "    return gbm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let us simulate a single path and inspect **major statistics**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RETURN SAMPLE STATISTICS\n",
      "---------------------------------------------\n",
      "Mean of Daily  Log Returns -0.000017\n",
      "Std  of Daily  Log Returns  0.012761\n",
      "Mean of Annua. Log Returns -0.004308\n",
      "Std  of Annua. Log Returns  0.202578\n",
      "---------------------------------------------\n",
      "Skew of Sample Log Returns -0.037438\n",
      "Skew Normal Test p-value    0.413718\n",
      "---------------------------------------------\n",
      "Kurt of Sample Log Returns  0.106754\n",
      "Kurt Normal Test p-value    0.239124\n",
      "---------------------------------------------\n",
      "Normal Test p-value         0.358108\n",
      "---------------------------------------------\n",
      "Realized Volatility         0.202578\n",
      "Realized Variance           0.041038\n"
     ]
    }
   ],
   "source": [
    "from gbm_helper import *\n",
    "I = 1  # index level paths\n",
    "gbm = simulate_gbm()\n",
    "print_statistics(gbm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Simulated **prices and resulting log returns** visulized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RvZQnqlvxyJvbUFmn9BD669ta3dB77b5oJWrCrBzHfQvgW6/NkwMc/3hkR9S/1AtPLMer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z9tw6kW75RJfbkaOTVaxTjcZ87LPA4ELR+xQC2P2upq9k6H9c1DWkoS/nBiaMicwtx0v++Xyf25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\nIiIiEjAlcyIiIiIB+x/R3qpOSrd6UwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10db3ef28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "quotes_returns(gbm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "A histogram of the **log returns compared to the normal distribution** (with same mean/std)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UGLNVk+tFwhep78ZxPbzRevzYgrDjSI6pLqlifd0aPN9ji5rsRTIi3fMSXwL+\nDmgAGoF/4Bd9XyISCp/o7KT6/raQs0iu+sXpxi1qshfJgHSb6/dba3805/YPjDH/JYhAIpIet3wE\nd8E4fqwYb6Qx7DiSo9bWGWpKqhk4NsTu4X2srl0VdiSRvJbuitewMWbZ7I2Zj/fNfPxnQQQTkVM7\n3lQ/0Aq+murl7KSa7C8HUqteIhKsdF+tPwzsMcZ0GWO6gN3Ax4wxHcAdgaUTkTc1GZ8kUtcDQLJf\ns7vk3Fy96HIcHF7p385YbDzsOCJ5Ld3C61FgBXDNzL+VwFuAm0htoC0iGbSl50Uc1yM5Woc/raZ6\nOTc1pdWsq19N0k9qkr1IwE7Z42WM+V1ShdV/tdZOneRzfjuIYCLy5nzfP35KSJPqZb5c23Ilrw3s\nZFP3Ft62+C18/O8fT+vr7r7j5oCTieSX0zXXu8DXgFpjzEPAfdbaZ+d+grV2MqhwIvJG+0cPcmSi\nV031Mq/W1hqqS6ronxpkz8i+sOOI5K1TFl7W2ruAu2aGpt4C/I4x5mvAc6RWwh6y1k4EH1NEZh1f\n7RpoS6up/vY7Hws6kuSBiBvh6kWX8+CBR3m6awuwKOxIInkp3cn149baH1prPwasB74KXAY8aYz5\nZID5RGSOyfgkL/a9AkBSs7tknl3bcgUODi/3b4PodNhxRPJSupPr/9fsx9Za31q72Vr759bay4Cv\nBxVORF5vS8+LxL0Ea2rPU1O9zLu5TfbR+q6w44jkpXSvany3MebbxpjfMsaUzr3DWhsPIJeInMD3\nfZ6eOc14bcuVIaeRfHVdy1UARBoPA364YUTyULqF10ettb8BdAL/Yoz5e2PMigBzicgJ9o0eoGei\nl4rici6oXxt2HMlTs5Ps3dJJ3MrBsOOI5J10C6/Zbev3AyPAJ4AvGmO+YYy5NJBkIvI6s031Vy+6\nnIgbCTmN5CvXcbl2Zv/GaGNnyGlE8k+6hdfdxpj7gaeASeAia+2twCeBPw0qnIikTMQnebHvVUCn\nGSV4V7dcju87uNV9UKQme5H5lO4m2a3AZ4H3ndDT1Qqsnu9QIvJ6W3peIDHTVF9fVht2HMlz1SVV\neMMNRGr7iNYfJnFEnSUi8yXdwus35w5ONcZErLVJa20HcEEw0UQEZprqu9RUL5mV6G8nUttHpOEw\niSPLASfsSCJ5Id1TjR83xvxszu3/NMa8N4hAIvJ6e0b20zvZR1VxhZrqJWO80Xq86TLc0incqoGw\n44jkjXTHlRh9AAAgAElEQVQLryJr7bvn3P4woMJLJAOe6toMwDUtV6qpXjLIIdmXGtIbbTgcchaR\n/JFu4dU394a11gdG5z+OiMx1NDbGy/3bcHCOX2kmkimJgTZ8z8Gt6YOiY2HHEckL6fZ4NRljfg/Y\nNHP7WqA+mEgiMuuZ7ufwfI8L6s+nprQ67DiSB85o7854Cd5II5HaXqINh0l0rwwumEiBSHfF6w+B\nK4GHgYeAy2eOiUhAPN87PrvrutarQk4jhSrRtxiYnenlhRtGJA+kteJlrR0EfmPusZnJ9RprLBKQ\nHYOWoWPD1JfWsqZ2VdhxpEB5R2vxphbilk3g1vTjDTeFHUkkp6VVeBljIsDNQBO/WCX7DeAdAeUS\nKXhPdaUmuFzXehWuk+7itMh8c0j0tVO8ZBfRxkPEVHiJnJN0e7x+BlQC+4DkzLHWQBKJCINTw2wf\n3EXUiXDVosvCjiMFLjnQit+2m0jVIE7JBP70wrAjieSsdAuvCmvttXMPGGNuDiCPiADPdG/Bx+ei\nxvVUFJeHHUcKXbKI5NAiog1dRBo7SXRqwxKRs5Vu4bXBGLPCWrtvzrHzgJNeHmOMaQY+B1xorb18\n5thngRvnfNrfWGsfOaPEInku4SXYdGQrANe3Xh1yGpGURN9iog1dRBu6SBxeBb5myomcjXQLr48C\ndxhjBoBpUntH1ABfOcXXXAfcC1w096C19sYzjylSOF4d2MFYbJxFC5tYUbU07DgiAPgTVXjjVbjl\no0TqjpAcaAs7kkhOSrfwOszrV6ocUptmn5S19gfGmBtPPG6M+QtSxVsEuMtaO5lmBpGCsPHwM0Cq\nqd5xtD+eZI9EXzvF5aNEGztVeImcpXQLr1tOLJCMMb91Fo/3feCAtXbCGPMp4C7g46f7opqaBUSj\n+b2s3dBQEXYEOUNBPGedo93sGdlPSbSE285/CwuKy+b9MUTOVnJoEf7iXbjlozgLRvEnqwJ77dJr\nYu7Rc5aedAuvcmPMl4Ey4LeA/wPcAQyfyYNZa7fPufkY8MfpfN3wcH4vijU0VNDfPxZ2DDkDQT1n\n99pHAbii6RImRhNMoJ8LySJehORAK9Hmg0QbO4kfqArk90CviblHz9nrnaoITXc40OeBjcC0tXaC\nVG/XP5xpEGPM5+fcXEVqPIWIAFOJY2zpeQGAG9RUL1lqdpJ9pK4bIvGQ04jknnRXvLqstf9ujLkM\nwFr7kjFm5FRfYIx5C/ARYJEx5i+B/w0kjDFfILXp9nrgU2cfXSS/bOl5gelkjOTRWv7yizuAHWFH\nEnkD/9hCkqN1RKoGidR3hR1HJOekW3jVzfzXBzDGLARWnOoLrLVPAk+ecPjPziidSIHwfZ+NhzcD\nkOhdHHIakVNL9C4mUjVItOkQnu9pZwWRM5Dub8ujxphtwNuNMfcD+4HvBhdLpLDY4b30TvZRXVKF\nN9IYdhyRU/JGGvCmS3FLJ9k5tDvsOCI5Ja3Cy1r7feCDwD8DDwA3WGu/F2QwkUJyfIREy5Xga/VA\nsp1LcqbX64nDm0LOIpJb0j3ViLV2F7Br9rYx5v3W2h8HkkqkgAwdG+bVgR1EnAjXtFzJ93ku7Egi\np5XobyPaupcdg5a+yQEaF9SHHUkkJ6RVeBlj7n6Tw1cCKrxEztFTXc/i43Nx43qqSjQHR3JEopjk\nYGr/xo1dz/DBVe8NO5FITkj3nEY7qUb5J4FngEngiYAyiRSMeDLOM92pfRnf0nZNyGlEzkyidwkA\nm7uf51hiOuQ0Irkh3VONt1trO+ceMMbcGUAekYLyYt+rjMcnaC9vYVnlkrDjiJwRf7KS5VVL2T96\ngK09L3JDm+bPiZxOuoWXY4yZvcbdBRYBensuco6e7Eo11d/Qdo32ZZSc9Ja2a9g/eoAnu57heu0v\nKnJa6RZerwGDpDbH9oEjnMXkehH5hY7Rgxw82snC6AIua7oo7DgiZ+XihvX8qLiCnoledg/vw9Su\nDDuSSFZLt/D6H9bafw40iUiBebzzaQCubb2S4khxyGlEzk7EjXBd61Xc3/EITx7epMJL5DTSba4/\n6S7VxpjfmacsIgVj+NgIL/W/huu42pdRct61LVcRcSK8OrCDwanhsOOIZLV0V7z+yhjz4Tc57pDa\n7Por8xdJJP9t7NqM53tc2nghNaXVYccROSdVJRVc3Lie53tfZmPXM7x/5W1hRxLJWumueD0IbALu\nnPn3NPA88FnghUCSieSpWDLGpq4tANzUfl3IaUTmx+zP8qbuLRotIXIK6a54TVlr//uc2w8bY/7V\nWvukMWZvEMFE8tXWnheZSEyytHIxy6o0QkJy2+13Pnb84+I11UxVjPB73/xPkn2v/9m++46bMx1N\nJCulu+K13hhzvPvXGFMCGABrbVcQwUTyke/7PD6zt91NbdeGnEZkfiV6lgIQbT5I6gJ4ETlRuite\nPwIOGmNmN5G7DPibYCKJ5K9dw3vomeilqriSixsvCDuOyLzyhhvxpktxSydxq/vxRhrDjiSSddIq\nvKy1dxljngBunDn0F9ba14IKJZJvZk/HFJ/3ApFqGNjXxCeffjLkVCLzzSXZuwR3sSXafICYCi+R\nN0j3VCPAFLAT+DIwEkwckfzllE4Qqe7H91wS/e1hxxEJRKK/DT8ZIVI5hLPgaNhxRLJOWoWXMeZj\nwEPAn5EaIfFPxpjfCDCXSN6JNh0EIDnQAgkNTJU8lSwi2d8GQLT5QLhZRLJQuite15Oa17XbWhu3\n1n4Q0NRHkXRF4kTqU9ehJHp1JaPkt0TPEnwfIrVHoOhY2HFEskq6hVePtdY74diJt0XkJKKNh3Ai\nSZKjdfhTFWHHEQmUH1uAN9yE4/pEGw+FHUckq6R7VWODMebXgGpjzOXAO4Da4GKJ5I94Mn78NGPi\nyLKQ04hkRqJnKZHaXqKNnSS6V4QdRyRrpFt4/SnwBeBtM/8eBD4dVCiRXDF3eOTJRBo6KV4Ww5uo\nwDtal4FUIuHzxqvxxitxy48Sqe9K63cFNGhV8l+6hddHgK9baz8aZBiR/OMfbzBO9CwjdW2KSCFw\nSPQspXjlq0SbD5Dsb0c//yLp93j9MdAZZBCRfORW9+OWTeBNl5Icag47jkhGJYeaUwNVyyZxa3rD\njiOSFdItvJ4C9s09YIz5zfmPI5Jfoos6gJmtVPwzGZsnkg/cmZVeKFrUgbYREkn/VOMY8NTM9PrZ\nbeffBXwjiFAi+cBZOEKkYhg/ET0+10ik0CT7W/Fb9uKWj+JWDOGNqc9RCtsp34IbY75kjKkk1VD/\nMBAjdZJeJ+pFTqNodrWrbzF46b7HEckzXvT47LrZFWCRQna6vwbT1tqjxhjHWvs/595hjEkGmEsk\npzklE7g1vfieQ6J3cdhxREKV6FtMdFEHkeoBnLIxzbKTgna6wssYY24H9hpjTryi8YaAMonkvGjz\nARwHEgMtEC8NO45IuBLFJPvbiDYfJLpoP/H9F4adSCQ0pyu8/hb4KNAG3HTCfa2BJBLJddFpIg0z\n2wNpYKoIkNpGKNJ0iEhdD4nDq/BjC8KOJBKKUxZe1tqngaeNMR+w1v5o7n3GmA8EmkwkR0WbD+C4\nHsnhRvxj5WHHEckKfmwBycF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cHjn0BF/f/h3iyXjYwSSH6FSjhKvoGCWrXsItH8VPusQ7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\niYkCLxEREZGYKPASERERicn/ARfYLqwzUvA6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114057cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_histogram(gbm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "And a Quantile-Quantile QQ-plot of the log returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114109d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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TZ08HOjbEhzvnngGeiTo2LOLrcuD6GNf9DdijIWoQkdQoLs6iX79sIIP9+JTpjOBiHgbg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\nAkREROpFASIiIvWiABERkXr5fwKwR4HsIcN9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11456c7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_qqplot(gbm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The **realized volatility** over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9b5rJiVMrEm0tK46tR3f54pm8tu0gZ5xYTXN7DwWBHBoOdRKORKmtPnLrreEq\nKczjg28+8XXfZzBvOGUybzhlMpFIlD89vYWHVsRmDYeS9qKdUFnI/hQLIT/18l6eenkvV79rHgvn\n1PDsq/v4+YOvJY7PrC3jg28+karSAooLc2lu62HLnhYqSvOpm1BC3lE8HzkS1mxuJMfvY96MqpTD\n+itdPT/+09o+Zb3LsqQSCkf52QPr+NkD65hWU8Kps8ZTUphHcWEu55w0EZ8P1m5toqsnzGmzxhFb\ngTHqmc+XiEimpdPjNur1PkvW2T30UOmEyqGHHtNRUxnrldrb2MHexg4g1sv27z8//MB9WVFeymuP\nh6k1Jdz4oYUDHi8uyGPhnBrg8LN10yakt7RKtukdan37OXU0t/ew50A7f31+B1/4p9OIEmXb3lYm\nVxfz3Kv7sWkVFOXn8vDzO3h81W6W3P8q3H9kUNm8+/Bwb39F+bmcUFvGKbNrWO32s27bQS6/YCZv\nPnMqm3c34/P5OHHq4M8IHkuRSJTuYJhoFNZta+K02ePpDob52V/W8cqWvlujLbRqTppexcI5NezY\n35oIbTl+H+84bzp1E0t56uU9vLq1icsXz+KC0yfTE4yweuMB8gM5TKku5n8e3cjLmxvZUd/W57nD\n5ODb34SqIvJy/Jw8s4rZtRXMraskkOdPBMmXNjbw8qZGzps/kdlTytWbdwyEwhH+9sJOKkvzsakV\nlBUHaO0IJv6/i8jIUHAjzaHSRI/bsQluPp+P80+elHIortdVl849Jh9L0lOYn0thfi4Tq4o448Tq\nRPmceO/om5O2NfvQJcai+ZO4/X9W0RM8vHft1686i6qyAm67ZxW7GtoSixD3qqkspKmlm7Vbmli7\npSlR/ocnNvOHJzYn3k8aV8Sn3jmvTxhubutm2ardLDixmrqJxyYkb9rVnHKB5IG86Bp40TXwhyc2\nJX7RqZtYyr9fdTY5kVg7T501nkg0mniWrTDf32f27rWXn0ooHKHhUCdLX9hJKBxlZ0Mb2/e1Js7J\nzfEnep4B9jfFfrnZ1dDGw8SW05k8vpii/NxEDzjAUy/voaaykLPnTuCihVMGXScxm/QEw+Tk+PjJ\nn9YSjkQ5e+4ExlcUUFNROOgjE7vq2whFItRNKCUSjXKwpZuG5i52NbQxb3oVk8f3Xdi6rTNIfl4O\noXCEgkAOPp+PSDRKOBwlL9dPOBLh2Vf385u/uT7/rpPNqi3n7JMmcPZJEygpHLlfLgfT2NxFTyjM\nxKqiYYcIOJUuAAAgAElEQVT4zu4Qew60EwxFeGL1bkLhKG7HQebNiH0+C/NzOX32eCpK8l/X4zIi\nR+uogpuZLXbOPX6sK5NRg/zfLSyIB7eeQYZKo709boXMratk/oyqAc9N10ffNofK0nyef21/yuG4\nOo/2YI0VJ0wu4zufXsSWPS34/TB/xuEJC1//+OHJHpFolP1NHUyoKsLv87FjfyuPrdrN5j3N7G5o\n5+IFU+jsDrE8ac26vY0dfOs3K3n3G2Zw8YIptHYEeeCZbTy5eg8PPrMNgHcums4/nDed3Bx/n6AE\nsR/QwKA/WNs6g0OGtk+/ez5nnFhNR3eI7p4w9z25mZc2HSCS9DP9po8spGZcMQ0Nh4PXUBMQcnNi\nu2V8+K2xbeCi0SiNLV1UluYTjR5+frS3XVv3tvD0mr1UleZTf6iTVzY3pnyU4KTplbgdh3jgmW08\n8Mw26iaWcuHptSw6ZVLKOoXCEQ61dRPIzWH9joPsrG8jGIFV6/dTU1lIIDeH17Yf5OQTqjjjxGoW\nWE1iNnk0/j0hGIpwoLmLSeOKaGnv4eHndhAKR1izuZEzTqxm3owqaioK6QlFWLM5NqmnbmIpEyqL\nKCsK8Kent/C3F3b2qdeazYd7OsuKA5xz0gQWn15LdzDM+PICfD4f9yzdkFjn0OeDaIpd5IoLcjnn\n5Els2nmIto4gjfF9lnu/RuPK82ls7iZKNOX1NRWFnH3SBNbvOMjGXc0E8vxs3tPMpt3N/G7ZRmbW\nljO1poTa6mKqywuZNK6ISDRKQSCXfU0dNBzsZPL4Yl7bfpC5dZXH7BeO/sP2exvb2ba3lV0NbTy9\nZm/i339Rfi51E0spKw7w3Lr9FObnUBDIJS/Hz0kzqqgdX8zJM8dRVpTHfz30Gi8Osl3e868d3h7w\nfx7dSCDXz+ypFRxo7mJKdTGRSOxzWFyQi9/vY/4J46iuKOBgazc2tZKiglyi0ShLX9hJc3sP82ZV\nk58T2w5x0+5mXtnSyLiyAgK5sZ7kwvxcbGoFtdXFhCNRcnP8tHUG2dfUwf6mDgJ5OeT4fQTy/Jww\nqazPguQyuvmiqf63klgGZCBvd86dk5kqHXvv+ML90YsWTBnwmakte1r45q9f5K1nTeOfLpzF8lf2\n8ouHXuNbnzw7scTFf/91PU+u3tOn7Fhq7eihuCCPzp4QN/7sWc6ZN5H3XTT7mNy7urq0zw9VLxvN\nbWlq6WLDrkOcNXcCazY3cuf9rybWDExWUpiX+MFUU1nIpefU8eCKbfj9fj5w8WymVJfwhR8vB+Dq\nd83jrLkTEtcGQ2FWb2pkxdp9ibX5Sgrz+P5nF/Hk6j1MqCxi+qRS1m5pYk5dJeXFqXusOrqC3P/3\nbdRNLOG8+ZNG5OuyY38rqzY08KbTasnL9SdCantXkCde2s1z6+rZ3dBGlNhwfk8wzMknjKO2upj2\nrhCVJfk8vWYPuxqG/yzptJqSPsO80Pfr8nq8eeFU8gN+Vm9sJBqNsnuIZ11Li/LIz8uhtSNIdzBM\nZWk+5cUBigvzeHVrU59zC/Nz4r2ZUbp6QuT4/ZQW5ZGX46f+UOyXxxmTSplTV8llbzwh5Q4qh9q6\nefbV/ax4dR87+30OhlJalEdpUYAFJ1YzoaqQHL+flvYeTpxawdSaEvx+Hx1dQYLhKHk5frbva6Go\nII9dDW1s399K1Ofj7y/vobsn1pt2sLWbipLAEb/4xmbuV7Czvo2WjiO/Jjl+X5+1OWNPUvZVVpTH\n1AmlvOnUyQTDEWrHF7PnQDs76tvYVd/G3saOPkF4MH6fj8rSfDq6g4M+kjOYSeOK2NfUkTJg9x4f\nV1ZAfl4OXT0h9jV1kB/IJRgKU1mST01VEeXFAU6dOZ4TJpcd08lTo/n78gjWY8Av0GDB7QXgQWAW\nUAf8PX5oEdDknPvHY1zPjBkquO1tbOfGu57jjadO5qNvm8M1332S7mCYC8+o5cpLDIBf/t9rPL1m\nL9/+1DnH7Dm34yVb/iEeC2OpLXsb2/nvh9f32cpsbl0l/3r5KTzwzHZWb2xIO3S8+/wZnDt/Il/5\n2bN9fmAB3PyxM1/384nZ+nVpauni949t4oX19YOeN2daBdEonHFiNZ2hCOfOrSGQ62ft1iYK83PJ\nz8th5YYG1m5p5EDz0D+sT5k5jtlTyplaU8ormxtp7uihvTNIV0+Y2urYEO+exnZ21reRn5fDmxdO\n5ay5Next7GBmbVmfwLS3sZ21W5pYtaEBt/NQorymspBvffLsQben6+oJ0dAWZNeeZmqri5lSU5Lo\neezoChLIy0n02B5q7aayNH9YQ4sdXSH2H+xgZ30bO+vb2HOgnZwcX+IxgHnTK/H5feTG67insZ2G\nQ50pw0dhfg5+n4/2roFHPpIlz/4uLw4wtaaEuXWVnDZ7PBMqixLBpLWjh027m5lWU8q48oLEEPym\nXc1s29fKq9uaaGzuYubkMt52Th0TxxXhY+jJZ9FolO37W9m2r5WZk8uJRKKUFuXR3hUiGIrw8qYD\nrN50gMbmLiZXF7O7oZ1QOEJ1RSGXnDmV7nCUA00dNLfHenzrJpZSXVHAvsYO2rtC9ITCNLf1sLO+\njd0H2vH7fFSUBpg+sYySwjwKAjm0dwUpDOSy+0A7W/e2DLikVf9gWpSfS0F+DlOrSzht9ngikSiF\nBblMqipm2oSSYQ8vZ+r/fygcoaW9J/bLxXGaoDSS38si0Sh7GtopLszjxBPGH1VwW+yce9zMfuqc\nu6bfsSPKstlQwe1QWzfX/Wh5YuP2r/zsWfY1dbBwTg2fjm8vddcD61jx6j5uv/rcQXcjyEbZ+kP1\naIzFtgy2Fdv2fa386uH1tHb28OG3zOFPT22hsaWLceUFXHhGLY++uGvAXpGz5tbw/otmv65lZ3pl\n+9flte0HWbu1kanVsR9Kz63bz76mDoKhCF++8ozEjhswdFu6e8LsbGhjd0Mbp59YTSDXTyAvhwPN\nXazd0siikyeRP8jWcK9HKBwhN8cfH971pzU8lm1fm46uEOu2NXGwtZuGQ53samhjfHkhG3Yd4sCh\nrvjkhyihcJTm9h5m1ZZTf6iTc06awPjKIoLBEBecVpt4DrJ3HU4viESjiVA43K9LKBwhx+8b8HtB\nNBqlJxihub2b7fvbKCvKY2ZtOT4f9AQj1B/spKm1i5c3NeJ2HqKzO0RLe88R9ykuyOWEyeXYtAoO\ntnZTXJBLeUk+OX4ftdXFTJ9Yit8XC825Ob4j2tLS0cPmXc1UVxZSUZJPQSAn8ehDZ3eIcCT2+MOm\n3c2EIxG27Glhd0M7B5q7qKkspHZ8MRt3HWL9jsO/pOT4fYwrK6CmspApNSVUlxcQJRbYZ0wqI5CX\nQ1FBbp/HIXqCYQJ5OfQEw+Tl+vt83nqCYdo6g4TCEbp6wuzY34bPB8WFeUyfUsH++laC4djnbFxZ\nAVNrSqgszSccieLzEX9UJMr6HYd4YX09pUV5hOO92OFIlIqSfCKRKIG8HHbsb419fzjUSUd3iOkT\nS9nT2EEoFKG8JEB5cezfe3N7D+u2Hd4O/oHvvmvA4Dbgv/ikZ9hS7W80aaDrvKg4/oxba7xLvTDF\n8iBd8effCjz0TUJGh8F++62bWMpNH11IlNhwzCkz+y4MvGj+JFZuaODRF3eycVczPuDrnzib2vHH\nfrg/m82tq2RufJIJwNknTRjk7MHlB3KYVVue2NKtV01FIReeMfC6g8dC7w/AimMQtkdKUUFuYkb6\ncPUPO0e7e81IeT2LTw81EcLn85EfyKEmUERNv1Ghwnw/dRNLqZtYyumzD0+82tfUwaoNDextbKd2\nfAk761vZvLuFV7Y0HjGj/PDHOfw8pd/nIy/XT1V5AUWBHPCRWIi9V16un7KiALm5/sQko1T8Ph+7\nGtoSi7z3mjejio6uEHsa26k/1MnafsP/yR+nqqyArp4Q7Z0hQuFIoqex9/GB/Lwc2rtC7GoY3hB/\nn/Zz5LD6cPSuIgGkfAxifHkB0yeVDXqPdFJIvZndDzwZf/8mYPBxhzgzuxi4LH5+1Dl3S7/jNwAT\ngb3AQuAm59z6+LErgdOBMLC5d8/U+H6pXwU2AdOBLzjnjv6rAOTl5lBWlJd4XqEosTxILKxFotHE\nTgEFAa0nJdnF5xt4XxC/38eZc2o4c04N3cEw4XCUogL98iEiMLGqiLefU3dE+cHWbjbsPMTuA21M\nGleMzwftnbHAs/dAO3saO/D7fZQXB4hEo7S0B9nbL4S86bTJNLV009zWTXtXkM7uEEX5ueQHchKh\nqra6hJOmV3LarPFMHl9M/cHO2B7VPjhxSsURQ/ftXUF2N7TT1NJFR3eI1o4guxva6AlFaGrp5lBb\nd+I501lTyjnU2s2B5i7aOoM0t/UkFtKH2KMGMyeXkZebQ08ozMzJ5XT1hOiJQCgYgihMqS7hQHMn\nO+vb2NvUgY/Y99SCQC5+X6yTZ2pNCbOnVOD3kZhU0ntNIC+HksI8TphURntXkEnjimnvCrJpdzOT\nxxUztaaE5vYeWjuC5Of5GVdeQEFg6O/P6XwH/zTwKWBx/P3fgJ8NdZGZFQFLgHnOuW4zu8/MLnLO\nLUs6rQS4zjkXNbMrgDuAd5jZFOCLwOnxYy+Y2WPOuY3xe97knHvezD4L3EAsyA1qqN9zykvy4wvI\nRng13l3ZG9zCScsSaPq3eFV+Xg5o4pmIDKGyND/eK51ez3R1dSn797fQ2RMiL8dPbq7/qHoXJ1QV\nDbrkVnFB3qBrXEajURqbuyjIz+0zoz4ajRIlNqrW0RWkoiR/wCH2Y/FoQd3EUhZY6l7l5H29Aaor\nCqke5uNX6eycEAR+ZGb3OOcODnV+knOB7c657vj75cClQCK4OeeSA5cf6O05ewuw0jnXG49XAG8z\ns23EAuQLSff8OWkEt6GUFOaxs76NbXsPf8E6eoNbin1KRUREJMbv91E8wkuS+Hy+lM+g945KlBcH\nBpwp7yVDBjczOwu4F9hvZhcAfwU+75xbNcSlNUBybG2Jl6X6GAHgI8Bnhrh2PNCZFOgGvGd/hUUB\nqqsHnjk3rqIQth8kUHj4i9rc1kNpeSGF8QVUz543cdB7ZDOv1jsVtSU7qS3ZazS1R23JTmrL8ZPO\nUOm1wEXAF51znWb2VuBHwMeHuK4eSG59GSmejYuHtp8CNzrnNiddO6vftZuAA0Chmfni4S3lPVPp\n7OgZtPszLz51/Gs/67u5+nfvfpH3XRhbTy0cCmfV7Kx0ZdusstdDbclOakv2Gk3tUVuyk9qSmXoM\nJJ0HtrYlBSqcc53AoUHO77UCqDOz3ulPi4CHzKzKzMog8RzcncD3nHMrzew98XMfARaYWe8g+bnA\nw/Fh28eBM5PvmUZdhjTQCvOvbG5MDJXm6Pk2ERERGUHp9LjVmlkt8RmwZnY+MHOoi5xzHWZ2DfBD\nM2sA1jjnlpnZ7UATcBtwNzAfmGFmAMXAfc65XWb2HeD7ZhYGfh6fmABwNXCTmV0CTAOuG0Z7BxSK\npN6Xr70rlJickHMMV5oWERERGa50gtv3gSeIBbiPAPuILfExJOfcUmBpv7Lrk14PeB/n3N3Egl3/\n8m3AVel8/D6GyFz91yEuzM+lsztEeXGAJ1bvARTcREREZGQNOfbnnHsZmEtsePIswOJlo8qkcX2n\nIP/+W2+nrDhAbo6f/3t2O5B6E2cRERGR42XI4GZmvwPGO+dedc69CnzMzJ7OfNWOr/NPPrwZxPsu\nnBXbxqO8oM8mwgfbulNdKiIiInJcpPO0/QJgpZn9I4Bz7i5gdUZrNQKSV2cuKYpNVKhM2r8QUJeb\niIiIjKh0nnH7K/BL4Ldmdimx5UFGdYLpnadQVdp3P8ALF2R2H0IRERGRwaTT4xaNL7a7gFhgW01s\nJqinDLyb45G6g2EAqpJ63P5p8aw+m/OKiIiIHG/pBLczzOxDzrl259wngS8Bp2S4XiOqqye21dXk\npAkL+Xlaw01ERERGVjp7lZ7f7/19ZrYhc1UaOcUFubR3hejdmjR5M9uCQDqjyiIiIiKZM2AaMbOT\ngNeAD6U4fCVwSaYqNVK++L7TeXDFNi48oxaAQF5O4tiEqqIBrhIRERE5PgbrRroT+ACxodHn+h2r\nzViNRlDdxFI+848npzzWf503ERERkeNtwODmnHsDgJn9u3Puj8nHzCytnRNGg2vePZ/G5i4K8zVU\nKiIiIiMrnWfc/piiuDIDdcko31HuVnXmnJpjWxERERGRozTYM26PDXDIB8wCfpGRGomIiIhISoP1\nuLUC30tR7gM+l5nqiIiIiMhABgtu/+Kc25nqgJltylB9RERERGQAg01OSIQ2M5sIzAR618e4FnhP\nZqsmIiIiIsmGnJxgZp8CPk1sQsJmQBt2ioiIiIyAdPZxWuCcOxW4zzm3GDDgL5mtloiIiIj0l05w\na4z/XQjgnIsAVRmrkYiIiIiklM6qsvPN7E3APjP7M9AEzM5stURERESkv3SC28eBCLACuA4YB7w/\nk5USERERkSOls3NCvZmVEetlux0IOOe6Ml4zEREREeljyGfczOxtwAZgCRAAHjazSzJdMRERERHp\nK53JCe8ntsXV2nhP20XAezNaqww42r1KRURERLJFOsFtp3OurfdNfFZpe+aqJCIiIiKppDM5YbKZ\nnQfkmFk1cAkwNbPVEhEREZH+0gluXwPuBs4nNsN0OfDhTFZKRERERI6UTnA7Dfgsse2uSB42FRER\nEZHjJ53g9gvgHV4PbD40O0FERES8LZ3JCU86555NLjCzf8hQfURERERkAOn0uG0xs98DjwLd8bIr\ngQczVisREREROUI6we2DwN+A85LKajNTHREREREZSDrB7RvOuSXJBWZ2aYbqIyIiIiIDGPIZt/6h\nLV72UGaqIyIiIiIDSWdywuigSaUiIiLicWMnuImIiIh4nIKbiIiIiEekMznhqJnZxcBlQD0Qdc7d\nkuKcK4BbgWudcw/Gyy4Afgw0xE+rAe51zt1sZkuAOUm3+Kxz7pXMtUJEREQkO2QsuJlZEbAEmOec\n6zaz+8zsIufcsqRzZhALdTv7Xb4HuNI591L8vJ8Dv4wf2+ecuzpT9RYRERHJVpnscTsX2O6c6120\ndzlwKZAIbs65rcBWM/ta8oXOuQ29r81sAlDgnNseLyo1sxuBENAOLHHOhTLXDBEREZHskMngVgO0\nJr1viZcN1zXEeu563QOscc6FzOx24MvAN4a6SXFRgOrq0mF94OGen83UluyktmSn0dQWGF3tUVuy\nk9py/GQyuNUDya0vi5elzczygYXOuZt7y5xzq5JOeQy4gTSCW0dHDw0NrUOdllBdXTqs87OZ2pKd\n1JbsNJraAqOrPWpLdlJbMlOPgWRyVukKoC4evgAWAQ+ZWZWZlaV5j/cDv0suMLM7kt7OBja/7pqK\niIiIeEDGetyccx1mdg3wQzNrIDa8uSw+vNkE3GZmPuBGoA64wsyCzrlHkm5zOfDufrceb2a3AR2A\nAddlqg0iIiIi2SSjy4E455YCS/uVXZ/0Ogp8M/4n1fVH7InqnPvYMa6miIiIiCeMnQV4teWViIiI\neNzYCW4iIiIiHqfgJiIiIuIRCm4iIiIiHqHgJiIiIuIRCm4iIiIiHjFmgptP00pFRETE48ZMcBMR\nERHxOgU3EREREY9QcBMRERHxCAU3EREREY9QcBMRERHxiDET3HyaVCoiIiIeN2aCm4iIiIjXKbiJ\niIiIeISCm4iIiIhHKLiJiIiIeISCm4iIiIhHKLiJiIiIeISCm4iIiIhHKLiJiIiIeISCm4iIiIhH\nKLiJiIiIeMSYCW7a8kpERES8bswENxERERGvU3ATERER8QgFNxERERGPUHATERER8QgFNxERERGP\nGEPBTdNKRURExNvGUHATERER8TYFNxERERGPUHATERER8QgFNxERERGPGDPBTVMTRERExOtyM3lz\nM7sYuAyoB6LOuVtSnHMFcCtwrXPuwaTybcC2+NvdzrkPxsunA18FNgHTgS8459oy1QYRERGRbJGx\nHjczKwKWAJ93zt0MnGJmF/U7ZwaxULczxS1+5Zy7IP7ng0nlS4A7nXPfBtYCN2SkASIiIiJZJpND\npecC251z3fH3y4FLk09wzm11zj0+wPVvMLPrzewbZnYegJnlAYuBFwa6p4iIiMholcmh0hqgNel9\nS7wsXV92zj0f77lbZWb/ALQDnc656HDvWVQcoLq6dBgfnmGfn83UluyktmSn0dQWGF3tUVuyk9py\n/GQyuNUDya0vi5elxTn3fPzvDjNbDSwCfgsUmpkvHt7SvmdHew8NDa1DnxhXXV06rPOzmdqSndSW\n7DSa2gKjqz1qS3ZSWzJTj4Fkcqh0BVBnZvnx94uAh8ysyszKBrvQzC4ys7cmFc0CNjvngsDjwJnJ\n90ynMj5NKxURERGPy1iPW7yn7Brgh2bWAKxxzi0zs9uBJuA2M/MBNwJ1wBVmFnTOPUKsF+1mMzsD\nmAz80Tn39/itrwZuMrNLgGnAdZlqg4iIiEg2yehyIM65pcDSfmXXJ72OAt+M/0k+5xXgPQPccxtw\n1bGuq4iIiEi2GzML8IqIiIh4nYKbiIiIiEcouImIiIh4hIKbiIiIiEcouImIiIh4hIKbiIiIiEco\nuImIiIh4hIKbiIiIiEeMmeDm055XIiIi4nFjJriJiIiIeJ2Cm4iIiIhHKLiJiIiIeISCm4iIiIhH\nKLiJiIiIeMSYCW6aUyoiIiJeN2aCm4iIiIjXKbiJiIiIeISCm4iIiIhHKLiJiIiIeISCm4iIiIhH\njJ3gpmmlIiIi4nFjJ7iJiIiIeJyCm4iIiIhHKLiJiIiIeISCm4iIiIhHjJngprkJIiIi4nVjJriF\nI9GRroKIiIjI6zJmglsorOAmIiIi3jaGgltkpKsgIiIi8rqMmeAWVHATERERjxszwS2qZ9xERETE\n48ZMcBMRERHxurET3HxaEERERES8bewENxERERGPU3ATERER8YjcTN7czC4GLgPqgahz7pYU51wB\n3Apc65x7MF52JvCvwEuAAc875+6KH1sCzEm6xWedc68MVRcNlIqIiIjXZSy4mVkRsASY55zrNrP7\nzOwi59yypHNmEAt1O/tdPgn4gXPueTPLA+rN7E/OuQPAPufc1Zmqt4iIiEi2ymSP27nAdudcd/z9\ncuBSIBHcnHNbga1m9rXkC51zf+l3rxAQjL8uNbMb42XtwBLnXCgD9RcRERHJKpkMbjVAa9L7lnjZ\ncP0LcKtzrjn+/h5gjXMuZGa3A18GvjHUTQoL86iuLh3WBx7u+dlMbclOakt2Gk1tgdHVHrUlO6kt\nx08mg1s9kNz6snhZ2szsA0Cxc+6bvWXOuVVJpzwG3EAawa2zK0hDQ+tQpyVUV5cO6/xsprZkJ7Ul\nO42mtsDoao/akp3UlszUYyCZnFW6Aqgzs/z4+0XAQ2ZWZWZlQ11sZp8Aapxz3zSzk83sxHj5HUmn\nzQY2H+uKi4iIiGSjjPW4Oec6zOwa4Idm1kBseHNZfHizCbjNzHzAjUAdcIWZBZ1zj5jZu4DvAi+Z\n2buBccBngQ3AeDO7DeggNuP0unTqo1mlIiIi4nUZXQ7EObcUWNqv7Pqk11Hgm/E/yefcD5QPcM+P\nHU1d/No5QURERDxuTCzAe8qs8Vx6bt1IV0NERETkdRkTwe1b1yyivCR/6BNFREREstiYCG4iIiIi\no4GCm4iIiIhHKLiJiIiIeISCm4iIiIhHKLiJiIiIeISCm4iIiIhHKLiJiIiIeISCm4iIiIhHKLiJ\niIiIeISCm4iIiIhHKLiJiIiIeISCm4iIiIhHKLiJiIiIeIQvGo2OdB1EREREJA3qcRMRERHxCAU3\nEREREY9QcBMRERHxCAU3EREREY9QcBMRERHxCAU3EREREY/IHekKHC9mNhP4JrAKmAI0Oue+bmZV\nwG3AFmA28BXn3P74Nf8GlAGVwN+cc3+Jl/8ZqEi6/eXOuQaPtmUS8CmgFTgP+LVz7n6PtmU3sDF+\n6wDQ45y7wKNt+RCwGNgMLAT+2cP/xt4PnA/sjt/rOudcV5a3ZQHwPeAF59wXk+51GvAZYCtQA3zR\nORc6Xm3JQHvKga8AH3HOTTye7Yh//GPSFjOrBH4CvEzs32AZcK1zLuy1tsTLf03s/0sncAbwSQ/8\n/0/ZlvgxP/Aw0Oqce+/xakf8Yx/Lr8uI/uzvNWaCG1AF/K43lJjZOjN7CPgk8Khz7l4zewfwHeBD\nZnY2sNg593YzywVeM7MnnXPNwGrn3M0j1A44tm35MbFv2q1m9nOg3MNtuc459/v4fT4KHNcfqMeq\nLcRC9BJginPuoJn9APhn4FsebEs+8F2gzjkXNLPvAtcA38/WtsSvORl4Ev5/e3cTWkcVhnH834rY\nWiqmUg2oBCry4kKsCwvFgq0VXDSKLoqbUgVBQVJFVEitqF1oKwiCBNRiQPxYiS4CtVQQqSiF1oX4\nFR/RFqvYEEuLsUFETF2cM3Ryk5ukuWfOvcN9fxDIPXNn8j6cm8yZM2cIlxYHMbMlwLvAHZLGYpb7\ngeF8UYBEeaINwAfAg1kqnylVlhXAIUmvx+McAO4hZMslZb/8LGl3PE7H//7HfZplAXiKcBF6ZeWV\nz5QyS7vP/UAX3SqVdLRhJmkpMAlsAQ7Hti/ia4D+oj1eUY8Ct8Vt15rZ02a2K86MZJUqi5n1An3A\ndjN7kvBBPll9gvNS9ksxaIu2AuXXlUuVRdIUMA6sju9bBXxVbfXTJeyXPsIV7r/xfceAzdVWP90i\nsiDpLWCq4VBrgOWSxmbbJ5eEeZC0n/BZa4tUWST9VgzaSsc5W0XNzSTul92ll9cB36eudy4ps5jZ\nJsLM4ZGq6p1Lyiy0+dxf6JqBW5mZ3QsclPQD4Qrgr7hpAuiJMwbl9mJbcbXwhqQXJb0A9LezA1vM\n0gfcBHwk6WXCFPCuXLU3StAvxXE2AodLg4XsEmR5CNhnZkOEW49HsxQ+ixazjAKXm1kxCF1HuI3V\nFj+kVc8AAAK/SURBVAvM0sy8n73cWszTUVJlMbNb4r4fV1LowmpoOYuZrTOz94HfgZHKip2/jkVn\nMbOrgPskvVp9pfNL0C8dce7vuoFbHP1vAh6PTePAyvj9ZcCZOGNQbi+2jQNIKl85fArcXmXNzSTI\nMgH8Iel4bP8c2Fhx2bNK0S8lDxNuNbZFq1niTOibwF2SBoCDwFCO2hu1mkXSWeBu4AkzexT4FTiR\no/ZGF5ClmYV89rJJkKdjpMpiZjcCA8A2SW35f46pskg6ImkrMAbsqaLW+STI0g+cMbNBwoyWmdmg\nmV1SVc3NpOiXTjn3d9XAzcy2AHcCjwG9ZrYe2A+sj2+5Nb6m3G5mFwM3AJ+Z2Uoze7Z02OsJ9+6z\nSpGFsJB/0sICZQgzcD9mCVCSKEtxrDXAhKRTeaqfLlGWK4ApScXV4ElgWZYAJQn75ZykwXjVvRR4\nJ0+C8y4wSzPHgL/jwHqh+1QiUZ6OkCpLnGkbICz5OGdm/dVUPGcNLWcxs9VxjW7hOOE2fVYpskga\nlrRT0t74XknaK+mfCkufIVG/dMS5H7ron8xbeErkEPBlbFpBWJg/ArwE/EJYSzCo6U/J9cSvA5JG\nzGwZ8B7wHbAEuBrYIWmyblli+wbCgswTgBGekss2i5AyS9z2CjAs6dtcGUo/O2W/PAf0Emao1gLP\nS8q2ziVxlg+Bn4DTwJ+SXsuVI/78xWTZDjxAeDr5bUn7YvtaYEfcZxXteao0dZ5thAdG9hB+d7Kt\nc02VxcyuIfxN/hr4D7gI+CTnQvKEWXoIM+7fEB6wuhl4RtJo3bKUjrcZeIRwjhlqWI9YqYT90vZz\nf6FrBm7OOeecc3XXVbdKnXPOOefqzAduzjnnnHM14QM355xzzrma8IGbc84551xN+MDNOeecc64m\nfODmnHPOOVcTPnBzzjnnnKsJH7g555xzztXE/0OtvIZHTzK4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114625128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "realized_volatility(gbm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Some **rolling annualized statistics**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Tm88dhv69lJ4Fq9mAU0ZkYkRuMh66wl+JajEZkBjDhq/qm7qPXh6FxeX24uF3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yL+5nPZWeN7/9udvOlT2u/0YwZxzqzoxkNC/Me4bkcFj/yvrTzh8P45DB+Qw8fL2mpoFxdmctHx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\nr1jlPlbb2ENzp/la3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jmU/PkaVmutv+58nHB5n/Fn/wC+hHkxnx/wlvvGn/0Luzgmqqfj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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114572908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rolling_statistics(gbm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Market Stylized Facts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We work with **historical DAX data**. The following function equips us with the necessary time series data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from urllib.request import urlretrieve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('equities.h5', <http.client.HTTPMessage at 0x113fbfcf8>)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "urlretrieve('http://hilpisch.com/equities.h5', 'equities.h5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def read_dax_data():\n",
    "    ''' Reads historical DAX data from Yahoo! Finance, calculates log returns, \n",
    "    realized variance and volatility.'''\n",
    "\n",
    "    try:\n",
    "        h5 = pd.HDFStore('equities.h5', 'r')\n",
    "    except:\n",
    "        from urllib.request import urlretrieve\n",
    "        urlretrieve('http://hilpisch.com/equities.h5', 'equities.h5')\n",
    "        h5 = pd.HDFStore('equities.h5', 'r')\n",
    "    \n",
    "    DAX = pd.DataFrame(h5['data']['^GDAXI'])\n",
    "    DAX = DAX[(DAX.index >= '30-09-2004') & (DAX.index <= '31-08-2015')]\n",
    "    DAX.rename(columns={'^GDAXI' : 'index'}, inplace=True)\n",
    "    print(DAX.tail())\n",
    "    DAX['returns'] = np.log(DAX['index'] / DAX['index'].shift(1))\n",
    "    DAX['rea_var'] = 252 * np.cumsum(DAX['returns'] ** 2) / np.arange(len(DAX))\n",
    "    DAX['rea_vol'] = np.sqrt(DAX['rea_var'])\n",
    "    DAX = DAX.dropna()\n",
    "    return DAX"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Lets **retrieve and inspect** the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                   index\n",
      "Date                    \n",
      "2015-08-25  10128.120117\n",
      "2015-08-26   9997.429688\n",
      "2015-08-27  10315.620117\n",
      "2015-08-28  10298.530273\n",
      "2015-08-31  10259.459961\n",
      "CPU times: user 171 ms, sys: 25.4 ms, total: 196 ms\n",
      "Wall time: 227 ms\n"
     ]
    }
   ],
   "source": [
    "%time DAX = read_dax_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RETURN SAMPLE STATISTICS\n",
      "---------------------------------------------\n",
      "Mean of Daily  Log Returns  0.000308\n",
      "Std  of Daily  Log Returns  0.013992\n",
      "Mean of Annua. Log Returns  0.077584\n",
      "Std  of Annua. Log Returns  0.222112\n",
      "---------------------------------------------\n",
      "Skew of Sample Log Returns -0.001354\n",
      "Skew Normal Test p-value    0.977037\n",
      "---------------------------------------------\n",
      "Kurt of Sample Log Returns  6.520355\n",
      "Kurt Normal Test p-value    0.000000\n",
      "---------------------------------------------\n",
      "Normal Test p-value         0.000000\n",
      "---------------------------------------------\n",
      "Realized Volatility         0.220012\n",
      "Realized Variance           0.048405\n"
     ]
    }
   ],
   "source": [
    "print_statistics(DAX)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The (in-memory) **data structure**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 2695 entries, 2004-10-01 to 2015-08-31\n",
      "Data columns (total 4 columns):\n",
      "index      2695 non-null float64\n",
      "returns    2695 non-null float64\n",
      "rea_var    2695 non-null float64\n",
      "rea_vol    2695 non-null float64\n",
      "dtypes: float64(4)\n",
      "memory usage: 105.3 KB\n"
     ]
    }
   ],
   "source": [
    "DAX.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>index</th>\n",
       "      <th>returns</th>\n",
       "      <th>rea_var</th>\n",
       "      <th>rea_vol</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-08-25</th>\n",
       "      <td>10128.120117</td>\n",
       "      <td>0.048521</td>\n",
       "      <td>0.048369</td>\n",
       "      <td>0.219929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-08-26</th>\n",
       "      <td>9997.429688</td>\n",
       "      <td>-0.012988</td>\n",
       "      <td>0.048367</td>\n",
       "      <td>0.219924</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-08-27</th>\n",
       "      <td>10315.620117</td>\n",
       "      <td>0.031331</td>\n",
       "      <td>0.048439</td>\n",
       "      <td>0.220089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-08-28</th>\n",
       "      <td>10298.530273</td>\n",
       "      <td>-0.001658</td>\n",
       "      <td>0.048422</td>\n",
       "      <td>0.220049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-08-31</th>\n",
       "      <td>10259.459961</td>\n",
       "      <td>-0.003801</td>\n",
       "      <td>0.048405</td>\n",
       "      <td>0.220012</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   index   returns   rea_var   rea_vol\n",
       "Date                                                  \n",
       "2015-08-25  10128.120117  0.048521  0.048369  0.219929\n",
       "2015-08-26   9997.429688 -0.012988  0.048367  0.219924\n",
       "2015-08-27  10315.620117  0.031331  0.048439  0.220089\n",
       "2015-08-28  10298.530273 -0.001658  0.048422  0.220049\n",
       "2015-08-31  10259.459961 -0.003801  0.048405  0.220012"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DAX[['index', 'returns', 'rea_var', 'rea_vol']].tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The **index levels and log returns**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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go5jH39rCsZxSnnhnq9vzWqx2Kqstzk07nd3xHM9NS94s25IJwJnjerdlc4Ro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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113f90160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "quotes_returns(DAX)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "A histogram of the **log returns compared to the normal distribution** (with same mean/std)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qdFuLiPhFhZdIHjt4vI5DJ+opi5cyc+T0sOMUrIUVc4lGomw7soPjnSfCjiMi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\nf4I43pUgeN1wAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113e67be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_histogram(DAX)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The **QQ-plot**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113eac128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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uQD7B/9wD0HoukmWTJg1h1ar88FnXE8oQtnAiSxIF+RHUAEFB/m5Op5JTeGqX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11453a828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "return_qqplot(DAX)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The **realized volatility**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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bLl2rgchZljqu6RWnLSEeT7BtfzcdPUPsP9DHi7s6KIrmsXZJJXtavZX29x3o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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1140ff278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "realized_volatility(DAX)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "And finally the **rolling annualized statistics**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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xK6BgLJK9LXp/MX0AvTonEhkRxtvf7eAfH2/k9TnbXJTU5qzSFovF45q3WCxM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\nWJFgcGSc7z/yNrUtg6ysyuaGz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wdOdAc1N3Tc7uR326oZttq5+cKKqHbGw0l2upEr15ew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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114123470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rolling_statistics(DAX)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Finally, we want to look for **jumps** (heuristically). We use this simple function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def count_jumps(data, value):\n",
    "    ''' Counts the number of return jumps as defined in size by value. '''\n",
    "    jumps = np.sum(np.abs(data['returns']) > value)\n",
    "    return jumps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We define a **jump** as a log return higher in absolute value than 0.05."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_jumps(DAX, 0.05)  # \"jumps\" in the DAX index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_jumps(gbm, 0.05)  # \"jumps\" in the GBM path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In a Gaussian setting we have\n",
    "\n",
    "* negative jumps:\n",
    "\n",
    "$$P(r_n < −0.05) = 0.0002911$$\n",
    "\n",
    "* positive jumps:\n",
    "\n",
    "$$P(r_n > +0.05) = 0.0003402$$\n",
    "\n",
    "for the DAX index given a return observation $r_n$. In such a setting the number of return observations lower than $-0.05$ and higher than $+0.05$ would be expected to be:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7845144999999999"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.0002911 * len(DAX)  # 'lower than -0.05'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.916839"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.0003402 * len(DAX)  # 'higher than +0.05'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In summary, we \"discover\" the following stylized facts:\n",
    "\n",
    "* **stochastic volatility**: volatility is neither constant nor deterministic; there is no mechanism\n",
    "to forecast volatility at a high confidence level\n",
    "* **volatility clustering**: empirical data suggests that high volatility events seem to cluster\n",
    "in time; there is often a positive autocorrelation of volatility measures\n",
    "* **volatility mean reversion**: volatility is a mean-reverting quantity &mdash; it never reaches zero\n",
    "nor does it go to infinity; however, the mean can change over time\n",
    "* **leverage effect**: our data suggests that volatility is negatively correlated (on average) with asset returns; if return measures increase, volatility measures often decrease and vice versa\n",
    "* **fat tails**: compared to a normal distribution large positive and negative index returns are\n",
    "more frequent\n",
    "* **jumps**: index levels may move by magnitudes that cannot be explained within a Gaussian,\n",
    "i.e. normal, diffusion setting; some jump component may be necessary to explain certain\n",
    "large moves"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Important add-on topic: **volatility smiles and term structure** &mdash; here implied volatilities from European call options on the EURO STOXX 50 on 30. September 2014."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1146f9320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run es50_imp_vol.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Strike</th>\n",
       "      <th>Call</th>\n",
       "      <th>Maturity</th>\n",
       "      <th>Put</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>498</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3750.0</td>\n",
       "      <td>27.4</td>\n",
       "      <td>2015-09-18</td>\n",
       "      <td>635.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>499</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3800.0</td>\n",
       "      <td>21.8</td>\n",
       "      <td>2015-09-18</td>\n",
       "      <td>680.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>500</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3850.0</td>\n",
       "      <td>17.2</td>\n",
       "      <td>2015-09-18</td>\n",
       "      <td>725.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>501</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3900.0</td>\n",
       "      <td>13.4</td>\n",
       "      <td>2015-09-18</td>\n",
       "      <td>772.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3950.0</td>\n",
       "      <td>10.4</td>\n",
       "      <td>2015-09-18</td>\n",
       "      <td>818.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Date  Strike  Call   Maturity    Put\n",
       "498 2014-09-30  3750.0  27.4 2015-09-18  635.9\n",
       "499 2014-09-30  3800.0  21.8 2015-09-18  680.3\n",
       "500 2014-09-30  3850.0  17.2 2015-09-18  725.7\n",
       "501 2014-09-30  3900.0  13.4 2015-09-18  772.0\n",
       "502 2014-09-30  3950.0  10.4 2015-09-18  818.9"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The calculation of the **implied volatilities** and the visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 21.3 s, sys: 253 ms, total: 21.5 s\n",
      "Wall time: 22 s\n"
     ]
    }
   ],
   "source": [
    "%time imp_vols = calculate_imp_vols(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EhHTmpZeeY926T2nX7ho+/fQj3nvvHeLjZ1U7RkrKfxk8OJqMjPRK21etWsHv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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11449c908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_imp_vols(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Fourier-based Option Pricing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The Fourier-based option pricing approach has three main advantages:\n",
    "\n",
    "* **generality**: the approach is applicable whenever the characteristic function of the process driving uncertainty is known; and this is the case for the majority of processes/models applied in practice\n",
    "* **accuracy**: the semi-analytic formulas can be evaluated numerically in such a way that a high degree of accuracy is reached at little computational cost (e.g. compared to simulation techniques)\n",
    "* **speed**: the formulas can in general be evaluated very fast such that 10s, 100s or even 1,000s of options can be valued per second"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let us start with a **market model** of the form:\n",
    "\n",
    "$$\n",
    "\\mathcal{M} = \\{(\\Omega,\\mathcal{F},\\mathbb{F},P),T,(S,B)\\}\n",
    "$$\n",
    "\n",
    "* $(\\Omega,\\mathcal{F},\\mathbb{F},P)$ is a filtered probability space\n",
    "* $T>0$ is a fixed time horizon\n",
    "* $(S,B)$ are two traded assets, $S$ a risky one and $B$ a risk-less one"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We then know that the **arbitrage value of an attainable European call option** is\n",
    "\n",
    "$$\n",
    "C_{t}=e^{-r(T-t)}\\mathbf{E}^{Q}_{t}(C_{T})\n",
    "$$\n",
    "\n",
    "where $C_{T}\\equiv\\max[S_{T}-K,0]$ for a strike $K>0$. In integral from, setting $t=0$, call option pricing reads\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "C_{0}&=&e^{-rT}\\int_{0}^{\\infty} C_{T}(s) Q(ds) \\nonumber\\\\\n",
    "   &=&e^{-rT}\\int_{0}^{\\infty} C_{T}(s) q(s) ds\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "where $q(s)$ is the risk-neutral probability density function (pdf) of $S_{T}$. Unfortunately, the pdf is quite often not known in closed form &mdash; whereas the characteristic function (CF) of $S_{T}$ is.\n",
    "\n",
    "**The fundamental insight of Fourier-based option pricing is to replace both the pdf by the CF and the call option payoff $C_{T}$ by its Fourier transform.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let a random variable $X$ be distributed with pdf $q(x)$. The **characteristic function** $\\hat{q}$ of $X$ is the Fourier transform of its pdf\n",
    "\n",
    "$$\n",
    "\\hat{q}(u)\\equiv \\int_{-\\infty}^{\\infty}e^{iux} q(x) dx = \\mathbf{E}^{Q}\\left(e^{iuX}\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "For $u=u_{r}+iu_{i}$ with $u_{i}>1$, the **Fourier transform of the European call option payoff** $C_{T} = \\max[S_T - K, 0]$is given by:\n",
    "\n",
    "$$\\widehat{C}_{T}(u)= -\\frac{K^{iu+1}}{u^2-iu}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Lewis (2001)**: With $\\varphi$ as the CF of the rv $S_T$ and assuming $u_{i}\\in (0,1)$, the call option present value is\n",
    "$$\n",
    "C_{0}=S_{0}-\\frac{Ke^{-rT}}{2\\pi}\\int_{-\\infty+iu_{i}}^{\\infty+iu_{i}} e^{-iuk} \\varphi(-u) \\frac{du}{u^2-ui}\n",
    "$$\n",
    "\n",
    "Furthermore, setting $u_{i}=0.5$ gives\n",
    "\n",
    "$$\n",
    "C_{0}=S_{0}-\\frac{\\sqrt{S_{0}K}e^{-rT/2}}{\\pi}\\int_{0}^{\\infty} \\mathbf{Re}\\left[e^{izk} \\varphi(z-i/2)\\right] \\frac{dz}{z^2+1/4}\n",
    "$$\n",
    "where $\\mathbf{Re}[x]$ denotes the real part of $x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Merton (1976) Jump-Diffusion Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In the Merton (1976) jump-diffusion model, the **risk-neutral index level dynamics** are given by the SDE\n",
    "\n",
    "$$\n",
    "dS_{t}=(r-r_{J})S_{t}dt+\\sigma S_{t}dZ_{t}+J_{t}S_{t}dN_{t}\n",
    "$$\n",
    "\n",
    "The variables and parameters have the following meaning:\n",
    "\n",
    "* $S_{t}$ index level at date $t$\n",
    "* $r$ constant risk-less short rate \n",
    "* $r_{J}\\equiv \\lambda \\cdot \\left(e^{\\mu_{J}+\\delta^{2}/2}-1\\right)$ drift correction for jump\n",
    "* $\\sigma$ constant volatility of $S$\n",
    "* $Z_{t}$ standard Brownian motion\n",
    "* $J_{t}$ jump at date $t$ with distribution $\\log(1+J_{t}) \\approx \\mathbf{N}\\left(\\log(1+\\mu_{J})-\\frac{\\delta^{2}}{2},\\delta^{2}\\right)$\n",
    "* $\\mathbf{N}$ as the cumulative distribution function of a standard normal random variable\n",
    "* $N_{t}$ Poisson process with intensity $\\lambda$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The **characteristic function for the Merton (1976) model** is given as:\n",
    "\n",
    "$$\n",
    "\\varphi_{0}^{M76}(u,T)=\\exp\\left(\\left(iu\\omega -\\frac{u^{2}\\sigma^{2}}{2}+\\lambda \\left(e^{iu\\mu_{J}-u^{2}\\delta^{2}/2}-1\\right)\\right)T\\right)\n",
    "$$\n",
    "\n",
    "where the **risk-neutral drift term $\\omega$** takes on the form\n",
    "\n",
    "$$\n",
    "\\omega=r-\\frac{\\sigma^{2}}{2}-\\lambda\\left(e^{\\mu_{J}+\\delta^{2}/2}-1\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Combining this with the option pricing result from Lewis (2001) we get for the **price of a European call option**\n",
    "\n",
    "$$\n",
    "C_{0}=S_{0}-\\frac{\\sqrt{S_{0}K}e^{-rT/2}}{\\pi}\\int_{0}^{\\infty} \\mathbf{Re}\\left[e^{izk} \\varphi_{0}^{M76}(z-i/2,T)\\right] \\frac{dz}{z^2+1/4}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let us implement European call option in Python. First, the **characteristic function**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "from scipy.integrate import quad\n",
    "\n",
    "def M76_characteristic_function(u, T, r, sigma, lamb, mu, delta):\n",
    "    omega = r - 0.5 * sigma ** 2 - lamb * (np.exp(mu + 0.5 * delta ** 2) - 1)\n",
    "    value = np.exp((1j * u * omega - 0.5 * u ** 2 * sigma ** 2 +\n",
    "            lamb * (np.exp(1j * u * mu - u ** 2 * delta ** 2 * 0.5) - 1))  * T)\n",
    "    return value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Second, the **integration function**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def M76_integration_function(u, S0, K, T, r, sigma, lamb, mu, delta):\n",
    "    JDCF = M76_characteristic_function(u - 0.5 * 1j, T, r,\n",
    "                                       sigma, lamb, mu, delta)\n",
    "    value = 1 / (u ** 2 + 0.25) * (np.exp(1j * u * math.log(S0 / K))\n",
    "                                    * JDCF).real\n",
    "    return value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Third, the **evaluation of the integral** via numerical quadrature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def M76_value_call_INT(S0, K, T, r, sigma, lamb, mu, delta):\n",
    "    int_value = quad(lambda u: M76_integration_function(u, S0, K, T, r,\n",
    "                    sigma, lamb, mu, delta), 0, 50, limit=250)[0]\n",
    "    call_value = S0 - np.exp(-r * T) * math.sqrt(S0 * K) / math.pi * int_value\n",
    "    return call_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Fourth, a **numerical example**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "S0 = 100.0  # initial index level\n",
    "K = 100.0  # strike level\n",
    "T = 1.0  # call option maturity\n",
    "r = 0.05  # constant short rate\n",
    "sigma = 0.4  # constant volatility of diffusion\n",
    "lamb = 1.0  # jump frequency p.a.\n",
    "mu = -0.2  # expected jump size\n",
    "delta = 0.1  # jump size volatility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of Call Option   19.948\n"
     ]
    }
   ],
   "source": [
    "print (\"Value of Call Option %8.3f\" \\\n",
    "            % M76_value_call_INT(S0, K, T, r, sigma, lamb, mu, delta))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Monte Carlo Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "To value a European call option with strike price $K$ by MCS consider the following **discretization of the Merton (1976) SDE**\n",
    "\n",
    "$$\n",
    "S_{t}=S_{t-\\Delta t}\\left(e^{(r-r_{J}-\\sigma^{2}/2)\\Delta t+\\sigma \\sqrt{\\Delta t}z^{1}_{t}}+ \\left(e^{\\mu_{J}+\\delta z^{2}_{t}}-1\\right)y_{t}\\right)\n",
    "$$\n",
    "\n",
    "with the $z^{n}_{t}$ being standard normally distributed and the $y_{t}$ being Poisson distributed with intensity $\\lambda$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The Python code implementing the MCS:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def M76_generate_paths(S0, T, r, sigma, lamb, mu, delta, M, I):\n",
    "    dt = T / M\n",
    "    rj = lamb * (math.exp(mu + 0.5 * delta ** 2) - 1)\n",
    "    shape = (M + 1, I)\n",
    "    S = np.zeros((M + 1, I), dtype=np.float)\n",
    "    S[0] = S0\n",
    "\n",
    "    np.random.seed(10000)\n",
    "    rand1 = np.random.standard_normal(shape)\n",
    "    rand2 = np.random.standard_normal(shape)\n",
    "    rand3 = np.random.poisson(lamb * dt, shape)\n",
    "\n",
    "    for t in range(1, M + 1, 1):\n",
    "        S[t] = S[t - 1] * (np.exp((r - rj - 0.5 * sigma ** 2) * dt\n",
    "                           + sigma * math.sqrt(dt) * rand1[t])\n",
    "                           + (np.exp(mu + delta * rand2[t]) - 1)\n",
    "                           * rand3[t])\n",
    "    return S"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The function in action."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "M = 100  # time steps\n",
    "I = 10  # paths\n",
    "S = M76_generate_paths(S0, T, r, sigma, lamb, mu, delta, M, I)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The paths visualized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
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VIMxTgQupLJU6v4C4202kpXnU4yMtLZBITGvH9fEwrFmLHI0SvnZ1wufoz3gZ16ydqmEN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\nAwNDGytj6q2JAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1140ffa20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(S);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "As simple function to **value a European call option by MCS**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def M76_value_call_MCS(K):\n",
    "    return math.exp(-r * T) * np.sum(np.maximum(S[-1] - K, 0)) / I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of Call Option   19.941\n",
      "CPU times: user 3.94 s, sys: 1.06 s, total: 5 s\n",
      "Wall time: 5.19 s\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "I = 200000\n",
    "S = M76_generate_paths(S0, T, r, sigma, lamb, mu, delta, M, I)\n",
    "print (\"Value of Call Option %8.3f\" % M76_value_call_MCS(K))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The model of Merton (1976) is capable of generating a **volatility smile**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PWKOPPQdauO6GJil0KjYsRVExPY2YnkaoLaqvVkoUsgOz1nfla2c2TlF176zQ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11400bda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "start = pd.Timestamp('2015-1-1')\n",
    "end =  pd.Timestamp('2016-1-1')\n",
    "strikes = range(50, 151, 10)\n",
    "plt.figure(figsize=(10, 6))\n",
    "for l in np.arange(0, 1.0, 0.2):\n",
    "    imp_vols = []\n",
    "    for k in strikes:\n",
    "        call = call_option(S0, k, start, end, r, 0.2)\n",
    "        M76_value = M76_value_call_INT(S0, k, T, r, sigma, l, mu, delta)\n",
    "        imp_vols.append(call.imp_vol(M76_value))\n",
    "    plt.plot(strikes, imp_vols, label='$\\lambda$=%2.1f' % l)\n",
    "plt.legend(loc=0); plt.savefig('vol_smile.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Calibration of the Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In simple terms, the problem of **calibration** is to find parameters for the Merton (1976) model such that observed market quotes of liquidly traded plain vanilla options are replicated as good as possible. To this end, one defines an error function that is to be minimized. Such a function could be the Root Mean Squared Error (RMSE). The task is then to solve the problem\n",
    "\n",
    "$$\n",
    "\\min_{\\sigma, \\lambda, \\mu_{J}, \\delta } \\sqrt{\\frac{1}{N}\\sum_{n=1}^{N}\\left( C_{n}^{*} - C_{n}^{M76}(\\sigma, \\lambda, \\mu_{J}, \\delta )\\right)^{2}}\n",
    "$$\n",
    "with the $C_{n}^{*}$ being the market or input prices and the $C_{n}^{M76}$ being the model or output prices for the options $n=1,...,N$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**EXCURSION**: The minimization problem is ill-posed (I). Let's analyze properties of the error function for a single European call option."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "C0 = M76_value_call_INT(S0, K, T, r, sigma, lamb, mu, delta)\n",
    "def error_function(p0):\n",
    "    sigma, lamb, mu, delta = p0\n",
    "    return abs(C0 - M76_value_call_INT(S0, K, T, r, sigma, lamb, mu, delta))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**EXCURSION**: The minimization problem is ill-posed (II)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_error_function():\n",
    "    plt.figure(figsize=(10, 6))\n",
    "    # Plotting (lamb)\n",
    "    l = np.linspace(-0.5, 1.5, 100); EFv = []\n",
    "    for i in l:\n",
    "        EFv.append(error_function([sigma, i, mu, delta]))\n",
    "    plt.plot(l, EFv)\n",
    "    plt.xlabel('parameter values')\n",
    "    plt.ylabel('error function values c.p.')\n",
    "    # Plotting (mu)\n",
    "    l = np.linspace(-0.3, 0.3, 100); EFv = []\n",
    "    for i in l:\n",
    "        EFv.append(error_function([sigma, lamb, i, delta]))\n",
    "    plt.plot(l, EFv)\n",
    "    # Plotting (delta)\n",
    "    l = np.linspace(-0.3, 0.3, 100); EFv = []\n",
    "    for i in l:\n",
    "        EFv.append(error_function([sigma, lamb, mu, i]))\n",
    "    plt.plot(l, EFv);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**EXCURSION**: The minimization problem is ill-posed (III)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ChGlCjV0vPX06rR1eHvjdev69vdbqsMQYtHrbAMhwpVsciRBCxA5JwoSpDMPggpNK+c/L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\ne9qZtHrbeGXf6xF9byv4Ght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NPAjUALOAH2qtd40idjFOg20quhooTSsJ6zXu6QOd8/eW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      "text/plain": [
       "<matplotlib.figure.Figure at 0x115ac97b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_error_function()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**EXCURSION**: The simple example illustrates that the calibration of the Merton (1976) jump diffusion model leads to a number of problems:\n",
    "\n",
    "\n",
    "* **convexity**: the error function is only locally convex\n",
    "* **determinacy**: the error function exhibits multiple minima\n",
    "* **degeneracy**: different parameter combinations yield the same result\n",
    "* **consistency**: the approach mathematically allows parameter values that are economically implausible\n",
    "* **stability**: slight changes in the input values can change the solution significantly ('sudden' change from one local minimum to another is possible)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let us import some **real option quotes for European call options on the EURO STOXX 50 index**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "h5 = pd.read_csv('es50_option_data.csv', index_col=0)\n",
    "data['Date'] = data['Date'].apply(lambda x: pd.Timestamp(x))\n",
    "data['Maturity'] = data['Maturity'].apply(lambda x: pd.Timestamp(x))\n",
    "\n",
    "S0 = 3225.93  # EURO STOXX 50 level\n",
    "r = 0.005  # assumption\n",
    "\n",
    "# Option Selection\n",
    "tol = 0.05\n",
    "options = data[(np.abs(data['Strike'] - S0) / S0) < tol]\n",
    "mats = sorted(set(options['Maturity']))\n",
    "options = options[options['Maturity'] == mats[0]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "These are the **option quotes** we are dealing with (I)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Strike</th>\n",
       "      <th>Call</th>\n",
       "      <th>Maturity</th>\n",
       "      <th>Put</th>\n",
       "      <th>Imp_Vol</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>452</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3075.0</td>\n",
       "      <td>167.0</td>\n",
       "      <td>2014-10-17</td>\n",
       "      <td>9.3</td>\n",
       "      <td>0.272313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>453</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3100.0</td>\n",
       "      <td>144.5</td>\n",
       "      <td>2014-10-17</td>\n",
       "      <td>11.7</td>\n",
       "      <td>0.255501</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>454</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3125.0</td>\n",
       "      <td>122.7</td>\n",
       "      <td>2014-10-17</td>\n",
       "      <td>14.9</td>\n",
       "      <td>0.239363</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>455</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3150.0</td>\n",
       "      <td>101.8</td>\n",
       "      <td>2014-10-17</td>\n",
       "      <td>19.1</td>\n",
       "      <td>0.223913</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>456</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3175.0</td>\n",
       "      <td>82.3</td>\n",
       "      <td>2014-10-17</td>\n",
       "      <td>24.5</td>\n",
       "      <td>0.210099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>457</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3200.0</td>\n",
       "      <td>64.3</td>\n",
       "      <td>2014-10-17</td>\n",
       "      <td>31.5</td>\n",
       "      <td>0.197051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>458</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3225.0</td>\n",
       "      <td>48.3</td>\n",
       "      <td>2014-10-17</td>\n",
       "      <td>40.5</td>\n",
       "      <td>0.185345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>459</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3250.0</td>\n",
       "      <td>34.6</td>\n",
       "      <td>2014-10-17</td>\n",
       "      <td>51.8</td>\n",
       "      <td>0.174854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>460</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3275.0</td>\n",
       "      <td>23.5</td>\n",
       "      <td>2014-10-17</td>\n",
       "      <td>65.8</td>\n",
       "      <td>0.165798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>461</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3300.0</td>\n",
       "      <td>15.1</td>\n",
       "      <td>2014-10-17</td>\n",
       "      <td>82.3</td>\n",
       "      <td>0.158392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>462</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3325.0</td>\n",
       "      <td>9.1</td>\n",
       "      <td>2014-10-17</td>\n",
       "      <td>101.3</td>\n",
       "      <td>0.152121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>463</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3350.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>2014-10-17</td>\n",
       "      <td>122.4</td>\n",
       "      <td>0.146688</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>464</th>\n",
       "      <td>2014-09-30</td>\n",
       "      <td>3375.0</td>\n",
       "      <td>2.8</td>\n",
       "      <td>2014-10-17</td>\n",
       "      <td>145.0</td>\n",
       "      <td>0.143796</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Date  Strike   Call   Maturity    Put   Imp_Vol\n",
       "452 2014-09-30  3075.0  167.0 2014-10-17    9.3  0.272313\n",
       "453 2014-09-30  3100.0  144.5 2014-10-17   11.7  0.255501\n",
       "454 2014-09-30  3125.0  122.7 2014-10-17   14.9  0.239363\n",
       "455 2014-09-30  3150.0  101.8 2014-10-17   19.1  0.223913\n",
       "456 2014-09-30  3175.0   82.3 2014-10-17   24.5  0.210099\n",
       "457 2014-09-30  3200.0   64.3 2014-10-17   31.5  0.197051\n",
       "458 2014-09-30  3225.0   48.3 2014-10-17   40.5  0.185345\n",
       "459 2014-09-30  3250.0   34.6 2014-10-17   51.8  0.174854\n",
       "460 2014-09-30  3275.0   23.5 2014-10-17   65.8  0.165798\n",
       "461 2014-09-30  3300.0   15.1 2014-10-17   82.3  0.158392\n",
       "462 2014-09-30  3325.0    9.1 2014-10-17  101.3  0.152121\n",
       "463 2014-09-30  3350.0    5.1 2014-10-17  122.4  0.146688\n",
       "464 2014-09-30  3375.0    2.8 2014-10-17  145.0  0.143796"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "options"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "These are the **option quotes** we are dealing with (II)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Ag6OrAJbkE7XW2y4Ye3eST9Va/7CU8sok701yQ5ffAwAwMLoNYFeXUt6W5ClJvlBrHU8y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\ngMYEMACAxgQwAIDGBDAAgMYEMACAxv4/TH+09HzCiMAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113e40a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options['Call'].plot(style='o', figsize=(10, 6));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Next, we define an **error function** in Python for the calibration. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "i = 0; min_RMSE = 100.\n",
    "def M76_error_function(p0):\n",
    "    global i, min_RMSE\n",
    "    sigma, lamb, mu, delta = p0\n",
    "    if sigma < 0.0 or delta < 0.0 or lamb < 0.0:\n",
    "        return 500.0\n",
    "    se = []\n",
    "    for row, option in options.iterrows():\n",
    "        T = (option['Maturity'] - option['Date']).days / 365.\n",
    "        model_value = M76_value_call_INT(S0, option['Strike'], T,\n",
    "                                         r, sigma, lamb, mu, delta)\n",
    "        se.append((model_value - option['Call']) ** 2)\n",
    "    RMSE = math.sqrt(sum(se) / len(se))\n",
    "    min_RMSE = min(min_RMSE, RMSE)\n",
    "    if i % 100 == 0:\n",
    "        print ('%4d |' % i, np.array(p0), '| %7.3f | %7.3f' % (RMSE, min_RMSE))\n",
    "    i += 1\n",
    "    return RMSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The calibration is done in two steps. First, a **global optimization**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   0 | [ 0.100  0.100 -0.400  0.000] |  12.676 |  12.676\n",
      " 100 | [ 0.100  0.300  0.000  0.020] |  15.240 |   7.372\n",
      " 200 | [ 0.100  0.600 -0.100  0.060] |  11.777 |   2.879\n",
      " 300 | [ 0.125  0.200 -0.200  0.100] |   9.004 |   2.443\n",
      " 400 | [ 0.125  0.500 -0.200  0.000] |   5.056 |   1.125\n",
      " 500 | [ 0.150  0.100 -0.300  0.040] |   6.109 |   0.970\n",
      " 600 | [ 0.150  0.400 -0.400  0.080] |   4.135 |   0.970\n",
      " 700 | [ 0.150  0.600  0.000  0.120] |   6.333 |   0.970\n",
      " 800 | [ 0.175  0.200  0.000  0.020] |   5.955 |   0.970\n",
      " 900 | [ 0.175  0.500 -0.100  0.060] |   5.536 |   0.970\n",
      "1000 | [ 0.200  0.100 -0.200  0.100] |   8.596 |   0.970\n",
      "1100 | [ 0.200  0.400 -0.200  0.000] |  10.692 |   0.970\n",
      "1200 | [ 0.200  0.700 -0.300  0.040] |  17.578 |   0.970\n",
      "CPU times: user 1min 11s, sys: 1.33 s, total: 1min 12s\n",
      "Wall time: 1min 14s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "import scipy.optimize as sop\n",
    "np.set_printoptions(suppress=True,\n",
    "                    formatter={'all': lambda x: '%6.3f' % x})\n",
    "p0 = sop.brute(M76_error_function, ((0.10, 0.201, 0.025),\n",
    "                   (0.10, 0.80, 0.10), (-0.40, 0.01, 0.10),\n",
    "                   (0.00, 0.121, 0.02)), finish=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Second, the **local (convex) optimization**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1300 | [ 0.122  0.723 -0.247  0.110] |   0.798 |   0.798\n",
      "1400 | [ 0.119  1.001 -0.187  0.013] |   0.769 |   0.768\n",
      "1500 | [ 0.119  1.031 -0.183  0.000] |   0.767 |   0.767\n",
      "1600 | [ 0.119  1.033 -0.183  0.000] |   0.767 |   0.767\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.766508\n",
      "         Iterations: 278\n",
      "         Function evaluations: 477\n",
      "CPU times: user 23.6 s, sys: 362 ms, total: 24 s\n",
      "Wall time: 24.7 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "opt = sop.fmin(M76_error_function, p0, xtol=0.00001,\n",
    "                    ftol=0.00001, maxiter=750, maxfun=1500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The **optimal parameter values** are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   0 | [ 0.125  0.600 -0.300  0.120] |   0.970 |   0.767\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.9695219560421178"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = 0\n",
    "M76_error_function(p0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   0 | [ 0.119  1.033 -0.183  0.000] |   0.767 |   0.767\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.7665083562548708"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = 0\n",
    "M76_error_function(opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Comparison** of market and model prices (I)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def generate_plot(opt, options):\n",
    "    sigma, lamb, mu, delta = opt\n",
    "    options['Model'] = 0.0\n",
    "    for row, option in options.iterrows():\n",
    "        T = (option['Maturity'] - option['Date']).days / 365.\n",
    "        options.loc[row, 'Model'] = M76_value_call_INT(S0, option['Strike'],\n",
    "                                    T, r, sigma, lamb, mu, delta)\n",
    "    options = options.set_index('Strike')\n",
    "    fig, ax = plt.subplots(2, sharex=True, figsize=(8, 7))\n",
    "    options[['Call', 'Model']].plot(style=['b-', 'ro'],\n",
    "                    title='%s' % str(option['Maturity'])[:10], ax=ax[0])\n",
    "    ax[0].set_ylabel('option values')\n",
    "    xv = options.index.values\n",
    "    ax[1] = plt.bar(xv - 5 / 2., options['Model'] - options['Call'], \n",
    "                    width=5)\n",
    "    plt.ylabel('difference')\n",
    "    plt.xlim(min(xv) - 10, max(xv) + 10)\n",
    "    plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Comparison** of market and model prices (II)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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W/txzHl55xc3IkT4uushPVlayIxQRaZri7cEpMsY8aYy51BjTol4jEklDnTsH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\nxTHgSJKk4vwP+zTzrwFr4IgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14fad3b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "generate_plot(opt, options)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Finally, a look at the implied volatilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "S0 = 3225.93; r = 0.005\n",
    "def calc_imp_vols(data):\n",
    "    data['Imp_Vol_Mod'] = 0.0\n",
    "    data['Imp_Vol_Mar'] = 0.0\n",
    "    tol = 0.30  # tolerance for moneyness\n",
    "    for row in data.index:\n",
    "        t = data['Date'][row]\n",
    "        T = data['Maturity'][row]\n",
    "        ttm = (T - t).days / 365.\n",
    "        forward = np.exp(r * ttm) * S0\n",
    "        if (abs(data['Strike'][row] - forward) / forward) < tol:\n",
    "            call = call_option(S0, data['Strike'][row], t, T, r, 0.2)\n",
    "            data['Imp_Vol_Mod'][row] = call.imp_vol(data['Model'][row])\n",
    "            data['Imp_Vol_Mar'][row] = call.imp_vol(data['Call'][row])\n",
    "    return data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The calculation of the **model implied volatilities** and a comparison."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x14faf51d0>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bBXwzxnhGbvku4I1C/gKSNBAtXtyadgm7rKKxofPZmqtWMnzUaFqnzfD+aNJO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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113fae9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options = calc_imp_vols(options)\n",
    "options[['Imp_Vol_Mar', 'Imp_Vol_Mod']].plot(figsize=(10, 6), style=['b^', 'ro'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Conclusions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In conclusion, we can state the following:\n",
    "\n",
    "* **markets**: time series in financial markets strongly deviate from the Gaussian benchmark(s); there are generally eg stochastic volatility, jumps, implied volatility smiles observed in historical data\n",
    "* **Merton (1976) model**: the model of Merton is capable of accounting for some observed stylized facts like jumps and volatility smiles\n",
    "* **calibration issues**: numerical finance and optimization (i.e. calibration) faces a number of issues, eg with regard the determinacy of solutions and convexity of error functions\n",
    "* **Python**: Python is really close to mathematical and financial syntax; the implementation of financial algorithms generally is efficient and performant (when using the right libraries and idioms like NumPy with vectorization)\n",
    "\n",
    "All details, codes, proofs, etc. in the book \"Derivatives Analytics with Python\" &mdash; cf. [http://derivatives-analytics-with-python.com](http://derivatives-analytics-with-python.com)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://tpq.io\" target=\"_blank\">http://tpq.io</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a> | <a href=\"mailto:[email protected]\">[email protected]</a>\n",
    "\n",
    "**Training** |\n",
    "<a href=\"http://training.tpq.io\">http://training.tpq.io</a>\n",
    "\n",
    "**Quant Platform** |\n",
    "<a href=\"http://quant-platform.com\">http://quant-platform.com</a>\n",
    "\n",
    "**Python for Finance** |\n",
    "<a href=\"http://python-for-finance.com\" target=\"_blank\">Python for Finance @ O'Reilly</a>\n",
    "\n",
    "**Derivatives Analytics with Python** |\n",
    "<a href=\"http://derivatives-analytics-with-python.com\" target=\"_blank\">Derivatives Analytics @ Wiley Finance</a>"
   ]
  }
 ],
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diff --git a/02_cqf_demo.ipynb b/02_cqf_demo.ipynb
diff --git a/03_cqf_demo.ipynb b/03_cqf_demo.ipynb
diff --git a/BSM_imp_vol.py b/BSM_imp_vol.py
 #
 # Valuation of European Call Options in BSM Model
 # and Numerical Derivation of Implied Volatility
 # 03_stf/BSM_imp_vol.py
 #
 # (c) Dr. Yves J. Hilpisch
 # from Hilpisch, Yves (2014): Python for Finance, O'Reilly.
 #
 from math import log, sqrt, exp
 from scipy import stats
 from scipy.optimize import fsolve

 class call_option(object):
    ''' Class for European call options in BSM Model.
    
    Attributes
    ==========
    S0 : float
        initial stock/index level
    K : float
        strike price
    t : datetime/Timestamp object
        pricing date
    M : datetime/Timestamp object
        maturity date
    r : float
        constant risk-free short rate
    sigma : float
        volatility factor in diffusion term
        
    Methods
    =======
    value : float
        return present value of call option
    vega : float
        return vega of call option
    imp_vol : float
        return implied volatility given option quote
    '''
    
    def __init__(self, S0, K, t, M, r, sigma):
        self.S0 = float(S0)
        self.K = K
        self.t = t
        self.M = M
        self.r = r
        self.sigma = sigma

    def update_ttm(self):
        ''' Updates time-to-maturity self.T. '''
        if self.t > self.M:
            raise ValueError("Pricing date later than maturity.")
        self.T = (self.M - self.t).days / 365.

    def d1(self):
        ''' Helper function. '''
        d1 = ((log(self.S0 / self.K)
            + (self.r + 0.5 * self.sigma ** 2) * self.T)
            / (self.sigma * sqrt(self.T)))
        return d1
        
    def value(self):
        ''' Return option value. '''
        self.update_ttm()
        d1 = self.d1()
        d2 = ((log(self.S0 / self.K)
            + (self.r - 0.5 * self.sigma ** 2) * self.T)
            / (self.sigma * sqrt(self.T)))
        value = (self.S0 * stats.norm.cdf(d1, 0.0, 1.0)
            - self.K * exp(-self.r * self.T) * stats.norm.cdf(d2, 0.0, 1.0))
        return value
        
    def vega(self):
        ''' Return Vega of option. '''
        self.update_ttm()
        d1 = self.d1()
        vega = self.S0 * stats.norm.pdf(d1, 0.0, 1.0) * sqrt(self.T)
        return vega

    def imp_vol(self, C0, sigma_est=0.2):
        ''' Return implied volatility given option price. '''
        option = call_option(self.S0, self.K, self.t, self.M,
                             self.r, sigma_est)
        option.update_ttm()
        def difference(sigma):
            option.sigma = sigma
            return option.value() - C0
        iv = fsolve(difference, sigma_est)[0]
        return iv
diff --git a/es50_imp_vol.py b/es50_imp_vol.py
 #
 # Black-Scholes-Merton Implied Volatilities of
 # Call Options on the EURO STOXX 50
 # Option Quotes from 30. September 2014
 # Source: www.eurexchange.com, www.stoxx.com
 # 03_stf/ES50_imp_vol.py
 #
 # (c) Dr. Yves J. Hilpisch
 # Derivatives Analytics with Python
 #
 import numpy as np
 import pandas as pd
 from BSM_imp_vol import call_option
 import matplotlib as mpl
 import matplotlib.pyplot as plt
 mpl.rcParams['font.family'] = 'serif'

 # Pricing Data
 pdate = pd.Timestamp('30-09-2014')

 #
 # EURO STOXX 50 index data
 #

 # URL of data file
 es_url = 'http://www.stoxx.com/download/historical_values/hbrbcpe.txt'
 # column names to be used
 cols = ['Date', 'SX5P', 'SX5E', 'SXXP', 'SXXE',
        'SXXF', 'SXXA', 'DK5F', 'DKXF', 'DEL']
 # reading the data with pandas
 es = pd.read_csv(es_url,  # filename
                 header=None,  # ignore column names
                 index_col=0,  # index column (dates)
                 parse_dates=True,  # parse these dates
                 dayfirst=True,  # format of dates
                 skiprows=4,  # ignore these rows
                 sep=';',  # data separator
                 names=cols)  # use these column names
 # deleting the helper column
 del es['DEL']
 S0 = es['SX5E']['30-09-2014']
 r = -0.05

 #
 # Option Data
 #
 data = pd.read_csv('es50_option_data.csv', index_col=0)
 data['Date'] = data['Date'].apply(lambda x: pd.Timestamp(x))
 data['Maturity'] = data['Maturity'].apply(lambda x: pd.Timestamp(x))

 #
 # BSM Implied Volatilities
 #


 def calculate_imp_vols(data):
    ''' Calculate all implied volatilities for the European call options
    given the tolerance level for moneyness of the option.'''
    data['Imp_Vol'] = 0.0
    tol = 0.30  # tolerance for moneyness
    for row in data.index:
        t = data['Date'][row]
        T = data['Maturity'][row]
        ttm = (T - t).days / 365.
        forward = np.exp(r * ttm) * S0
        if (abs(data['Strike'][row] - forward) / forward) < tol:
            call = call_option(S0, data['Strike'][row], t, T, r, 0.2)
            data['Imp_Vol'][row] = call.imp_vol(data['Call'][row])
    return data

 #
 # Graphical Output
 #
 markers = ['.', 'o', '^', 'v', 'x', 'D', 'd', '>', '<']


 def plot_imp_vols(data):
    ''' Plot the implied volatilites. '''
    maturities = sorted(set(data['Maturity']))
    plt.figure(figsize=(10, 6))
    for i, mat in enumerate(maturities):
        dat = data[(data['Maturity'] == mat) & (data['Imp_Vol'] > 0)]
        plt.plot(dat['Strike'].values, dat['Imp_Vol'].values,
                 'b%s' % markers[i], label=str(mat)[:10])
    plt.grid(True)
    plt.legend()
    plt.xlabel('strike')
    plt.ylabel('implied volatility')
    plt.show()
diff --git a/es50_option_data.csv b/es50_option_data.csv
diff --git a/gbm_helper.py b/gbm_helper.py
 #
 # Analyzing Returns from Geometric Brownian Motion
 # 03_stf/GBM_returns.py
 #
 # (c) Dr. Yves J. Hilpisch
 # Derivatives Analytics with Python
 #
 import math
 import numpy as np
 import pandas as pd
 import scipy.stats as scs
 import statsmodels.api as sm
 import matplotlib as mpl
 import matplotlib.pyplot as plt
 plt.style.use('seaborn')
 mpl.rcParams['font.family'] = 'serif'

 #
 # Helper Function
 #


 def dN(x, mu, sigma):
    ''' Probability density function of a normal random variable x.

    Parameters
    ==========
    mu : float
        expected value
    sigma : float
        standard deviation

    Returns
    =======
    pdf : float
        value of probability density function
    '''
    z = (x - mu) / sigma
    pdf = np.exp(-0.5 * z ** 2) / math.sqrt(2 * math.pi * sigma ** 2)
    return pdf

 # Return Sample Statistics and Normality Tests

 def print_statistics(data):
    print("RETURN SAMPLE STATISTICS")
    print("---------------------------------------------")
    print("Mean of Daily  Log Returns %9.6f" % np.mean(data['returns']))
    print("Std  of Daily  Log Returns %9.6f" % np.std(data['returns']))
    print("Mean of Annua. Log Returns %9.6f" % (np.mean(data['returns']) * 252))
    print("Std  of Annua. Log Returns %9.6f" % \
                (np.std(data['returns']) * math.sqrt(252)))
    print("---------------------------------------------")
    print("Skew of Sample Log Returns %9.6f" % scs.skew(data['returns']))
    print("Skew Normal Test p-value   %9.6f" % scs.skewtest(data['returns'])[1])
    print("---------------------------------------------")
    print("Kurt of Sample Log Returns %9.6f" % scs.kurtosis(data['returns']))
    print("Kurt Normal Test p-value   %9.6f" % \
                scs.kurtosistest(data['returns'])[1])
    print("---------------------------------------------")
    print("Normal Test p-value        %9.6f" % \
                scs.normaltest(data['returns'])[1])
    print("---------------------------------------------")
    print("Realized Volatility        %9.6f" % data['rea_vol'].iloc[-1])
    print("Realized Variance          %9.6f" % data['rea_var'].iloc[-1])

 #
 # Graphical Output
 #

 # daily quotes and log returns
 def quotes_returns(data):
    ''' Plots quotes and returns. '''
    plt.figure(figsize=(10, 6))
    plt.subplot(211)
    data['index'].plot()
    plt.ylabel('daily quotes')
    plt.grid(True)
    plt.axis('tight')

    plt.subplot(212)
    data['returns'].plot()
    plt.ylabel('daily log returns')
    plt.grid(True)
    plt.axis('tight')

 # histogram of annualized daily log returns
 def return_histogram(data):
    ''' Plots a histogram of the returns. '''
    plt.figure(figsize=(10, 6))
    x = np.linspace(min(data['returns']), max(data['returns']), 100)
    plt.hist(np.array(data['returns']), bins=50, normed=True)
    y = dN(x, np.mean(data['returns']), np.std(data['returns']))
    plt.plot(x, y, linewidth=2)
    plt.xlabel('log returns')
    plt.ylabel('frequency/probability')
    plt.grid(True)

 # Q-Q plot of annualized daily log returns
 def return_qqplot(data):
    ''' Generates a Q-Q plot of the returns.'''
    plt.figure(figsize=(10, 6))
    sm.qqplot(data['returns'], line='s')
    plt.grid(True)
    plt.xlabel('theoretical quantiles')
    plt.ylabel('sample quantiles')


 # realized volatility
 def realized_volatility(data):
    ''' Plots the realized volatility. '''
    plt.figure(figsize=(10, 6))
    data['rea_vol'].plot()
    plt.ylabel('realized volatility')
    plt.grid(True)

 # mean return, volatility and correlation (252 days moving = 1 year)
 def rolling_statistics(data):
    ''' Calculates and plots rolling statistics (mean, std, correlation). '''
    plt.figure(figsize=(11, 8))

    plt.subplot(311)
    mr = pd.rolling_mean(data['returns'], 252) * 252
    mr.plot()
    plt.grid(True)
    plt.ylabel('returns (252d)')
    plt.axhline(mr.mean(), color='r', ls='dashed', lw=1.5)

    plt.subplot(312)
    vo = pd.rolling_std(data['returns'], 252) * math.sqrt(252)
    vo.plot()
    plt.grid(True)
    plt.ylabel('volatility (252d)')
    plt.axhline(vo.mean(), color='r', ls='dashed', lw=1.5)
    vx = plt.axis()

    plt.subplot(313)
    co = pd.rolling_corr(mr, vo, 252)
    co.plot()
    plt.grid(True)
    plt.ylabel('correlation (252d)')
    cx = plt.axis()
    plt.axis([vx[0], vx[1], cx[2], cx[3]])
    plt.axhline(co.mean(), color='r', ls='dashed', lw=1.5)
	#
	# Valuation of European Call Options in BSM Model
	# and Numerical Derivation of Implied Volatility
	# 03_stf/BSM_imp_vol.py
	#
	# (c) Dr. Yves J. Hilpisch
	# from Hilpisch, Yves (2014): Python for Finance, O'Reilly.
	#
	from math import log, sqrt, exp
	from scipy import stats
	from scipy.optimize import fsolve

	class call_option(object):
	''' Class for European call options in BSM Model.

	Attributes
	==========
	S0 : float
	initial stock/index level
	K : float
	strike price
	t : datetime/Timestamp object
	pricing date
	M : datetime/Timestamp object
	maturity date
	r : float
	constant risk-free short rate
	sigma : float
	volatility factor in diffusion term

	Methods
	=======
	value : float
	return present value of call option
	vega : float
	return vega of call option
	imp_vol : float
	return implied volatility given option quote
	'''

	def __init__(self, S0, K, t, M, r, sigma):
	self.S0 = float(S0)
	self.K = K
	self.t = t
	self.M = M
	self.r = r
	self.sigma = sigma

	def update_ttm(self):
	''' Updates time-to-maturity self.T. '''
	if self.t > self.M:
	raise ValueError("Pricing date later than maturity.")
	self.T = (self.M - self.t).days / 365.

	def d1(self):
	''' Helper function. '''
	d1 = ((log(self.S0 / self.K)
	+ (self.r + 0.5 * self.sigma ** 2) * self.T)
	/ (self.sigma * sqrt(self.T)))
	return d1

	def value(self):
	''' Return option value. '''
	self.update_ttm()
	d1 = self.d1()
	d2 = ((log(self.S0 / self.K)
	+ (self.r - 0.5 * self.sigma ** 2) * self.T)
	/ (self.sigma * sqrt(self.T)))
	value = (self.S0 * stats.norm.cdf(d1, 0.0, 1.0)
	- self.K * exp(-self.r * self.T) * stats.norm.cdf(d2, 0.0, 1.0))
	return value

	def vega(self):
	''' Return Vega of option. '''
	self.update_ttm()
	d1 = self.d1()
	vega = self.S0 * stats.norm.pdf(d1, 0.0, 1.0) * sqrt(self.T)
	return vega

	def imp_vol(self, C0, sigma_est=0.2):
	''' Return implied volatility given option price. '''
	option = call_option(self.S0, self.K, self.t, self.M,
	self.r, sigma_est)
	option.update_ttm()
	def difference(sigma):
	option.sigma = sigma
	return option.value() - C0
	iv = fsolve(difference, sigma_est)[0]
	return iv
	#
	# Black-Scholes-Merton Implied Volatilities of
	# Call Options on the EURO STOXX 50
	# Option Quotes from 30. September 2014
	# Source: www.eurexchange.com, www.stoxx.com
	# 03_stf/ES50_imp_vol.py
	#
	# (c) Dr. Yves J. Hilpisch
	# Derivatives Analytics with Python
	#
	import numpy as np
	import pandas as pd
	from BSM_imp_vol import call_option
	import matplotlib as mpl
	import matplotlib.pyplot as plt
	mpl.rcParams['font.family'] = 'serif'

	# Pricing Data
	pdate = pd.Timestamp('30-09-2014')

	#
	# EURO STOXX 50 index data
	#

	# URL of data file
	es_url = 'http://www.stoxx.com/download/historical_values/hbrbcpe.txt'
	# column names to be used
	cols = ['Date', 'SX5P', 'SX5E', 'SXXP', 'SXXE',
	'SXXF', 'SXXA', 'DK5F', 'DKXF', 'DEL']
	# reading the data with pandas
	es = pd.read_csv(es_url, # filename
	header=None, # ignore column names
	index_col=0, # index column (dates)
	parse_dates=True, # parse these dates
	dayfirst=True, # format of dates
	skiprows=4, # ignore these rows
	sep=';', # data separator
	names=cols) # use these column names
	# deleting the helper column
	del es['DEL']
	S0 = es['SX5E']['30-09-2014']
	r = -0.05

	#
	# Option Data
	#
	data = pd.read_csv('es50_option_data.csv', index_col=0)
	data['Date'] = data['Date'].apply(lambda x: pd.Timestamp(x))
	data['Maturity'] = data['Maturity'].apply(lambda x: pd.Timestamp(x))

	#
	# BSM Implied Volatilities
	#


	def calculate_imp_vols(data):
	''' Calculate all implied volatilities for the European call options
	given the tolerance level for moneyness of the option.'''
	data['Imp_Vol'] = 0.0
	tol = 0.30 # tolerance for moneyness
	for row in data.index:
	t = data['Date'][row]
	T = data['Maturity'][row]
	ttm = (T - t).days / 365.
	forward = np.exp(r * ttm) * S0
	if (abs(data['Strike'][row] - forward) / forward) < tol:
	call = call_option(S0, data['Strike'][row], t, T, r, 0.2)
	data['Imp_Vol'][row] = call.imp_vol(data['Call'][row])
	return data

	#
	# Graphical Output
	#
	markers = ['.', 'o', '^', 'v', 'x', 'D', 'd', '>', '<']


	def plot_imp_vols(data):
	''' Plot the implied volatilites. '''
	maturities = sorted(set(data['Maturity']))
	plt.figure(figsize=(10, 6))
	for i, mat in enumerate(maturities):
	dat = data[(data['Maturity'] == mat) & (data['Imp_Vol'] > 0)]
	plt.plot(dat['Strike'].values, dat['Imp_Vol'].values,
	'b%s' % markers[i], label=str(mat)[:10])
	plt.grid(True)
	plt.legend()
	plt.xlabel('strike')
	plt.ylabel('implied volatility')
	plt.show()
	Date	Strike	Call	Maturity	Put
0	2014-09-30	1850.0	1373.6	2014-12-19	0.5
1	2014-09-30	1900.0	1323.7	2014-12-19	0.6
2	2014-09-30	1950.0	1273.8	2014-12-19	0.8
3	2014-09-30	2000.0	1223.9	2014-12-19	0.9
4	2014-09-30	2050.0	1174.1	2014-12-19	1.1
5	2014-09-30	2100.0	1124.3	2014-12-19	1.3
6	2014-09-30	2150.0	1074.5	2014-12-19	1.5
7	2014-09-30	2200.0	1024.8	2014-12-19	1.7
8	2014-09-30	2250.0	975.1	2014-12-19	2.1
9	2014-09-30	2300.0	925.4	2014-12-19	2.4
10	2014-09-30	2350.0	875.9	2014-12-19	2.9
11	2014-09-30	2400.0	826.4	2014-12-19	3.4
12	2014-09-30	2450.0	777.0	2014-12-19	4.0
13	2014-09-30	2500.0	727.8	2014-12-19	4.8
14	2014-09-30	2550.0	678.7	2014-12-19	5.7
15	2014-09-30	2600.0	629.9	2014-12-19	6.9
16	2014-09-30	2625.0	605.6	2014-12-19	7.6
17	2014-09-30	2650.0	581.3	2014-12-19	8.3
18	2014-09-30	2675.0	557.2	2014-12-19	9.2
19	2014-09-30	2700.0	533.2	2014-12-19	10.1
20	2014-09-30	2725.0	509.2	2014-12-19	11.2
21	2014-09-30	2750.0	485.4	2014-12-19	12.4
22	2014-09-30	2775.0	461.8	2014-12-19	13.8
23	2014-09-30	2800.0	438.3	2014-12-19	15.3
24	2014-09-30	2825.0	415.0	2014-12-19	17.0
25	2014-09-30	2850.0	391.9	2014-12-19	18.9
26	2014-09-30	2875.0	369.0	2014-12-19	21.0
27	2014-09-30	2900.0	346.4	2014-12-19	23.4
28	2014-09-30	2925.0	324.1	2014-12-19	26.0
29	2014-09-30	2950.0	302.0	2014-12-19	29.0
30	2014-09-30	2975.0	280.4	2014-12-19	32.4
31	2014-09-30	3000.0	259.2	2014-12-19	36.2
32	2014-09-30	3025.0	238.4	2014-12-19	40.4
33	2014-09-30	3050.0	218.1	2014-12-19	45.1
34	2014-09-30	3075.0	198.5	2014-12-19	50.5
35	2014-09-30	3100.0	179.4	2014-12-19	56.4
36	2014-09-30	3125.0	161.1	2014-12-19	63.1
37	2014-09-30	3150.0	143.5	2014-12-19	70.5
38	2014-09-30	3175.0	126.8	2014-12-19	78.8
39	2014-09-30	3200.0	110.9	2014-12-19	87.9
40	2014-09-30	3225.0	96.1	2014-12-19	98.1
41	2014-09-30	3250.0	82.3	2014-12-19	109.3
42	2014-09-30	3275.0	69.6	2014-12-19	121.6
43	2014-09-30	3300.0	58.1	2014-12-19	135.1
44	2014-09-30	3325.0	47.8	2014-12-19	149.8
45	2014-09-30	3350.0	38.8	2014-12-19	165.8
46	2014-09-30	3375.0	31.0	2014-12-19	183.0
47	2014-09-30	3400.0	24.4	2014-12-19	201.4
48	2014-09-30	3425.0	18.9	2014-12-19	221.0
49	2014-09-30	3450.0	14.5	2014-12-19	241.5
50	2014-09-30	3475.0	10.9	2014-12-19	262.9
51	2014-09-30	3500.0	8.0	2014-12-19	285.1
52	2014-09-30	3525.0	5.9	2014-12-19	307.9
53	2014-09-30	3550.0	4.3	2014-12-19	331.3
54	2014-09-30	3575.0	3.1	2014-12-19	355.1
55	2014-09-30	3600.0	2.2	2014-12-19	379.2
56	2014-09-30	3625.0	1.6	2014-12-19	403.6
57	2014-09-30	3650.0	1.1	2014-12-19	428.1
58	2014-09-30	3700.0	0.6	2014-12-19	477.6
59	2014-09-30	1000.0	2128.6	2015-12-18	0.7
60	2014-09-30	1100.0	2029.1	2015-12-18	1.1
61	2014-09-30	1200.0	1929.6	2015-12-18	1.7
62	2014-09-30	1300.0	1830.4	2015-12-18	2.5
63	2014-09-30	1400.0	1731.4	2015-12-18	3.4
64	2014-09-30	1500.0	1632.7	2015-12-18	4.7
65	2014-09-30	1600.0	1534.4	2015-12-18	6.4
66	2014-09-30	1700.0	1436.6	2015-12-18	8.6
67	2014-09-30	1750.0	1388.0	2015-12-18	9.9
68	2014-09-30	1800.0	1339.5	2015-12-18	11.5
69	2014-09-30	1850.0	1291.2	2015-12-18	13.2
70	2014-09-30	1900.0	1243.2	2015-12-18	15.1
71	2014-09-30	1950.0	1195.4	2015-12-18	17.3
72	2014-09-30	2000.0	1147.8	2015-12-18	19.7
73	2014-09-30	2050.0	1100.6	2015-12-18	22.5
74	2014-09-30	2100.0	1053.7	2015-12-18	25.6
75	2014-09-30	2150.0	1007.1	2015-12-18	29.0
76	2014-09-30	2200.0	961.0	2015-12-18	32.8
77	2014-09-30	2250.0	915.3	2015-12-18	37.1
78	2014-09-30	2300.0	870.1	2015-12-18	41.9
79	2014-09-30	2350.0	825.4	2015-12-18	47.3
80	2014-09-30	2400.0	781.4	2015-12-18	53.2
81	2014-09-30	2450.0	738.0	2015-12-18	59.8
82	2014-09-30	2500.0	695.5	2015-12-18	67.3
83	2014-09-30	2550.0	653.6	2015-12-18	75.4
84	2014-09-30	2600.0	612.9	2015-12-18	84.7
85	2014-09-30	2650.0	573.2	2015-12-18	94.9
86	2014-09-30	2700.0	534.5	2015-12-18	106.2
87	2014-09-30	2750.0	496.9	2015-12-18	118.6
88	2014-09-30	2800.0	460.3	2015-12-18	132.1
89	2014-09-30	2850.0	425.0	2015-12-18	146.6
90	2014-09-30	2900.0	390.5	2015-12-18	162.2
91	2014-09-30	2950.0	357.6	2015-12-18	179.3
92	2014-09-30	3000.0	325.8	2015-12-18	197.7
93	2014-09-30	3050.0	295.7	2015-12-18	217.3
94	2014-09-30	3100.0	267.2	2015-12-18	238.8
95	2014-09-30	3150.0	240.1	2015-12-18	261.7
96	2014-09-30	3200.0	214.7	2015-12-18	286.4
97	2014-09-30	3250.0	191.1	2015-12-18	312.9
98	2014-09-30	3300.0	169.3	2015-12-18	340.9
99	2014-09-30	3350.0	149.1	2015-12-18	370.7
100	2014-09-30	3400.0	130.7	2015-12-18	402.3
101	2014-09-30	3450.0	113.9	2015-12-18	435.5
102	2014-09-30	3500.0	98.7	2015-12-18	470.3
103	2014-09-30	3550.0	85.1	2015-12-18	506.7
104	2014-09-30	3600.0	72.9	2015-12-18	544.4
105	2014-09-30	3650.0	62.0	2015-12-18	583.6
106	2014-09-30	3700.0	52.4	2015-12-18	624.0
107	2014-09-30	3750.0	44.0	2015-12-18	665.5
108	2014-09-30	3800.0	36.6	2015-12-18	708.2
109	2014-09-30	3850.0	30.3	2015-12-18	751.8
110	2014-09-30	3900.0	24.9	2015-12-18	796.4
111	2014-09-30	3950.0	20.4	2015-12-18	841.8
112	2014-09-30	4000.0	16.6	2015-12-18	888.0
113	2014-09-30	4100.0	10.8	2015-12-18	982.3
114	2014-09-30	4200.0	7.0	2015-12-18	1078.4
115	2014-09-30	4300.0	4.5	2015-12-18	1175.9
116	2014-09-30	4400.0	2.9	2015-12-18	1274.2
117	2014-09-30	4500.0	1.8	2015-12-18	1373.2
118	2014-09-30	4600.0	1.1	2015-12-18	1472.5
119	2014-09-30	4700.0	0.7	2015-12-18	1572.1
120	2014-09-30	4800.0	0.5	2015-12-18	1671.8
121	2014-09-30	700.0	2337.6	2016-12-16	0.5
122	2014-09-30	800.0	2238.1	2016-12-16	0.9
123	2014-09-30	900.0	2138.9	2016-12-16	1.7
124	2014-09-30	1000.0	2040.1	2016-12-16	2.7
125	2014-09-30	1100.0	1941.6	2016-12-16	4.2
126	2014-09-30	1200.0	1843.7	2016-12-16	6.3
127	2014-09-30	1300.0	1746.4	2016-12-16	8.9
128	2014-09-30	1400.0	1649.8	2016-12-16	12.2
129	2014-09-30	1500.0	1554.0	2016-12-16	16.4
130	2014-09-30	1600.0	1459.2	2016-12-16	21.6
131	2014-09-30	1700.0	1365.6	2016-12-16	27.9
132	2014-09-30	1800.0	1273.3	2016-12-16	35.5
133	2014-09-30	1900.0	1182.5	2016-12-16	44.7
134	2014-09-30	2000.0	1093.6	2016-12-16	55.7
135	2014-09-30	2100.0	1006.8	2016-12-16	68.8
136	2014-09-30	2150.0	964.3	2016-12-16	76.3
137	2014-09-30	2200.0	922.4	2016-12-16	84.4
138	2014-09-30	2250.0	881.2	2016-12-16	93.2
139	2014-09-30	2300.0	840.8	2016-12-16	102.6
140	2014-09-30	2350.0	801.2	2016-12-16	113.0
141	2014-09-30	2400.0	762.2	2016-12-16	124.0
142	2014-09-30	2450.0	724.0	2016-12-16	135.9
143	2014-09-30	2500.0	686.8	2016-12-16	148.7
144	2014-09-30	2550.0	650.7	2016-12-16	162.5
145	2014-09-30	2600.0	615.3	2016-12-16	177.1
146	2014-09-30	2650.0	581.1	2016-12-16	192.9
147	2014-09-30	2700.0	547.8	2016-12-16	209.5
148	2014-09-30	2750.0	515.6	2016-12-16	227.3
149	2014-09-30	2800.0	484.3	2016-12-16	246.0
150	2014-09-30	2850.0	454.4	2016-12-16	266.0
151	2014-09-30	2900.0	425.4	2016-12-16	287.0
152	2014-09-30	2950.0	397.8	2016-12-16	309.1
153	2014-09-30	3000.0	370.9	2016-12-16	332.4
154	2014-09-30	3050.0	345.6	2016-12-16	357.0
155	2014-09-30	3100.0	321.2	2016-12-16	382.6
156	2014-09-30	3150.0	298.1	2016-12-16	409.6
157	2014-09-30	3200.0	276.2	2016-12-16	437.5
158	2014-09-30	3250.0	255.2	2016-12-16	466.7
159	2014-09-30	3300.0	235.7	2016-12-16	497.0
160	2014-09-30	3350.0	217.0	2016-12-16	528.3
161	2014-09-30	3400.0	199.7	2016-12-16	560.9
162	2014-09-30	3450.0	183.2	2016-12-16	594.4
163	2014-09-30	3500.0	167.9	2016-12-16	629.0
164	2014-09-30	3550.0	153.6	2016-12-16	664.8
165	2014-09-30	3600.0	140.2	2016-12-16	701.4
166	2014-09-30	3650.0	127.7	2016-12-16	738.8
167	2014-09-30	3700.0	116.3	2016-12-16	777.3
168	2014-09-30	3750.0	105.8	2016-12-16	816.8
169	2014-09-30	3800.0	95.9	2016-12-16	857.0
170	2014-09-30	3850.0	86.9	2016-12-16	897.9
171	2014-09-30	3900.0	78.5	2016-12-16	939.6
172	2014-09-30	3950.0	71.1	2016-12-16	982.1
173	2014-09-30	4000.0	64.1	2016-12-16	1025.0
174	2014-09-30	4100.0	52.0	2016-12-16	1112.9
175	2014-09-30	4200.0	42.0	2016-12-16	1202.8
176	2014-09-30	4300.0	33.8	2016-12-16	1294.5
177	2014-09-30	4400.0	27.1	2016-12-16	1387.7
178	2014-09-30	4500.0	21.6	2016-12-16	1482.2
179	2014-09-30	4600.0	17.2	2016-12-16	1577.8
180	2014-09-30	4700.0	13.7	2016-12-16	1674.2
181	2014-09-30	4800.0	10.9	2016-12-16	1771.3
182	2014-09-30	4900.0	8.6	2016-12-16	1869.0
183	2014-09-30	5000.0	6.8	2016-12-16	1967.1
184	2014-09-30	5200.0	4.2	2016-12-16	2164.4
185	2014-09-30	5400.0	2.6	2016-12-16	2362.7
186	2014-09-30	5600.0	1.6	2016-12-16	2561.6
187	2014-09-30	5800.0	1.0	2016-12-16	2760.8
188	2014-09-30	6000.0	0.6	2016-12-16	2960.3
189	2014-09-30	1200.0	1946.1	2015-06-19	0.5
190	2014-09-30	1250.0	1896.2	2015-06-19	0.6
191	2014-09-30	1300.0	1846.4	2015-06-19	0.8
192	2014-09-30	1350.0	1796.5	2015-06-19	0.9
193	2014-09-30	1400.0	1746.7	2015-06-19	1.1
194	2014-09-30	1450.0	1697.0	2015-06-19	1.4
195	2014-09-30	1500.0	1647.2	2015-06-19	1.6
196	2014-09-30	1550.0	1597.6	2015-06-19	1.9
197	2014-09-30	1600.0	1547.9	2015-06-19	2.3
198	2014-09-30	1650.0	1498.3	2015-06-19	2.7
199	2014-09-30	1700.0	1448.8	2015-06-19	3.2
200	2014-09-30	1750.0	1399.3	2015-06-19	3.7
201	2014-09-30	1800.0	1349.9	2015-06-19	4.3
202	2014-09-30	1850.0	1300.6	2015-06-19	5.0
203	2014-09-30	1900.0	1251.4	2015-06-19	5.8
204	2014-09-30	1950.0	1202.3	2015-06-19	6.7
205	2014-09-30	2000.0	1153.3	2015-06-19	7.7
206	2014-09-30	2050.0	1104.5	2015-06-19	8.9
207	2014-09-30	2100.0	1055.9	2015-06-19	10.3
208	2014-09-30	2150.0	1007.6	2015-06-19	11.9
209	2014-09-30	2200.0	959.4	2015-06-19	13.8
210	2014-09-30	2250.0	911.6	2015-06-19	16.0
211	2014-09-30	2300.0	864.1	2015-06-19	18.5
212	2014-09-30	2350.0	817.1	2015-06-19	21.4
213	2014-09-30	2400.0	770.4	2015-06-19	24.8
214	2014-09-30	2450.0	724.3	2015-06-19	28.7
215	2014-09-30	2500.0	678.7	2015-06-19	33.1
216	2014-09-30	2550.0	633.8	2015-06-19	38.2
217	2014-09-30	2600.0	589.6	2015-06-19	44.0
218	2014-09-30	2650.0	546.2	2015-06-19	50.6
219	2014-09-30	2700.0	503.7	2015-06-19	58.1
220	2014-09-30	2750.0	462.2	2015-06-19	66.6
221	2014-09-30	2800.0	421.8	2015-06-19	76.2
222	2014-09-30	2850.0	382.6	2015-06-19	87.0
223	2014-09-30	2900.0	344.8	2015-06-19	99.1
224	2014-09-30	2950.0	308.5	2015-06-19	112.9
225	2014-09-30	3000.0	274.0	2015-06-19	128.3
226	2014-09-30	3050.0	241.3	2015-06-19	145.7
227	2014-09-30	3100.0	210.8	2015-06-19	165.2
228	2014-09-30	3150.0	182.4	2015-06-19	186.8
229	2014-09-30	3200.0	156.4	2015-06-19	210.6
230	2014-09-30	3250.0	132.4	2015-06-19	236.8
231	2014-09-30	3300.0	110.9	2015-06-19	265.3
232	2014-09-30	3350.0	91.7	2015-06-19	296.1
233	2014-09-30	3400.0	74.8	2015-06-19	329.1
234	2014-09-30	3450.0	60.1	2015-06-19	364.4
235	2014-09-30	3500.0	47.6	2015-06-19	401.9
236	2014-09-30	3550.0	37.1	2015-06-19	441.4
237	2014-09-30	3600.0	28.5	2015-06-19	482.9
238	2014-09-30	3650.0	21.6	2015-06-19	526.0
239	2014-09-30	3700.0	16.2	2015-06-19	570.5
240	2014-09-30	3750.0	12.0	2015-06-19	616.3
241	2014-09-30	3800.0	8.8	2015-06-19	663.2
242	2014-09-30	3850.0	6.4	2015-06-19	710.8
243	2014-09-30	3900.0	4.7	2015-06-19	759.0
244	2014-09-30	3950.0	3.3	2015-06-19	807.7
245	2014-09-30	4000.0	2.4	2015-06-19	856.7
246	2014-09-30	4100.0	1.2	2015-06-19	955.5
247	2014-09-30	4200.0	0.6	2015-06-19	1054.9
248	2014-09-30	800.0	2248.7	2016-06-17	0.6
249	2014-09-30	900.0	2149.2	2016-06-17	1.1
250	2014-09-30	1000.0	2050.0	2016-06-17	1.9
251	2014-09-30	1500.0	1559.5	2016-06-17	11.2
252	2014-09-30	1600.0	1463.1	2016-06-17	14.8
253	2014-09-30	1700.0	1367.6	2016-06-17	19.2
254	2014-09-30	1800.0	1273.0	2016-06-17	24.6
255	2014-09-30	1850.0	1226.2	2016-06-17	27.8
256	2014-09-30	1900.0	1179.8	2016-06-17	31.3
257	2014-09-30	1950.0	1133.6	2016-06-17	35.2
258	2014-09-30	2000.0	1088.0	2016-06-17	39.5
259	2014-09-30	2050.0	1042.7	2016-06-17	44.2
260	2014-09-30	2100.0	998.0	2016-06-17	49.5
261	2014-09-30	2150.0	953.8	2016-06-17	55.2
262	2014-09-30	2200.0	910.1	2016-06-17	61.6
263	2014-09-30	2250.0	867.1	2016-06-17	68.6
264	2014-09-30	2300.0	824.8	2016-06-17	76.2
265	2014-09-30	2350.0	783.1	2016-06-17	84.5
266	2014-09-30	2400.0	742.2	2016-06-17	93.6
267	2014-09-30	2450.0	702.2	2016-06-17	103.5
268	2014-09-30	2500.0	662.8	2016-06-17	114.2
269	2014-09-30	2550.0	624.4	2016-06-17	125.8
270	2014-09-30	2600.0	586.9	2016-06-17	138.3
271	2014-09-30	2650.0	550.5	2016-06-17	151.8
272	2014-09-30	2700.0	515.1	2016-06-17	166.2
273	2014-09-30	2750.0	480.7	2016-06-17	182.0
274	2014-09-30	2800.0	447.7	2016-06-17	198.9
275	2014-09-30	2850.0	415.7	2016-06-17	216.9
276	2014-09-30	2900.0	385.2	2016-06-17	236.5
277	2014-09-30	2950.0	355.9	2016-06-17	257.0
278	2014-09-30	3000.0	327.9	2016-06-17	279.1
279	2014-09-30	3050.0	301.4	2016-06-17	302.6
280	2014-09-30	3100.0	276.3	2016-06-17	327.4
281	2014-09-30	3150.0	252.5	2016-06-17	353.6
282	2014-09-30	3200.0	230.1	2016-06-17	381.2
283	2014-09-30	3250.0	208.9	2016-06-17	410.2
284	2014-09-30	3300.0	189.3	2016-06-17	440.4
285	2014-09-30	3350.0	170.9	2016-06-17	472.0
286	2014-09-30	3400.0	153.9	2016-06-17	504.9
287	2014-09-30	3450.0	138.2	2016-06-17	539.2
288	2014-09-30	3500.0	123.7	2016-06-17	574.7
289	2014-09-30	3550.0	110.4	2016-06-17	611.3
290	2014-09-30	3600.0	98.3	2016-06-17	649.2
291	2014-09-30	3650.0	87.2	2016-06-17	688.0
292	2014-09-30	3700.0	77.2	2016-06-17	728.0
293	2014-09-30	3750.0	68.1	2016-06-17	768.9
294	2014-09-30	3800.0	59.9	2016-06-17	810.7
295	2014-09-30	3850.0	52.5	2016-06-17	853.3
296	2014-09-30	3900.0	45.9	2016-06-17	896.7
297	2014-09-30	3950.0	40.0	2016-06-17	940.8
298	2014-09-30	4000.0	34.7	2016-06-17	985.5
299	2014-09-30	1400.0	1817.2	2015-03-20	0.5
300	2014-09-30	1450.0	1767.3	2015-03-20	0.5
301	2014-09-30	1500.0	1717.4	2015-03-20	0.7
302	2014-09-30	1550.0	1667.5	2015-03-20	0.8
303	2014-09-30	1600.0	1617.7	2015-03-20	0.9
304	2014-09-30	1650.0	1567.8	2015-03-20	1.1
305	2014-09-30	1700.0	1518.0	2015-03-20	1.3
306	2014-09-30	1750.0	1468.2	2015-03-20	1.5
307	2014-09-30	1800.0	1418.5	2015-03-20	1.8
308	2014-09-30	1850.0	1368.8	2015-03-20	2.1
309	2014-09-30	1900.0	1319.2	2015-03-20	2.4
310	2014-09-30	1950.0	1269.6	2015-03-20	2.8
311	2014-09-30	2000.0	1220.0	2015-03-20	3.3
312	2014-09-30	2050.0	1170.6	2015-03-20	3.9
313	2014-09-30	2100.0	1121.2	2015-03-20	4.5
314	2014-09-30	2150.0	1071.9	2015-03-20	5.2
315	2014-09-30	2200.0	1022.8	2015-03-20	6.0
316	2014-09-30	2250.0	973.7	2015-03-20	7.0
317	2014-09-30	2300.0	924.9	2015-03-20	8.1
318	2014-09-30	2350.0	876.2	2015-03-20	9.5
319	2014-09-30	2400.0	827.8	2015-03-20	11.1
320	2014-09-30	2450.0	779.7	2015-03-20	12.9
321	2014-09-30	2500.0	731.9	2015-03-20	15.2
322	2014-09-30	2550.0	684.5	2015-03-20	17.8
323	2014-09-30	2600.0	637.6	2015-03-20	20.9
324	2014-09-30	2650.0	591.2	2015-03-20	24.4
325	2014-09-30	2700.0	545.4	2015-03-20	28.6
326	2014-09-30	2750.0	500.3	2015-03-20	33.6
327	2014-09-30	2800.0	456.2	2015-03-20	39.5
328	2014-09-30	2825.0	434.5	2015-03-20	42.8
329	2014-09-30	2850.0	413.1	2015-03-20	46.4
330	2014-09-30	2875.0	392.0	2015-03-20	50.3
331	2014-09-30	2900.0	371.2	2015-03-20	54.5
332	2014-09-30	2925.0	350.8	2015-03-20	59.1
333	2014-09-30	2950.0	330.7	2015-03-20	64.0
334	2014-09-30	2975.0	311.0	2015-03-20	69.3
335	2014-09-30	3000.0	291.7	2015-03-20	75.0
336	2014-09-30	3025.0	272.8	2015-03-20	81.1
337	2014-09-30	3050.0	254.5	2015-03-20	87.8
338	2014-09-30	3075.0	236.6	2015-03-20	94.9
339	2014-09-30	3100.0	219.3	2015-03-20	102.6
340	2014-09-30	3125.0	202.6	2015-03-20	110.8
341	2014-09-30	3150.0	186.4	2015-03-20	119.7
342	2014-09-30	3175.0	171.0	2015-03-20	129.2
343	2014-09-30	3200.0	156.1	2015-03-20	139.4
344	2014-09-30	3225.0	142.0	2015-03-20	150.3
345	2014-09-30	3250.0	128.5	2015-03-20	161.8
346	2014-09-30	3275.0	115.8	2015-03-20	174.0
347	2014-09-30	3300.0	103.7	2015-03-20	187.0
348	2014-09-30	3325.0	92.5	2015-03-20	200.8
349	2014-09-30	3350.0	82.0	2015-03-20	215.3
350	2014-09-30	3375.0	72.2	2015-03-20	230.5
351	2014-09-30	3400.0	63.3	2015-03-20	246.6
352	2014-09-30	3425.0	55.1	2015-03-20	263.4
353	2014-09-30	3450.0	47.7	2015-03-20	281.0
354	2014-09-30	3475.0	41.0	2015-03-20	299.3
355	2014-09-30	3500.0	35.1	2015-03-20	318.4
356	2014-09-30	3525.0	29.8	2015-03-20	338.1
357	2014-09-30	3550.0	25.2	2015-03-20	358.4
358	2014-09-30	3575.0	21.1	2015-03-20	379.4
359	2014-09-30	3600.0	17.6	2015-03-20	400.8
360	2014-09-30	3625.0	14.5	2015-03-20	422.8
361	2014-09-30	3650.0	11.9	2015-03-20	445.2
362	2014-09-30	3700.0	7.9	2015-03-20	491.2
363	2014-09-30	3750.0	5.1	2015-03-20	538.4
364	2014-09-30	3800.0	3.2	2015-03-20	586.5
365	2014-09-30	3850.0	2.0	2015-03-20	635.3
366	2014-09-30	3900.0	1.3	2015-03-20	684.6
367	2014-09-30	3950.0	0.8	2015-03-20	734.1
368	2014-09-30	4000.0	0.5	2015-03-20	783.8
369	2014-09-30	2025.0	1202.2	2014-11-21	0.5
370	2014-09-30	2050.0	1177.3	2014-11-21	0.5
371	2014-09-30	2075.0	1152.3	2014-11-21	0.6
372	2014-09-30	2100.0	1127.3	2014-11-21	0.6
373	2014-09-30	2125.0	1102.4	2014-11-21	0.7
374	2014-09-30	2150.0	1077.5	2014-11-21	0.7
375	2014-09-30	2175.0	1052.5	2014-11-21	0.8
376	2014-09-30	2200.0	1027.6	2014-11-21	0.9
377	2014-09-30	2225.0	1002.7	2014-11-21	0.9
378	2014-09-30	2250.0	977.8	2014-11-21	1.0
379	2014-09-30	2275.0	952.8	2014-11-21	1.1
380	2014-09-30	2300.0	928.0	2014-11-21	1.2
381	2014-09-30	2325.0	903.1	2014-11-21	1.3
382	2014-09-30	2350.0	878.2	2014-11-21	1.4
383	2014-09-30	2375.0	853.3	2014-11-21	1.6
384	2014-09-30	2400.0	828.4	2014-11-21	1.7
385	2014-09-30	2425.0	803.6	2014-11-21	1.9
386	2014-09-30	2450.0	778.8	2014-11-21	2.0
387	2014-09-30	2475.0	753.9	2014-11-21	2.2
388	2014-09-30	2500.0	729.1	2014-11-21	2.4
389	2014-09-30	2525.0	704.3	2014-11-21	2.6
390	2014-09-30	2550.0	679.6	2014-11-21	2.8
391	2014-09-30	2575.0	654.9	2014-11-21	3.1
392	2014-09-30	2600.0	630.2	2014-11-21	3.4
393	2014-09-30	2625.0	605.5	2014-11-21	3.8
394	2014-09-30	2650.0	580.9	2014-11-21	4.2
395	2014-09-30	2675.0	556.3	2014-11-21	4.6
396	2014-09-30	2700.0	531.8	2014-11-21	5.1
397	2014-09-30	2725.0	507.4	2014-11-21	5.6
398	2014-09-30	2750.0	483.0	2014-11-21	6.3
399	2014-09-30	2775.0	458.7	2014-11-21	7.0
400	2014-09-30	2800.0	434.5	2014-11-21	7.8
401	2014-09-30	2825.0	410.5	2014-11-21	8.8
402	2014-09-30	2850.0	386.6	2014-11-21	9.9
403	2014-09-30	2875.0	362.8	2014-11-21	11.1
404	2014-09-30	2900.0	339.3	2014-11-21	12.6
405	2014-09-30	2925.0	316.0	2014-11-21	14.2
406	2014-09-30	2950.0	292.9	2014-11-21	16.2
407	2014-09-30	2975.0	270.2	2014-11-21	18.4
408	2014-09-30	3000.0	247.8	2014-11-21	21.1
409	2014-09-30	3025.0	225.9	2014-11-21	24.2
410	2014-09-30	3050.0	204.5	2014-11-21	27.8
411	2014-09-30	3075.0	183.7	2014-11-21	32.0
412	2014-09-30	3100.0	163.6	2014-11-21	36.9
413	2014-09-30	3125.0	144.3	2014-11-21	42.5
414	2014-09-30	3150.0	125.8	2014-11-21	49.1
415	2014-09-30	3175.0	108.3	2014-11-21	56.6
416	2014-09-30	3200.0	91.9	2014-11-21	65.2
417	2014-09-30	3225.0	76.7	2014-11-21	75.0
418	2014-09-30	3250.0	62.8	2014-11-21	86.1
419	2014-09-30	3275.0	50.4	2014-11-21	98.7
420	2014-09-30	3300.0	39.6	2014-11-21	112.9
421	2014-09-30	3325.0	30.3	2014-11-21	128.6
422	2014-09-30	3350.0	22.6	2014-11-21	145.9
423	2014-09-30	3375.0	16.4	2014-11-21	164.7
424	2014-09-30	3400.0	11.6	2014-11-21	184.9
425	2014-09-30	3425.0	8.0	2014-11-21	206.3
426	2014-09-30	3450.0	5.4	2014-11-21	228.7
427	2014-09-30	3475.0	3.5	2014-11-21	251.8
428	2014-09-30	3500.0	2.3	2014-11-21	275.6
429	2014-09-30	3525.0	1.5	2014-11-21	299.8
430	2014-09-30	3550.0	1.0	2014-11-21	324.2
431	2014-09-30	3575.0	0.6	2014-11-21	348.9
432	2014-09-30	2575.0	658.2	2014-10-17	0.5
433	2014-09-30	2600.0	633.3	2014-10-17	0.5
434	2014-09-30	2625.0	608.3	2014-10-17	0.6
435	2014-09-30	2650.0	583.4	2014-10-17	0.6
436	2014-09-30	2675.0	558.5	2014-10-17	0.7
437	2014-09-30	2700.0	533.6	2014-10-17	0.8
438	2014-09-30	2725.0	508.7	2014-10-17	0.9
439	2014-09-30	2750.0	483.8	2014-10-17	1.0
440	2014-09-30	2775.0	458.9	2014-10-17	1.2
441	2014-09-30	2800.0	434.1	2014-10-17	1.3
442	2014-09-30	2825.0	409.3	2014-10-17	1.5
443	2014-09-30	2850.0	384.5	2014-10-17	1.8
444	2014-09-30	2875.0	359.8	2014-10-17	2.1
445	2014-09-30	2900.0	335.2	2014-10-17	2.4
446	2014-09-30	2925.0	310.6	2014-10-17	2.8
447	2014-09-30	2950.0	286.1	2014-10-17	3.4
448	2014-09-30	2975.0	261.8	2014-10-17	4.0
449	2014-09-30	3000.0	237.7	2014-10-17	4.9
450	2014-09-30	3025.0	213.8	2014-10-17	6.0
451	2014-09-30	3050.0	190.2	2014-10-17	7.4
452	2014-09-30	3075.0	167.0	2014-10-17	9.3
453	2014-09-30	3100.0	144.5	2014-10-17	11.7
454	2014-09-30	3125.0	122.7	2014-10-17	14.9
455	2014-09-30	3150.0	101.8	2014-10-17	19.1
456	2014-09-30	3175.0	82.3	2014-10-17	24.5
457	2014-09-30	3200.0	64.3	2014-10-17	31.5
458	2014-09-30	3225.0	48.3	2014-10-17	40.5
459	2014-09-30	3250.0	34.6	2014-10-17	51.8
460	2014-09-30	3275.0	23.5	2014-10-17	65.8
461	2014-09-30	3300.0	15.1	2014-10-17	82.3
462	2014-09-30	3325.0	9.1	2014-10-17	101.3
463	2014-09-30	3350.0	5.1	2014-10-17	122.4
464	2014-09-30	3375.0	2.8	2014-10-17	145.0
465	2014-09-30	3400.0	1.5	2014-10-17	168.7
466	2014-09-30	3425.0	0.8	2014-10-17	193.0
467	2014-09-30	1500.0	1644.3	2015-09-18	3.1
468	2014-09-30	2000.0	1154.6	2015-09-18	13.4
469	2014-09-30	2100.0	1058.8	2015-09-18	17.5
470	2014-09-30	2200.0	964.1	2015-09-18	22.8
471	2014-09-30	2300.0	870.9	2015-09-18	29.6
472	2014-09-30	2400.0	779.7	2015-09-18	38.4
473	2014-09-30	2500.0	690.8	2015-09-18	49.5
474	2014-09-30	2550.0	647.4	2015-09-18	56.0
475	2014-09-30	2600.0	604.7	2015-09-18	63.4
476	2014-09-30	2650.0	563.0	2015-09-18	71.6
477	2014-09-30	2700.0	522.2	2015-09-18	80.8
478	2014-09-30	2750.0	482.4	2015-09-18	91.1
479	2014-09-30	2800.0	443.9	2015-09-18	102.6
480	2014-09-30	2850.0	406.5	2015-09-18	115.2
481	2014-09-30	2900.0	370.6	2015-09-18	129.2
482	2014-09-30	2950.0	336.1	2015-09-18	144.7
483	2014-09-30	3000.0	303.1	2015-09-18	161.8
484	2014-09-30	3050.0	271.9	2015-09-18	180.5
485	2014-09-30	3100.0	242.3	2015-09-18	201.0
486	2014-09-30	3150.0	214.7	2015-09-18	223.3
487	2014-09-30	3200.0	188.9	2015-09-18	247.5
488	2014-09-30	3250.0	164.9	2015-09-18	273.4
489	2014-09-30	3300.0	143.0	2015-09-18	301.6
490	2014-09-30	3350.0	123.0	2015-09-18	331.7
491	2014-09-30	3400.0	104.9	2015-09-18	363.5
492	2014-09-30	3450.0	88.8	2015-09-18	397.4
493	2014-09-30	3500.0	74.5	2015-09-18	433.1
494	2014-09-30	3550.0	62.0	2015-09-18	470.6
495	2014-09-30	3600.0	51.2	2015-09-18	509.8
496	2014-09-30	3650.0	41.9	2015-09-18	550.5
497	2014-09-30	3700.0	34.0	2015-09-18	592.6
498	2014-09-30	3750.0	27.4	2015-09-18	635.9
499	2014-09-30	3800.0	21.8	2015-09-18	680.3
500	2014-09-30	3850.0	17.2	2015-09-18	725.7
501	2014-09-30	3900.0	13.4	2015-09-18	772.0
502	2014-09-30	3950.0	10.4	2015-09-18	818.9
	#
	# Analyzing Returns from Geometric Brownian Motion
	# 03_stf/GBM_returns.py
	#
	# (c) Dr. Yves J. Hilpisch
	# Derivatives Analytics with Python
	#
	import math
	import numpy as np
	import pandas as pd
	import scipy.stats as scs
	import statsmodels.api as sm
	import matplotlib as mpl
	import matplotlib.pyplot as plt
	plt.style.use('seaborn')
	mpl.rcParams['font.family'] = 'serif'

	#
	# Helper Function
	#


	def dN(x, mu, sigma):
	''' Probability density function of a normal random variable x.

	Parameters
	==========
	mu : float
	expected value
	sigma : float
	standard deviation

	Returns
	=======
	pdf : float
	value of probability density function
	'''
	z = (x - mu) / sigma
	pdf = np.exp(-0.5 * z ** 2) / math.sqrt(2 * math.pi * sigma ** 2)
	return pdf

	# Return Sample Statistics and Normality Tests

	def print_statistics(data):
	print("RETURN SAMPLE STATISTICS")
	print("---------------------------------------------")
	print("Mean of Daily Log Returns %9.6f" % np.mean(data['returns']))
	print("Std of Daily Log Returns %9.6f" % np.std(data['returns']))
	print("Mean of Annua. Log Returns %9.6f" % (np.mean(data['returns']) * 252))
	print("Std of Annua. Log Returns %9.6f" % \
	(np.std(data['returns']) * math.sqrt(252)))
	print("---------------------------------------------")
	print("Skew of Sample Log Returns %9.6f" % scs.skew(data['returns']))
	print("Skew Normal Test p-value %9.6f" % scs.skewtest(data['returns'])[1])
	print("---------------------------------------------")
	print("Kurt of Sample Log Returns %9.6f" % scs.kurtosis(data['returns']))
	print("Kurt Normal Test p-value %9.6f" % \
	scs.kurtosistest(data['returns'])[1])
	print("---------------------------------------------")
	print("Normal Test p-value %9.6f" % \
	scs.normaltest(data['returns'])[1])
	print("---------------------------------------------")
	print("Realized Volatility %9.6f" % data['rea_vol'].iloc[-1])
	print("Realized Variance %9.6f" % data['rea_var'].iloc[-1])

	#
	# Graphical Output
	#

	# daily quotes and log returns
	def quotes_returns(data):
	''' Plots quotes and returns. '''
	plt.figure(figsize=(10, 6))
	plt.subplot(211)
	data['index'].plot()
	plt.ylabel('daily quotes')
	plt.grid(True)
	plt.axis('tight')

	plt.subplot(212)
	data['returns'].plot()
	plt.ylabel('daily log returns')
	plt.grid(True)
	plt.axis('tight')

	# histogram of annualized daily log returns
	def return_histogram(data):
	''' Plots a histogram of the returns. '''
	plt.figure(figsize=(10, 6))
	x = np.linspace(min(data['returns']), max(data['returns']), 100)
	plt.hist(np.array(data['returns']), bins=50, normed=True)
	y = dN(x, np.mean(data['returns']), np.std(data['returns']))
	plt.plot(x, y, linewidth=2)
	plt.xlabel('log returns')
	plt.ylabel('frequency/probability')
	plt.grid(True)

	# Q-Q plot of annualized daily log returns
	def return_qqplot(data):
	''' Generates a Q-Q plot of the returns.'''
	plt.figure(figsize=(10, 6))
	sm.qqplot(data['returns'], line='s')
	plt.grid(True)
	plt.xlabel('theoretical quantiles')
	plt.ylabel('sample quantiles')


	# realized volatility
	def realized_volatility(data):
	''' Plots the realized volatility. '''
	plt.figure(figsize=(10, 6))
	data['rea_vol'].plot()
	plt.ylabel('realized volatility')
	plt.grid(True)

	# mean return, volatility and correlation (252 days moving = 1 year)
	def rolling_statistics(data):
	''' Calculates and plots rolling statistics (mean, std, correlation). '''
	plt.figure(figsize=(11, 8))

	plt.subplot(311)
	mr = pd.rolling_mean(data['returns'], 252) * 252
	mr.plot()
	plt.grid(True)
	plt.ylabel('returns (252d)')
	plt.axhline(mr.mean(), color='r', ls='dashed', lw=1.5)

	plt.subplot(312)
	vo = pd.rolling_std(data['returns'], 252) * math.sqrt(252)
	vo.plot()
	plt.grid(True)
	plt.ylabel('volatility (252d)')
	plt.axhline(vo.mean(), color='r', ls='dashed', lw=1.5)
	vx = plt.axis()

	plt.subplot(313)
	co = pd.rolling_corr(mr, vo, 252)
	co.plot()
	plt.grid(True)
	plt.ylabel('correlation (252d)')
	cx = plt.axis()
	plt.axis([vx[0], vx[1], cx[2], cx[3]])
	plt.axhline(co.mean(), color='r', ls='dashed', lw=1.5)