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Market-Based Valuation of Equity Options

CQF Lecture, 09. April 2018, London

Dr. Yves J. Hilpisch, The Python Quants GmbH

Resources

Short link to this Gist:

General resources:

Abstract

This lecture covers numerical methods for the market-based valuation of equity options. The lecture is mainly based on the book Derivatives Analytics with Python (http://dawp.tpq.io).

Slides

You find the slides under http://tpq.io/p/cqf_lecture_april_2018.html

Python

This Gist contains the files needed to replicate all the results shown during the lecture. The code base has been updated to Python 3.6.

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{
"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, 09. April 2018, London**"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"import warnings\n",
"warnings.simplefilter('ignore')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## About TPQ & 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/py4fi_2nd_shadow.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": [
"<img src=\"http://hilpisch.com/images/algo_brochure_low_shadow.png\" width=800px>"
]
},
{
"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",
"* 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://certificate.tpq.io](http://certificate.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",
"* **Basic Option Pricing with Python &mdash; Complete Markets**\n",
"* **Basic Option Pricing with Python &mdash; Incomplete Markets**\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": {},
"outputs": [],
"source": [
"import numpy as np\n",
"a = np.random.standard_normal(1000)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-0.017192852033572143"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a.mean()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.012459601404084"
]
},
"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": {},
"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": {
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SnTE9t3+TA5AQoy42LOjInTp1GL7b6jLGFhZneTTyBATZEyE0q3yGCJiMehhU9OqE/Rta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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f218240>"
]
},
"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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FjDvDSz0vBx1HZMlItfB6yFobttY6s//CwJ/5GUxEUvN6U30duHkBp5FsckPD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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x118fa1ef0>"
]
},
"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 0x118ff4c88>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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A2SHnfw1hV4wzJm5CJwQ2poy/cydjmEBrNrKczgxmJs/zR/YcvuuQnOywdq3V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\nUy2WQIwxxlSLJRBjjDHVYgnEGGNMtfw/f4JhAad3FGwAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x118f88748>"
]
},
"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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LshcDm9y9LbX9EHAe0Bvi3P2LaedHgcbU/j/1K6sT6Eh9rjCzK1P7mkguPDwi321VGI8B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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1193e6978>"
]
},
"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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gmrni7Hy8fOdEWdFoOMwSo7SIN+S8Xh8+W34Qb369Cw+9ux6Pvr8BP6wrxPyv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\nRwNnAKWAW0r5Z7/ltwHFwF5gIvBHKeU6IcRk4HpgOSCAxVLKFzs6nt1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SSuNOZ0XrGmUs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5t21eB269b14Sfx04DxnJhZxVFvP0lLq5MhfXI9JZ8a7viTz7XX2uZky55aeuSmU5CXQeozf6Os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\nh8dteDGbTXzk2iXEx5n51bPHRvVzcNjK3Y/s5uFnj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L6VOFNy7T3SSHFmeDMhTKWP+442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\nRXiohdTEKOqae9E0LWCc7d1lrZiAs04TCxaMZKfGsvdoK919Q1ijvXPz0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9cAABR7SURB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\nGYo/CwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119488f60>"
]
},
"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": {},
"outputs": [],
"source": [
"from urllib.request import urlretrieve"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"('equities.h5', <http.client.HTTPMessage at 0x118e2fb00>)"
]
},
"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 80 ms, sys: 11.2 ms, total: 91.2 ms\n",
"Wall time: 94.7 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",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\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": {
"image/png": 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UiG7JeXXZjNF9mDy8N6EhTe/8YbFYuOGPExzPh/WP45Rpadxz+dQmv6E3xJ6D\nrri0ZT1xB7NKeHfZLqxW9w9w0XUdzC5hx4EC+porozfuzuWZj+u+mOw5VMS9r67l0xXpACw4eTjJ\niZGO469+pdH783ns/U0e7384t2skUs/z8svRL5uNzYI8TaUQwle8CeIu0lrPx8jf9oRS6j6llHxl\nEN2G1Wbju7VGNvWk+Ajmz21emsSYyBDuWjCZWy48qk3qEx4aRIDFQmllTdMne3Dbi6v4YuV+dh4s\naJP6iI4tu6Ccj5fv5TZzAv7pMwY4jq3alkVWQTkZOaXc/coadmUUUmR+OZgxpg/XneOalNY+FNvQ\n6/jSTxsP8dwnWx31bSvLzF0VjlKJjZ6XU1hBbGQIk4bJXsbCf7zpCrCvSt2DkdftcmCsUioLeFRr\nvbbBK4XoAuyJO2MjQ7j3iqktukdKG+Zzs1gsRIQFtSjFyBvf7nA8vv+NdVxz1mgmDG38w0p0Llab\njc9WpDN2UAJ9e0Zyw9MrXI4fVe/f+5dNmfSIcl8lDZ4X3tiNHZTABqce6gNZ7bMVVENe+tyYl7di\ny2FuvKAul2JLrd+Vw/qd2dTUGj3UJ0/tz4KTh2O12dh/uJiSihrW7cjmKNWLJz4weiNH19tdQQhf\n8yaIe1EpVQ6MA14ExmmtDyilQoDXgHntWUEhfMVqs/Hu0l3syihk8bnjHMOdK7YcxmKBGy+Y0MQd\nfCciLIiyihrW78ohNDiQguJKcgrLGT8kscGA8cOf9jj2Z7R7/P1NPHf9MY3O7ROdx5e/7uedpbsA\n+ODHPW6BzdB+PQgIsHDXpZPJK6rg3+9uJLuggt925Hi6HQC3XHgU97zq+l192sgkTp6aymnTB/DT\nxkP8sP4Q2YW+64mrrK51eX7f67/xryun0dNp8UVz5BVV8Oj/NrqUxUeHOhYrDE+LB3DrdUuVZNvC\nz7wJ4pIxtr06Q2tdXa98WLvUSggf256ez7/erBsqyswtY0CfGPKLKyksqWJ4/7gOlacpMiyIrPxy\ntw+e5ZsPc9+fp7mdX1Nr5ePl+zzea19mMYOSG19JKzq+lVsOOwI4ux0H6obMzzlmECdM6gdASmIU\nSfERWCyw73CRY3eQ2y+exP+W7WL6mD6O6wYlx/LCDXM4mF3K/iPFTBuV5LLd28C+MWzZm0d2fvsH\ncWUV1Wzak8ca7b5NdlZBeYuCuHU7sj3O84sIazrdR7SZ7kcIf/EmiPuT1nqlc4FSapTWejMwpn2q\nJYTvLFufwStfapeyssoatqXn84AZ2KX16Vhb3UQ28AGT5eGDtKq61mUu06N/ncnDb69n32FjpsSh\n3FIJ4joxm83GjgMFPGumuwDL20d2AAAgAElEQVQjYHvXaf/OG/44HpXqmmw6KDCAfr2i2H+kbhg0\nOTGSxeeNd3sNi8VCv15RDW7zFhcdyq6MQqw2W7vt51tVXcs1//6pweOVVbUNHmvMDxsOeSwPDmq4\nd/rK00fy/dqDjB0sw6nCvxoM4pRSFzk9rj+Tez4wt70qJYQvffTTXsfj4f3j2JaeT3lFDRt21w0x\nnTCxnz+q1qBiL+bDlVZUc229D70//U4RFR7MbRdP4rcd2Tz+/iZe+nw7wYEBTB3Z8jQJwj/yiiq4\n4ekV1DqtNH584SwiwoJITYrmhU+3UlBSRVJCpMfr05KiHUHcJScPc9ts3VsRoUHYbEYg1VC+tNbY\nf6SYR97Z4FZ+54LJ3P6isWBj5dYj/LrtCAEWC2fPHkRCbOPJFGpqjXx49pXnfzljFMmJkXyz+gB/\nOKbxtXuTh/dm8vCGc0QK4SuN/bbdDKxo4FhyO9RFCJ+w2WxkF5Tz0c/7WLHFSBMQHhrEPZdPYcve\nPLal5/PO0l2OhKeBAZYGJ377S04jKwGra2oJDgrkobfWux2bPa7uV3dAnxjH42c/2cqUEb27/TZK\nnUmt1cqSJ39xKw8LNVLfjEyL5/4rj6a0oprYSM/Dfs4BV2qvlvc227eLKquoafMgrqS8mjteWu3x\nWEpiJNfNG8sj72xg9fa6IdadBwt44C/TG73vkid/cVnZat/T9KLfySwh0Xk09tt2m9b6HU8HlFJ/\naKf6CNHuPluRzvs/7nEpmzqyNz2iQh37neYU1uWKeviaxj8M/KF+sDVvzmCyC8pZui6DRY8v57GF\ns9yuGT+kp8vzuHr7th7IKiG1t+sHudVma3DnCOE/ZRXVvPndTo/HnIczg4MCGv0C4vzv2j+pFUFc\nqPF7U1ZZQ1sPMOYWuuZt+8elkx37lVosFkYOiHe/pqiSsorqRue1tXVqEiH8ocG+84YCONPEdqiL\nEO3qre92suC+790CuOSekZx37GAA+tRbvNAnIaJDTl62f/YeMz6ZF288lt9NSXXssVpaUcOa7VmO\nOW9215w12u0+J06uGyau39tRVlHNZfcv5b7Xf2vj2ovWuubfP7F802HH8z4JEZwzZxB//UPzpikf\nyTMWNMRGte5nPNzsiStvYe7CxuSXVAKQEBPGw9dMp1ecsXghKND4JQiwWBy/v86e+GCzxx0pft16\nhK9W7W/zegrhD43NiVsKXASkA86/CRbz+Y3tWzUhWq+iqobqGithIUEuG9fb3blgsstk7cQ419Vt\nvTvoXoaO/hOnDynnvS2f/HCzy/nxMaEee9POPXYIKYlRvPDZNvN2Ng7llnHr8786ztl5sJDKqlpe\n/2YHowbGy1wgP0uvF5zff+U0l3/75rDPpYtt5ReViNC64dS2VFZR41iB/fvpaY5exX9cOplopyHi\nKSOT+Hj5Psqcgsht6fnszSxmYN8Yl3s671Jht2jeWLcyITqDxmax/hXIAB7QWgc6/RcAPOib6gnR\ncpv35vKXh3/k5mdXsnJLXa9FUnwEzyw5hn9eMdVttV2AxeLSmzE8zXVFX4dhBmTO36487d84qG8M\nfztvHEs8rDi0mz66Lp1EZm4Z365xD3Yffmc9P2/KdNk/VvjH858aq1D7J0Xz7N+OaXEAB3DmzIEE\nBlj44wnN24WkPsecuMrmJ6BuzP+W1aVMcQ7akhOjiHEKPGMjQ3hs4UyOnZDMrLF9HeWPv7/R0dsI\nDc8lHTVQVpmKzqnBnjittT0B1Q0eDj/bPtURom1s2JXDf8xv8KUVNbz0xXYCAyzcdvEkkuIjCA4K\naDDv29jBPVl4zlg++nkP01uxsXV7OnfOYJ77dCszx9R9YAVYLCw+b5zLgobr5o31Kt/VjDF9+Hlj\nJn936oFztvNgYesr3c1YrTaKyxteVOBJZXUtP244xNQRvRscxi+pMAKlG/44vsWrSe36J0Xz3PVz\nWnUPaF5PXGFpFQeOFDcZOJVVVLNsfV36j0H1etTqs1gszJ+rsNpsrNVZlFbUUFBSxU3PrmTJeePI\nLazgpS+2u10XEiyJrkXn5dUyIqXUJGAoYN/xW1KMiA6pptbKu0t3842H3qSoiOAG81zVN2ZQAmM6\n8JY600YlMWVkb7ecXCPTXCd5exPAAcyd1I+fN2Z6da7NZpOFDo2otVr5/rcM3vzWWHjw8DXT3RYX\n5BSU882ag5wxc4BjNafNZuOqh34AYPOePK4zh/iKy6p46sPNbN9fwBkzB1BYUsXg5FjHjiIdQbij\nJ67pIO7ht9dzIKuEey6fQp8GUp8A7M6o++Lw7N+O8TpgDbBYeOTaGVzxwDJH2fb9+Xz6S7rLeecf\nP4T9R4o5VjawF51Yk38FlFJ3YCxkSANWA6lA6zapE6IdWK02Xv5iO79srhs6feK6WVz9yI8AnDot\nzU81ax9NJVU9e/ZAr+/Vt2ckQ1JiHT1uQ/v14NxjBxMZHsyN9fbevPT+pbx447HNr3A38PnKdMde\nu3afrUjnu7UHueXCoxxJla832zQqIpjZ4/qyZU+eyzWb9uRSUl5NYICFvz76s6P8QzOn4bSRHWte\nYnN64ux7rGbmljUaxO0yd5u48vSRze5xDAoMICwkkAozAXBFvUTAi84dy6gBHfdLmhDe8uY3I15r\nfSrwjdb6Eq31ccD37Vwv0cXZbDbW78ph6768pk/20qInlrsEcFefOYrw0CDmzx3KuME9mTW2TyNX\ndz3OeeCaEmCxcNP8oxzPs/KNbcd69Qjn8lNHMDjFdUeHBfd9z7J1GW1W164gI6fULYAD+G6tsV+t\nff/RAnO1JRj7mz7w5jqe+3Qrz3261eW6e15dy7v1ttGym9PBeo8imtETZ7duR7bjsc1mw2ou0rFa\nbTz09npe/MSYf5nWwtQndy2YzIVzjbl+9fcMzi6o8HSJEJ2ON/3x9p9259+k1Na8qFJKAecD5cBs\n4A4gC7gV2IXR67dYa12ilAoA7gVKgP7AC/ZtwJRSxwNnmdfatNZ3tqZeon3ZbDaqqq1c9fAPjjKL\nBZ5Z4v1QSUPe+m6nI+9TcmIkdy6Y7OipOnZCSrcaMrnn8ims25nD8P4tX5RRVW11PJ42Kolpo5JY\n8uRy8orqApBXvtIcM7575P0uLKmk1molMKDhn9O3vt3heNwnIcKxH2n9+7z+9Q6XsozsUo/3O5JX\n5piUf/qMAWQXlPPL5sOM7YDD/PaeuPJmrE5dvvkwJ03tT1BQADc+vYLw0CAeXziTrIJytuyt+3LX\n0oUbPXuEM2VEb16t195Ah2xDIVrCmyBumFLqTGCzUmotUAi0OEuiUioQeBg4TWttVUq9AtQAr2Ik\nGF6llLoWY0HFrcA8IEZrfaNSKh5YqZQaDoQCTwMjtdaVSqn3lFLHaa2/a2ndRPuoqq7lq1X7+cBp\neys7mw3yiivp1YoVdss3ZTrShwxJiWXRuePabf/GzqBPQmSjw1SNsSdSvey0EW7H/n7RRF77ege/\nOfWgdHX2rcnsHl840+M8w6W/HWTLvnwAnlo8m9DgQDJzS7nlOdeFItc9vrzR17v0lOH0iArlobdd\nd9v4/fQ0LBYLpx6d1qyFEr5in9e3dkc2X6xM56Sp/d3OySksZ+WWIy5lf3/+V1ISjXmq5ZU15BZV\nkO20gnTGmD6tmn/pvHvE+CE9Ofe4IViA+JjGt+QSorPwJog7E0BrXauUOgLEYwRcLTUJI83VtUqp\nCCAXeAmYgzHnDmA58DxGEHcK8LVZhzylVAUwEkgE0rXWlU7XnAI0GsTFxUUQFBTY2CmimRIT3Yc7\n0jOLCAy00Ds+kluf+YUte3IbvD44NNjjPZqy91Ah//fQMsfz02cN4rLTRzX7Pp1RS9rL2/t+8tDp\nDR47fkqlI4iLjghpt3p0BN+uSncJ4MBIslu/fX7bnuXo7RmYHEtKX2PKcGJiNPNPGsZrHlZEAvxu\nWhpfrtjnUjZ7Uipx0WH89yvtSIfx13PH0atXjOOeHd27y3Zz0Wnuv4cL7vM8CycsrO5j6P431nHO\nsUMcz0+dOajV77lHVCgFJZUcOymVkUN6tepe3UFn+BnrSlrb3k0GcVrrWqfHbwIopa6g5WlG+gPT\ngPO11oVKqdeABKBca21Pe1UE2H/begHO2S3txxIbKG9Ufr77EIdoucTEaLKzXZOPph8u5s6XjXjc\nebK83YA+0cybM5gnPthMSXk1a7ZkEhfu3Uq7rPwy1u3M4e3v3ecK/W5SiltduiJPbe4rltq6CeLF\nZVVkZRV1ypWqtVYrb3+3C5sN/njCELf3sDeziP+YvWGxkSEUOm3R5Nz2pRXV3P5c3cKPq88Y5XI8\nIqjh4dfE6LoetYtPGobVZqOmoprsimouO2W4Y6eMIAud7uc683Ch11Mk0jOLHI9zCyt4+gMjcH7w\n/2YSHxHc6vd+658m8uOGQwztG9Pp2tHX/Pm3pTvytr0bC/Qa27GhscULQ2h5EFcEbNda2z/ZfwZm\nAuFKKYsZyMVgzHPD/L/zO7AfszVQLvyovLKGe15d43huD+DGDErgpCmp7DtczNGjkoiOCOHuy6aw\n6PHlvPXtToICA5jTxPyqw3ll3PzsSo/H/vnnqYQGSw9re+vTM5LQ4EAqq41g7oOf9nDWrEF+rlXz\nff9bBt+aCw56xYdz7IRkFj/xi8f9NB+5dgYFFTUs+rexytl5bpzz3K2b5k9w24/W02bwCTFhnDi5\nHxOH9XL04DknqAUYnBJr7FAQHcqIVsxt9JeVW47QOz6cISlGr6SRlsZlgxGH6hqreyHQp2cUlWWV\nHo81R1x0KKfPGNDq+wjRETXW/VGMMXftFKAS+MksnwFsbOgiL/wKJCilAs1evv7AFozeuEnAKmA6\n8Jl5/mfALOBVc05cmHl+KNBfKRVqDqlOB55sRb1EK1RV1/LMx1tYtzPH7dgtFx3FoL7G6kaVWveB\nFBMZQkRYECXl1bz6lSY8NJCpI4zkuiu3HObzlfu59JThhIUE8u6y3R7nYo0cEM/ic8e107sS9cVE\nGJnxr3vsZ0oravj0l/ROE8Qt35TJC59tc+wbaLcvs4h9h2M8BnBXmHMDh/SLY/LwXqzalsWXv+5n\nyvDerNx6hC9+NfbgvGn+BEfA4swe7Dr711XTHD1/f/3DGJI8JJ0OsFg4Y6b3KWI6mhc/N7Zxs6ei\nKS6vdgngTp8xgAALHufJ2sVEhpDdBkGcEF1ZY0HcX7TWGUqp87TW1zuVf62UerSlL2jOa7sB+LdS\nKhtjWPQu4A3gNqXUXIzVr4vMS94BxiulbjfLLzKDvzKl1FXAo+Z9NsqiBv957ZsdLgHc4nPHOSZn\n921kkn1Jed02Pc9+vJWjhiaSXVDBs58Y6RbufHk1I9PiHJPGAebNGcxxR6WwP6vYERwK3wkKDGD6\n6D4e96LtqKprauv2h613bOfBQrLyPW/HNHVk3Y4dMeaCgvd+2MN7P+xxOa+hNBj2fTvnTurnaC/n\noduxg3t6/yY6qdKKam5/YRVg5LebNLw348z3vX5XLnudhlPt/nnFVJ/WUYjOqrFtt+xJoIYrpUK0\n1lUASqlQYHRrXlRr/QHwQb3ifcACD+da8bz1F1rrb4BvWlMX0XI2m42svDLKK6rZtLtu4cKS88Yx\nIi2ev5wxiiP5ZR6HlBqyaU+e25CLcwAHcPzEFIICAySA86NTj07rFEFcUWkVmbml7PCwbVhkWBB9\nEiLZlVFITqF73rD6Q3ATVS+3fGN2wQ0sluoZG84zS2YTGBhAfEwYQYGdb/5ga3z/20Fec0rxMSIt\n3hHAAfRNiHAEcTfNn8A/X/uNS04a1uCWeEIIV958ur4HpCulVmN8iZ0E3NOutRKdwsPvbHDMCQoM\nsJDaO4o7LpnsOD5xWNMrwa44bYSj1w1wWw3obFhqD/500rBW55QTrRcVHkxkWJDbdlIdhc38JrDk\nyV+oqa2bczVucE/W7zJ6jOfNGeyyl2ZEaBCPLZzJ1n35DE6JdZtjObSf541qghtZvGAcN+4zd1K/\n5r+RTuSuSydzzytrXYaQX6uXoy2i3he6vj3reumHpPSQnUCEaKYmPw211o8BJ2D0eH0HnKi1fqK9\nKyY6ruoaK4+/v8llUnet1daiD/QpI3pzxWkj+NPvlNsx59xxfzx+CNf/cQK94+QbekcRHhrUrAz9\nvlJYUsml9y/lqod+cAngYiND+L8/jHE8T+kV5bKp+tnHDMJisTByQHyDi2RuvGCCy/O5k/px+8WT\n2vgddE4piVGcOLnxQDUkxLVdY6OMIerunNdRiNbwapxLa70Z2NzOdRGdgNVm4+/Pr3RsW9O3ZySH\ncoyM8yFN9Eh4YrFYmDoyieKyKv77pXaUjxvck2H943jrO2MT8Zlj+jZ0C+EnEaFBHCnwPJfMnxaZ\nCXWr6q16nDA0ETCG+wtKKhnQJ4YL5g7lrpeN1dTDUpveEnpovx7MGZ/Mup3Z3HXpFKLC3RP/dmdz\nJ/UjMjyYjbty3KZBAG7B8fghiRw9Kp/fTWnVJkBCdFveT1YS3d6ix3+moKRuBd8FJwzl7OMVZ93w\nCUCrhtbqfxj+3x/GYLXZCAywkJIYSWiIpA/paCLCgqisqnWk3Fi/K4feceEt3i2iLVhtNreFC3b2\n/V9HpMU7yvr3jibAYsFqs3m9vdOFJyoumDtUeo88iAgL5oSJ/cgtrPAYxAXXmwoRHhrEZae67w4i\nhPCOBHHCK6u3Z7kEcFeePpLJw3sTHBTA4wtnsXr7EUdPR0tYLBauP388j7+/ib+caWR7D7BYOO6o\n7rPnaWdjX7CyYVcuw1J78Oj/jMxD/pzXdNMzK9zKBvaNobbW5hK82VksFp5aPJuaWmuz5lpKANe4\n+nPf7BoOsYUQLSEzxIVDUVkVX68+gNXq+of2tx3ZPPVh3Wj64wtnMnl4b8fziLAgZo9LJjqidXs6\nDusfx2MLZ3r8sBUdj/2D+vH3N/l0blxOYTlvfLuD7IJyrPWWMtuH+cNDAx0LDs49djC3XzKpwT1H\ng4MCmrWCWjRtoNNcQ2e9esicViHakvzlEg5LnlhOTa0xhGnvAVu6LoNXvzLmqkWGBXH35VM9bgDe\nVjrjFk7dlXPgU1bhmyCusqqWt7/bxdod2Xy75iC/n57mSIpbVlGXc/DmCycSHx1KYWmVx2S6on2N\nGpjg8nzxueNQqT1kZbkQbUx+o7qZkvJqftpwyNHbtmZ7Fv98bS1Pf7SZmlqj7PVvdqD357N8U6Yj\ngEtJjOKxhbMa7M0Q3U+E08blh/Pq9iTeti/P7dyaWit3vbyaj35uOEN/U2w2G1c9/ANrnXbu+Hj5\nPsfjQ7lGHY6dkExyz0jCQ4MkgPOjBScPB+DOBZMZOSBeAjgh2oH0xHUjuw8Vcs8rawF46YvtnDlr\nIB/8uMfjufe/sc7xOC0pmtskjYKox7knbvW2um2LP16+j+H1hsT1gQL2HS5m3+HiFu1jeTCrhK3p\n7hPlwdivt6CkkmXrjPzkYwYleDxP+NaMMX04elQSAQHSuy5Ee5EgrpvYcaCA+17/zaXMUwB314LJ\n3PbiKpcyCeCEJ86T17em1/W+JSW4935t3JXrVuatqupat5/J1N5RWCwW0g8Xc/Ujxsb0MRHBhAQH\nMHqgBHEdhQRwQrQv6d/uBiqqanjk3Q0NHp883NhZIbVXFCm9ohjr1JMhq0NFQ5yHx8or67L02z+4\nt6Xnc/uLq9D789m0py6Iq66Xv60p2+r1wI1Ii+P2iyeRUy9HXVFZNXFRoTKvUgjRbUhPXDfw3dqD\nVFbVMnl4L8YO7kmPqFAO55byqrklzpWnj2L+3GpHDqe/nDmKlz7fTkVVLWfMbP7Ql+geqms9B2M/\nb8zkwrmKZz7aTFFZtcvQPIDen+828b3B16ix8tWq/S5lp0xLw2KxsOjccfzjv2tcjsXHhDXjHQgh\nROcmQVwXZLPZyMovZ09mEbmFFbxvDpueMLEfg5KNhKfD+8dx9Kg+jiS6zsl2g4MCueL3I31fcdGp\n1NQL4nr1CCeroJzqGis3Pr2CorJql+NR4cGUlFejDxQwckA8z32ylUM5pdx28SSPw245heVc/1Rd\n3reJw3phs9oYYibtHdAnhqT4CJdFFck9/ZdoWAghfE2CuC5me3o+/3pznVv5SVNTHQGcneyCIFqj\n/rBocHDd8GqWh+24TpqayrtLd1NYUkVuYQUrtx4BoLSi2mOOwRVbjrg8//PvRxAY4DoDZOG8sRSV\nVnHvq8aCHZvkkhVCdCMyJ64L2ZVR6DGAAzhr1kAf10Z0dQn1hi6tVhtpSdFu5z1yzXRumj+BGaP7\nAGYP29N1PWx7DhW5XWO12VwW3oSGBLoFcGD0/g1OjiXSTHcyt4kN2IUQoiuRnrgOKjO3lLCQINIP\nF7Nq+xHOnDmQxB7h2Gw2tuzLo6rayvghPR2TuCuqahy9EQCL5o3lt5051NZaGZwS6/EDUIjWmKAS\nufy0EazccoRNe3KprrFy6SkjuPsV13lqsVGhxEaFOoZft+8vcDm+N7OIsYN7upSlHy52ef7w1dMb\nrctjC2e19G0IIUSnJUFcB2C12rDabAQFBmC12rj1hV/JzC1zOWflliMkxISRW1ThKLtp/gSGpPTA\nZrNx18vGB2fv+Ahuv3giYSFBXk8eF6IlAiwWpo1MYucBIyirqq4lPLThIfqGkr3uqxewVdfUOhYs\nTBnRm3lzBsu2WEII4YH8ZfSjyqpalq3P4O3vdwFw4wUT+G1HtlsAZ+ccwAFk5JSybmcOX/5at3rv\n+vPHExYi/6zCd+y9wRaLxeVnLzQkkIV/GNPk9Xn1fq6dh1cH9IkhLjq0jWoqhBBdi3za+9CRvDKC\nAgO4/43fyCmscDvunIz3/OOGUF1rZdfBQs6YOYC7Xl6D1WZj/tyhRIQF8ezHW3nlS+1y/ZkzB8gH\nnvC5KSN6s/NgAZeeMoIwp8UyT143yy1n25wJySz9LcPxPDw0iIPZpeQVVRAfE0Zlda1LSpJjJyS3\n/xsQQohOSoI4H3n4nfVs3uO+pyTUpV6wGz+kJydMcp2g/fwNcxyPa2qtPMtWx/PoiGAG9Y3luKNk\nUrfwvaH9enDXpVMAY0GCnaeku3+YPcgRxN17xVSe+2QLezOL2XGwgKkjktD76xL7Hj8xRfbbFEKI\nRvgtiFNKhQO/Al9rrZcopcKAB4EMYAhwn9Z6h3nufGA8UAvs1lo/Y5anAbcCu4A0YLHWusTHb8VN\nfnElR/LKGNY/DoCvVx/wGMCdenQav5+eRlBgABVVNdRabRzMKmFg31i3c50FBQZw7Vmj2bgnl7Sk\naGaN7StZ6kWHENDEz2F4aBCLzx0HQFJ8BLPHJbM3czs1NUbw9+mKdK/vJYQQ3Z0/e+LuBpzzYSwE\n9mut/6WUGg28AMxUSqUAS4DxWmubUmq1Uup7rfVO4GngNq31KqXUtcANGEGd35RV1HDvq2vILapk\nUN8YzpkzmLe+2wkY+z3OHpfMsNQe9ElwTUpqn0ukUuO8ep3xQxMZPzSxbSsvRBv497UzoJH4a+SA\neMdj+/BreVUNa3U2uw4WOo5ZJembEEI0yi9BnFLqQmA5MAaIMotPAW4G0FpvUkqNVUrFACcCa7XW\n9r/oK4CTlFL7gDnAarN8OfA8TQRxcXERBAW1X5LbfZlF5BZVArD7UJFjntv/zRvHCVP6t9vr+lNi\nontuMNG+OnKbJzbju8XwKiPtyJvf7nQ7dvyUtA71PjtSXboLaXPfkzb3rda2t8+DOKXUCGC41vpm\npZTz0rVegHOugSKzrKHynkC5U3BnL29Ufr7nlZ9tJTLIwlOLZ/PP19ay/0jdyO64gfFkZxc3cmXn\nlJgY3SXfV0fWldo8Kti9y+6pxbOpqKolNjKkw7zPrtTmnYW0ue9Jm/uWt+3dWKDnj1nDZwIVSqkb\ngRnAZKXUQiALcK5pjFnWUHkOEK6UstQr97vQ4EDuuGQyF56oADj/+CF+rpEQHVP9uZypvaMIDQ4k\nNtJ9Gy4hhBCufB7Eaa3v0VrfpbW+D/gZWKW1/jfwGTANwJwTt0FrXQR8BRzlFKxNA77QWlcDS4FJ\nZvl08x4dxpzxyTx/wxxOmCirRoVoyO0XT2r6JCGEEG78uTr1bGAWEKKUOh/4D/CgUurvwGDgUgCt\n9UGl1IPAI0qpWuB5c1EDwJXAbUqpuUAqsMjX76MpssJOiMb16x3leBwXJXkOhRDCWxZbN1sBlp1d\n3L3ecDuTORS+1xXbfM32LH7ccIhLTx3RIYdSu2Kbd3TS5r4nbe5bzZgT12BvkCT7FUL43cRhvZg4\nrMl1SUIIIZxIOnQhhBBCiE5IgjghhBBCiE5IgjghhBBCiE5IgjghhBBCiE6o261OFUIIIYToCqQn\nTgghhBCiE5IgTgghhBCiE5IgTgghhBCiE5IgTgghhBCiE5IgTgghhBCiE5IgTgghhBCiE5IgTggh\nhBCiEwrydwVEx6aUGgYkACu01lZ/10cIIYQQBumJEx4ppSKUUn8AFmMEcZF+rlK3oZRK9Xcduhul\nVF9/16G7kTb3PaXUQKfHFn/WpbtQhrOUUsHtcX/ZsUF4pJQ6EagEfgQGAhlAtda6Rill0VrLD04b\nU0pFAb8H/gDsBz7XWn/t31p1bUqpSOB0YA6QDuzQWr8jP+PtRykVAZwKnAPsBL7VWn/v31p1fUqp\nk4AXgVu11s8rpQK11rX+rldXpZQKB04CZgArgKVa65y2fh3piRMOSqlA8/8BGB9sNuA84CLgX8AN\nAPLh1vbMX/jrMQLnq4FAjB5Q0b5+j9HOi4EtwN+UUuO01jbpqWh7SqlRwBPAQeCvQAQw3vybI9qB\nU9tage+BPymlYrXWtdLu7WoyRsfHImATUKOUCoO27QWVf0CBUqqvUuomYIlSapY5920D8ACwRmt9\nG/A5cJxS6hg/VrXLsQfOpguBXVrrTKAAGKiUGuCfmnVtSimL+QE2B9iitS4CPgG+xvi5ly8r7WMf\nUAys0lofArYDqTLftt5fKHwAACAASURBVH2YPcr2th0MvI8RUCxRSsVjBNGiDSmlAswg7RigWil1\nFjAPuB3jC0yb/m2RIK6bU0oNx+j5+RxjOOlBpdTxGN/YBgGTzFN/AlYB1f6oZ1dTL3CerbUuB14D\n7lFKvQaEYPTGvayU+p0/69pVKKUGKKWuUErFaK1t5ofbQeA+AK11DfAkEKiUmurPunYVzm0OoLUu\nAW4z2xpgF8aUDZRSvf1UzS6l/s+50xfFHIwvKT9jfGG83vz3kPlxrVSvza1mkHYI+A9wSGt9F8bf\nlslKqTPb8rUliBNRwHCt9Qat9VvAF8AZQBhwB3Cbed4oIBXjB1O0QgOB8xyt9a3ATcBerfUNwD+A\n74Bov1W2i1BKhWAMV5+FMVXA7l9AklLqHPN5PrASKPJtDbuehtpca13gdNpk4Ful1BDgGt/WsOvx\n1OZO896OB+YDAzC+pKcppUab50ivcws18rflZSAemAagtd4JvE4bx10SxHUzSqlhSqmblVKTzQnG\n+UCBUmqaecp/gd5Ab631Y8AnSqm7gWOBv2mt9/qn5l1K/cD5M2Ce+UE2FPiTed40jOB5u3+q2aWE\nABuBb4Fp9mFqrXUFRuB8v1JqKDAB6IsEcW3BY5vbe33M4ex+GB98TwJFMker1Rpq81BgHcYCtfvN\n43OAY6XNW62hvy3VwN+ARUqpPkqp6cAIYGtbvrisTu0G7CvtlFJXATHAXoxfYIC/YHxjWAe8pLUu\nVEo9BtRora8zf8FDzA870QJmrr2zMH7JN2MECTcDz2mtV5i/9A8AT2OsYnoZKMOYl/i21jrDH/Xu\nzOq1+VatdYk5rDQWuMose8Tp/MuARIzcmS+Y87VEMzSnzc1AbjrGF5iXgWe01m364dYdNLPNo7XW\nxeYiquOAbVrr3f6qe2fVgr8t12F8ca8F/tvWf88liOvizD+W4VrrMnMO1uda6w1KqQSMNBbHAj0w\nJl5u1Fr/Ryn1ZyBTa/2x/2reubUwcK7QWv/N7CHtLb2ezdNAm88GIrXWFzud938YPZyPaK23+aWy\nXURr2tz8MByttX7X9zXvvFr7cy7pc5qvDdq83dK5SDdqF2YOkT6MMedqJMYPXX8ArXUuxpy3x7TW\nX2HkD5qklLoXCAe+8UuluwB74Gw+7QF8qbV+B/g7RrqWycAbwGjgYvO8zRiLR9Bal0kA1zyNtPlt\nwNlKqblOp78LVAEPKaWuNue0iGZqZZuHaa23SwDXPC1s8wedf84lgGuetvjb0p75+CSI64KUUlFK\nqQeBMcBdGHPczgQ+xZjIbfcokKeUGqW1Xg4sBP6jtf63uVpSNJMEzr7nRZvfDjzodEkgxu/EOuAV\nrXWVb2vc+bVBm8v0jGZqRZuvR37OW6Qz/G2RIK5rsmFMYP1Wa50P3AlM1lo/jpFwcKF5XgKwzfwP\nrXWO1vqIPyrc2Ung7HvNaPMngIP2lXhABXCd1voWrXWxL+vc2Umb+560ue91pjaXIK5rKgP+V2/S\n6grz/7cCw5VSDwCXYiTzla1XWk8CZ99rTptvx1wVZrb5QX9UuAuQNvc9aXPf6zRtHuTLFxO+Yc55\nOOBU1B8zaMBYDn0vxkq8vWaXsGg9e+Ds3O7OgfPvzMC5CAmc20pz2nyttHmbkDb3PWlz3+s0bS5B\nXPfQB2MI702MvTm/1lqn+7lOXYoEzr4nbe570ua+J23ue52pzSWI6+KUUknAjRj75b2jtX7dz1Xq\nLiRw9j1pc9+TNvc9aXPf67BtLnniujilVC/gcuBBrXWlv+vTHZiB8y9I4Owz0ua+J23ue9LmvtfR\n21x64ro4rXUWcI+/69HNWIEXkMDZl6TNfU/a3PekzX2vQ7d5t+uJy84u7l5vuJ3FxUWQn1/m72p0\nK9Lmvidt7nvS5r4nbe5b3rZ3YmK0paFjkmJEtEpQUKC/q9DtSJv7nrS570mb+560uW+1RXtLECf+\nv73zDnOjOBv4T9L1s8/1XLBxt8e9grGxARsIJUCoJhDqRwsloWM6gZAQWkKAQBxaIIGE0Hvv4IIb\nxn1ccO/9bN/5mvT9oXIraVfaVTlJ5/f3PH58Wo12X412Z9552wiCIAiCkIOIEicIgiAIgpCDiBIn\nCELC7Kupo6q6LtNiCIIg7JdIdqogCAlz5V++AWDi2cMoLsyja4fmGZZIEARh/0EscYIgJM2D//2B\ne56fkWkxBEEQ9itEiRMEQRAEQchBMu5OVUodDZwGbAZ8Wut7TNqcCfwJuEZr/Z6TzwqCIAiCIDRF\nMmqJU0qVAJOA67TWdwODlVJHRbTpDmwhfDNaW58VBEEQBEFoqmTanToaWGXYymIycIKxgdZ6hdb6\ny0Q+KwiCIAiC0FTJtDu1HbDb8LoicCxtn23VqkSqUqeY8nLJSGxssrXPy8ubM/nH9Tz5+o88ev04\n2rYszrRIKSNb+7wpI33e+EifNy7J9nemlbjNgPEblAWOpe2zsi9caikvb86WLbvjNxRSRjb3+ZYt\nu7n/X/4s1Xe+XsZJh3bLrEApIpv7vKkifd74SJ83Lnb7O5ail2l36lSgq1KqMPB6DPC+Uqq1Uqos\nkc+mSU5BEBxiuWOzIAiCkBIyqsRprSuBK4DHlFJ/AOZqrT8HbgGuBFBKuZRSdwBdgV8qpY6N81lB\nEARBEIQmT6bdqWitPwU+jTg20fC3D/hD4F/czwqCkB24xBQnCIKQVjLtThUEQRAEQRASQJQ4QRDS\ngktMcYIgCGlFlDhBEARBEIQcRJQ4QRDSgtjhBEEQ0osocYIgpAfR4gRBENKKKHGCIKQFl2hxgiAI\nacV2iRGl1NFAc631m0qpm4BRwL1a6zlpk04QBEEQBEEwxYkl7lJgnlJqJHAZ8AJwa1qkEgRBEARB\nEGLiRIlbprVeBkwAHtVavwOsSo9YgiDkOlJhRBAEIb042bGhp1LqDOBXwFCllBvonB6xBEHIdUSH\nEwRBSC9OLHGPAecBd2mttwAPAPPTIpUgCIIgCIIQE9uWOK31FOBkw+ublFIHp0UqQRByngUrd1Dv\n83H8IV0zLYogCEKTxEl2akv88XDtabDg/Rx/lqogCEIY837axryftnHk8M4U5nsyLY4gCEKTw0lM\n3AfACmA5UB84JmEvgiDExpdpAQRBEJomTpS4Kq31OcYDSqm3UiyPIAhNDJ9ocYIgCGnBSWLDG0qp\nw5VS+YZjJ6RaIEEQBEEQBCE+Tixxjwf/UEr58LtSfcB9qRZKEARBEARBiI0TJe5trfWpxgNKqd+n\nWB5BEJoYPvGmCoIgpAUn7tSVSqkJxgNa67tSLI8gCE0MUeIEQRDSgxMl7njgs3QJIghCU0W0OEEQ\nhHTgRImbDFQZDyilrkutOIIgNDW8CehwdfVefGLCEwRBiImTmLgWwEKl1FSgOnDsEOCRlEslCEJc\ntu3aR+uyQlxNbKf5quo6rnrkG0b2a8flJw/MtDiCIAhZixNLXF/gHuAT4OvAv/XpEEoQhNhMW7iR\nm/4+hfemrMy0KHHxOrSobdnpN/hPX7Q5HeIIgiA0GZxY4i7VWk81HghY5QRBaGTmLN0KwJT5Gzlp\nTPcMSxMH8YoKgiCkBduWuEgFLsApKZRFEASb5JIL1U5sm8/no67e2wjSCIIgNB1sW+KUUiuIXlO3\nBh5MVgil1NHAacBmwKe1vifi/SLgYWAd0Bu4X2u9JPDeSmBloOm6yK3BBEHILHYMcfe+MJOVG3fz\n1E3j0i1Oo7Nrbw3VtfW0a1mcaVEyQl29ly07q+jYphSAJWt2smbzHo4a0TnDkglC7uPEnfoJDbsz\n5APDgPbJCqCUKgEmAQO01tVKqdeVUkdprT83NLsWWK21flApNQh4Fjgs8N7zWuu7k5VDEHKRXPBU\n2gmJW7lxNwC3Pz2Nq04dlGaJGpfrHv8OgOduOTLDkmSGp95dyMzFm7ntvBH06tSC+1+aDcChAztQ\nXOhkChIEIRLbT5DW+tcRh5Yppf6aAhlGA6u01sGM18n492Q1KnEnALcF5JinlBqilCrTWlcAhyul\nJgLNgQ+11lNSIJMgZDXZ6kzdurMq6piTUiFbdu5LpThCFjBzsT9BZeWGCnp1ahE6Hkx4qfd6WbF+\nNz0OKMPtztY7WxDC2VNVS01tPa3LijIqhxN36vmGl26gI3BwCmRoB+w2vK4IHLPTpgK4RWs9PWDR\nm62UOlFrvczqYq1alZCX50mB2EKQ8vLmmRZhv6OwMB8Aj9vd6P0fVMrM4vImTooOnW3duhnlrey7\nElu1Kg39nU33VrKyZNN3yQT/+WwpPz+sZ+h12zbNaFZSwIsfLeJ/ny7hwhP6c/qRvcM+s7/3WSaQ\nPrfHRTe8DcC7fz45qfMk299ObNm3AN8H/vYBG4ELkrq6n834rWhBygLHbLXRWk8P/F+plJoDjAEs\nlbgdOypTILIQpLy8OVu27I7fUEgZ5eXNqa6pBaC+3tvo/X/zpCmUFuVz14X21nBbt+2Gujrb59+x\nY2/o72y5t1Jxn2fLd8kkb36xJPT31m17qNqbz/T5GwGYuWgjhw/qEHpfxpbGR/rcOcn0l93+jqXo\nOVHibtJavx98oZQq0VqnQiOaCnRVShUGXKpjgCeVUq2BuoDL9H38btdvAzFxP2qtK5RSRwH5WuuP\nAufqBSxPgUyCkBP4MhAVt2XnPrbgwO0ZIaLP52P2kq307dqS0qL86Oa5EOgnJITZb7tiQwUA9fUN\nb34yYw0j+negTWn0/SEIQgNOiv0Oj3j9c6XUS8kKEFAErwAeU0r9AZgbSGq4Bbgy0OxR/IreHcAN\nwMWB45uBS5VStyml/ga8rrX+LlmZBCHbyaXIocjCIbP0Fp54cx6PvzY3I/IImSNWfOTaLXsA2LG7\nmpc/X8pNj3+b8ut7fT7Wb90rW7oJTQYnlrjyiNdvkKI6cVrrT4FPI45NNPxdBVxl8rl5wOmpkEEQ\nhDQRMWFuCoQ0LFm7KxPSCBnEeCtE6lHBpIZ9NfZd7055b8pK3vp2BRccpzhiaKe0XUcQGou4SpxS\nykvAIaKUMipS1cCLaZJLEIQmQuRknawRZNOOSj76fjUTxvWkxMQdK2QH709diTqwVdixWD+9O5Ao\nU+9Nn5Vslt4CwI/LtokSJzQJ4ipxWms3gFLqbqnHJgjZRS54hVIt4t9en8e6rXspKcpjwrheKT67\nkAq27Kzi9a9/ijoey40ZVOK8aVTigtY+436+705ZSevmhYwZ1DFt1xWEdOGkTtzdSqky4EBgIVCo\ntZaiToKQETIfFWc3riiyXbJT9K69NQDsq6lP8kxCurDaQi2WfuYORGin0xLncUcrim9+41c2RYkT\njPzxXzPp0LqEi0/sn2lRYmI7sUEpdTywBPgHUAh8qJQ6Jl2CCYKQ3didaiN1vfok90gNKoXuLFBk\nBWfE2h+3MdypQUtcOq8hNA2Wr69gcqD8TTbjJDv1bPwlPOYFLHBHAWekRSpBEGISrLNrZgyr3FfL\nt3PXp39DeZvzYKQl7p3JK5O6bHD+dTkZvYS0U7G3hhc+WsyeqlrLNh99vzr0d5QlN6jEpfG+9TSC\noig0PnX13rS64bMZJ8PgGq31nuALrbUX2BujvSAIacJog5r09nz+9dHi0Otn3lvEPz9YzGcz1za+\nYCY4HVrj1b4L7RgRYYnbXwfxbGHS2/P5es563vh6ueluHpHsrqxle0V0RE46f0ePJ/1xd0Ljc9lD\nX3H7M9/Hb9gEcaLEHaCUOhTwKKXKlVLn4I+PEwQhY/iYvmgzX81ZHzoSLJ66cXt6dyexW2g4meQL\nr8mHg4eMekLlvjouefBLHsvi2nPrtu7lqx/WZVqMtLElsG9uTZ3XlqP7jme+58YnDVtd+3wsXLmd\n2Uu3hg7NXLyZqurUlRwRd2rusHVXFe9PXWnbo7ApheOdkzqCO3ZXx2+URpzUifsd/pIiY/EX250M\nnB/zE4IgND6hGTS9E5XdcS7WgKhX70B1aWX5/p9fnoPP52PC+F5071gWdj63QYtbv9XvFJizbGv0\nSbKEOwOWgt4HtqRT29I4rTPHJ9NXk5/vYfwwZyU4PIHMBK/Xl1DejQ94+OU5YceefGs+I/qUc9Vp\ng5yf0ASPjQzY6tp6duyupkPrkpRcU0iMP//vRzZtr6S0OJ9xjVwOxjhk1dZ52V1ZY7nR/Y/LtjLO\n4bOSSpxY4oYCv8W/b2kLrfXhWuuVaZFKEISECc6fMxdv4al3Fphas7KFB/7zQ8z3F63aweLVO7n3\nhZms2eyP5jDGxPl8PnZX1phaBatr6rn96Wl882ODlbLe62WW3kx1BjNb01nMNhW8/MUy/v2xdvy5\noKuyLlErl8XH9JqdiZ3PhEhL3NaA9dDIn16cxW1PTWPbLim+kEmClrWKQDZ6JBu3V/L1nPRYto1j\n5v0vzebGJ6dQUWkuR6ZHVydK3LNAsdZ6jzE2Tginrt7L9EWbUuoCSBden4/7X5wVFmycbSxauZ0f\nlmzJtBgZw9KKZcPSUVldx7SFm9i4LTE3w9K1O3n1y2WWMti3xDm77jvfrTQ9/rvnpgfO1xAT9+Kn\nS7jmse9YuTF6E2m9ZicbtlXy/IcN8YKfz1rHE2/O54q/fM38n7ZFfaau3ssTb85jwcrtzoROAxV7\na3j01R9Dyms85izbyhvfRNdmayyClriZizfz6pfOt7C2cs8HFa946NU7+HDaqphtPBF14iZOmhrV\nZvUmf39v3RWt4AmNj3H8mL9iW8htf9tT03jhI83KjRVxz/Hu5BUssnimV2yo4PNZ4fHDRnd7MDxl\nR0Vm3aZWOFHivtZaTzMeUEqdmGJ5ch69eieT3l7AtAXZn5pcsbeGJWt38cqXyzItiiUPvTyHx9+Y\nl2kxMsJH36/m4ge+tFwBQvgqcNk6/zZWkUHlPp+P2jrnlqc/vTibD79fbaoggd+qZYd4sXOrIs4f\nyyVaV+8Ni4n7crZ/Jb5kdYO1JrgHZ9AyFH6thgH/L6/8SG1d+Hd4f+oqZukt/DnCrZduFq3czn3/\nnhWW2fnelJX8uHyb7Ti/x16by3tTVlK5zzo7NJ3kGfp7dgILL8v1ist/jxhdoNsr9rFua3he3QP/\n+YFXv1oe83lJVUxcvdfLm9/8lNK4U7vPUyaoqa3nhyVb0p/xbkJw0bZ3Xy1/+d+P3ByheFfui20w\n2bWnmje/XcFDFs/0vS/M5KVPl4RZXs3c7ZYejQx7OpwocT8ppf6nlLpUKXW+Uup84Op0CZarNNxw\nOWCJM9yoy9fv4q+v/sjeBCeARDeUrqv3cvc/p/PJjDVhcq3YUBEmX3C/zWxly84qy5WeGRWVNXw1\nZ13MgTuoXC9auSPqvcjMTID7/j3L9DzvTlnJrx/+OkpZsktNrbkCeOVfvrH1+Xi3xu+fn2Fblsse\n+io0mBpj4ioNlu+7nvVb7PJMLDiRY/MLgazeW5+axm1PTePt71bYliWVPPTyHJat28XVj37LssCe\nssEJ06kC7lRBqQnEgCWLmdKcCnbtqeGe52fw0fQGj8GNT04JxRhG4ovx/RuK/cZXRmJl2E5ftJl3\np6zkj/+aGfc8RlZt3M33CzeFHdtTVcunM9dw6YNfJfyMpptXv1rO42/M4/2psS2dqSTY+z9tqGDq\n/I3UGRZclz74pe3z2H0eagLP2eR5G7jqkeixLVvDUpwocecAlcChwPjAP9l8LoKCfA/QcENkM0Yl\n6f4XZzN3+baw7Lll63bZHtyvf2JyQpmBm7ZXsnrTHl7+fClen4+XP1/KU+8u4N4XZvKBwTXyhxec\nDZbJUlfvZebizXw7d72th/fmSVN56OU5tmOtnnhjHv/6SPPt3A1x28ayZEWKtmN3dVSdremLNgOJ\nB/0Hr7F1ZxV3Pes8jd/n8yuYT1hYVBMdGo1z7KJV0Ypu0L1nJHKFHdxLc9P2yrRn89rlvhfNlXG7\nOOnP2rp6Lv/z19zwxOQoq6RTzPrbCfEes7nLo93fppgoX6FkmIASt2N3DQvjLLpiLUz3BiymkYv1\nFRsqeOOb5aaf9Xp93PP8DP7xzgKqAwuj7RX7uPrRb/nvZ0sB+H5Rg4K3p6o2I5YvM4ILi6BrsVEI\n/Izzf9rO0+8tDFPGrBSzuctjj3GrN1krybc//T0/LN3CS58uMX2/xmJsz7Rq5+Spu1dr/X/Gf8DE\ndAmWqxTk+7u0pjY7Hr5Y1Jk8FMHVZ1V1Hff9exY3PDHZ1rl27alJOjNw4crtfDJjTUjp+GFpg0um\nsS2bb3z9E0++NZ9/frCYmYs32/5cdV3D4BxrEvhpvX8wTDh42sJIcMMTk6moNLemJlobK/g93pm8\nkrVbnJeG9Pl8LFu3i1kpjm2MV4vMLJYqegswX1I1wybP28Cz7y90ZInesLWSnXscWL4ivue/PtZh\nCxyvzxdyIYMz78538xrCPtZt3ZOUtSEvaUtcaqbDSCmWrd3FxQ98yZylW0OWuLp6b1QmrJPvbnXv\n3fvCTN6bsioU2hDk05lruMRgPQoqZ5HP00ffr2brzipq67xc/ei33P3PcCv1k2/N554Yluvpizbx\n97fmh77Lpu2VocxtO2zYupfXv14eUujf+vYn/wIpA5ujRHob7Ci0f311bszx2mjNhejx4Jn3Fpqt\nAQCoztI53bYSp7WeZHLs/dSKk/sU5AUtcdn5gxupM5Ex3+O/JeLFGRhJ1JUaSaTim84+rK6pZ+bi\nzZYDw/wVDat+J4pWba2XBSu3c+OTU/jfFw2xhpFu0+Aga6coaqqWenbrur07ZSULVjRYKYKSJ/o7\np8sLEavrtuysCvu+lfvqqNxXG+VOran1hqwiifDs+4uYPG8jVdX2z/HcB4u4/m+TQ3K9Y8OFW1vn\nZfaSLdTW1fPVD+t47auGxIHPZqwJuZAh/Heqq/cyd/k2y/vc6Cr//fMzeetb88SIyn11bNjmVwZe\n/nwpU01ifpO1xG1LUeB45H3x8Qz/xD3p7fnMX2FtfauvT92NGjm2Bi1tQXw+vxX0r6/+GPXZP700\nOxQesH7rXm5/uiEUfebizTFdrpPeXsCMxZvZEEhmuvWpadzhoAju7ZMm8/7UVXw3dz1bd1XxzuSV\nPPTfHwiuh1L1LPt8Pp56dwHf/rieBSu2m3owIn9HK+tbpExPvjXf8rr7qutDVvua2noufiDcLeuO\nMahYjROZ9rI6qRMn2KAgL2iJ8//gb337E53Lm3FQ33Zpu6bX5+O9KSsZ0aecTuXN4rbdUVFN67JC\nak0G9uAE4MSMn7oHO/y1VSxWKnjxE83k+Rs5c3wvjjuki0mLhofZh9+V+M8PF/Oro3vH7OPaem/I\nTfPF7LX07tyC9dsqefObn/jFmG6cclgP/zkD39VO4t0/P1xMj04tWLd5D8P6lIe95ySWyU7cdFV1\nXWhD8CB7q2qZPG9DwsHgxnspVQo/xB5wb540lV+M6RZ6fcMTkykq8IRqzRl542tzxWXDtr0sWrWD\nI4d3BmDago2UFOUxuGdbvF5fyJoK0VYcn8/Htop9tLGoLRXk0dd+ZOnaXabvGc/47pQVvDdlFceO\nbKivXlVdx61PTYsqwWC0LL47eSXvTlnJz0d15YxxPaOuEdmDn0xfE9UG4M5nv2fH7mquPn1wKH61\nIM/DCNVwPyZviYuNWca/z+eLWgi9/PkyLjmxHy6Xi+0V+0LfsabOy/YYimK910u+I+eUNfEyar1e\nH3OXmyuUkSERG7ZVUlfvZfOO8GxZn8+Hz2dhcbb5rG6v2MfvX5jJBccqhvUpZ0vgGnv31UU87/5r\n+PDh8/nw+nyWSvsrXy5j9pIt3HfpKMt+2F1Vy7QFm5i2wO8+Hta7Lb89fXBYm8jHu85CyXYypsxZ\ntpU5y7YyZmAHlq2Pdg173C68FtOOtRKXO4kNgg1CMXG19Xi9Pt6ZvJIn35rPuq17ueGJySxJYc2j\nIAtXbOetb1dw57PTWb1pd1hcQF29l10G180rXyzjpr9P4eIHvmSGidn55YD1yDjxxrNEOZncq2vq\n+XzW2obzG57UXXvDB9hIS1xVdV3MzDMnBCdOqxgJ4wDy2cw13Pb0NBat2hFVP2tPVW1YnMjU+RvZ\nsNW/Cvb54Ik354eUoncmr+SbH9czZX5DHJyVJc54n9TWebll0lQef2NeKCMvkenSjtvQzKX0j3cW\n8Oz7i5gWEZBtlwf/21ALLpXW1XhGTOMerdW19ezaW2O6cPl8tvn2ZLc//T0vfrIkZPl46t2F/PVV\nf9znx9NXh8Wu1dV7Wbmxgk8C7prv5m1g4t+n8rGFUhTESoF76dMlrA2UFnEBKzbsjmqvV+80raFl\n/A2Dbr2la3eya091VF20yPvP+PtMW7iRyfP892pwsfDY6w1xr0+8GR7j6LFZCiRRzEqteH0+9Ood\n/PuThudy6oKNbKvYx+JVO7jxySnM1Pbc+GbjWFV1HdMWbESv3sETb84zncjNfoN4FvZ6ry/m5B+5\niP54+uooi9rDL88Jc9Easesafu2r5VTsrTGtALDBrDSRD/72xjwuffArvF4fn85YEzaegd8lvHlH\nVcx6iJFWT7NQnMivECwxZCJSFFt2VvHGN8upras3/S0mz99ousODx+O2XFgvXr2DXXtreO6DRWFz\nYqZj4mxb4pRSnbXW2bEZYxYTiomr84Y9SO98t4Idu6u5/6XZlJUW8PuLR1JWUhD1eZ/Px6YdVZS3\nLLLtnthnMEUHYyjuveQQOrUt5b+fLeXLH9Zx5wUH0b1jWVg9nFj14Yyrnpv+PoW//GYMX89Zz4Bu\nrenVuUVYW6NyoFfv4MB2zSkpMr+1XvhoMdMWbqJibw2nHt4j7L0XPwkPKK2NcK8GM4YuO6k/owZ0\nAPxKWFV1XVTV/w+nrWJPVS0TxveKkmHt5j1sDkxmZoPd9op9YRPGzj0Ng/SKwIResbeGJ9+aH6WU\nvztlZfSXNmCsWQbhiki914sLF263i/tfmm36+c1JZOnaUbbNFL1ULjRTWT/Rlis6ArMQgniYTdzz\nImrM/bS+gr8FfigiWgAAIABJREFUJkLVpRU/LPFPSrHK98Ra0EXWrQr+7sYwByslwPgbGttcF3Dh\nPnfLkQ2NY3ThU+8sBGDMoI7WjQzkedJvE3jmvYWcZhg3du2pMS0YXe/1Oa71F6lYfDJjDR63K0wJ\nHNB9Y9TuAWZjiNvlYt5P21i8aoepBTQy+SiSSKvTpxH7IHu9vpBb0OfzsWbzHtq0aLD62n1m98VI\nxDImqgUftY3bK9kaUGCWrt3Jfz/3u4n/9bHm0hMHhFlmI9m8s4p/vr+Ic4/pQ2HA2BE6Py7q6r38\n7/NlHDakI13aN7f3BTAfsx767w9s3bWPZsUFHOzACxZrHTJtwSZcuPyLBKNhI4fcqY8qpf5K+GNf\nAyzWWqfevJSjhGLiauv51FA2w1g3qWJvDbMWb2Z8wE1j5Nn3FzFl/kaOGt6Zc47pY+uaZibrir01\ndGpbypeBbNPZS7bQvWOZbatZZPDsj8u28vZ3K3j7uxXhkwDhysED//mBngeUceWpg5ixeDNrt+zh\nnKP74Hb75QxaBjZsr2Tq/I0cEGP7oUqLCX/awk2MGtCB5z5YxHeB7M5ImV4NxAxNGN+Le1+YyYoN\nFdx/+WjatSzm0ThZtO9Mto5RCgb8fj5rbVyrqp2+NioiVz/6HSWFeTx05aGW7XcHkhYS0F9iljOZ\nsXgz+2rqLDOzUkVqlTjnn0mk+n/k8zV90aaoSfJvBktGrMBzI1aKuhlbdvonDWMGrVX9RLP7LrKr\nvF4fC1dttzXZx/rNLrr/C445+EB+eWSvtFviAKbM38iU+Q3xeJGB/0G8Xp/jbNvIfvthabR1KKjo\nhS2+TNx8Lhc88oo/3m388OgiDvHGhkhLXGRoifFZ3rW3hrv/OYOWzRqMAqs376Zrh/iKUJ3FmBD5\nbAVfbjUoL0+82RB7VlPrL5J9lGFOM37F7RX7+Ptb81m1cTd3Pjudey8eGXZ+r8/Hfz5bylc/rOPL\nH9bxzM3jbT/fZj0ZlHO3Q89NvLjMoCfIWIorZyxxQFfgPWBB4PUAYBHQVil1i9b6tVQLl4u43S7y\nPC72VNWFFAmIfmgXrtpB/+6tad+qJCyuIzhAfT57LWce2ZN/faxZsmYnf7pstGV8QazYoDyPi7p6\nH5/NXMvPDjrQsp0RsyBTY9LBO5NXcHDfdrw3ZRWrN+9h4tlDw9ouX18RltXatkURb327gnYti0OD\n0czFm5m5eDNHDD3AlkxGgpPFdxHlOapr6/nf50s5akS4chx0d971zPdMunFc2IO9d18d2yv2he2L\nZ0fPtVtFPu55DKepqq6Lq+RYbUFjhy9mr+Ocn/Xhp/UVeH0+Vm7czeFDDqAw38PfYwQDpxIrxTwR\nEtkVIBE8bleYRWvS2wsotbA0ZwPB+3fzzioWrzZXWl/9ahkfT19Du5bFcc8XtLZY8cmMNXTvWJa2\nOnGxMBZHNuLzYeo6j0W91xtWr9L8vL6onRymL97E0F5t6dimYUFqHB/MYrle/Wo5I/tZW4gi54tI\ni9mazQ0Zp7sCngKjx+CfHyxmb1X0s1bv9bJyw266dyzD7XbZTuZYbhI/ZlZT1BiaELRQ+nw+bnxy\nSlg7s0z1YHkrxxnSMZpX7qtj4zbnGfVWBBO+tu40uFMzHBPnZCT6FviZ1noHgFKqJXBb4N/zgChx\nAQryPHH3R5yltzBLb+G5W47k+icm071DGVefER7Y+euHvw79vWtvDa2aF4a97/P5+GTGmlAyRcSb\ngT9cgI/q2nquffw7W/J/+UP0fnTG1e9b367gg6mrQvEz8WKttlf4b/jNO6vIj5DVapKJhZkCde8L\nM+nduQVfzVlvWcoiKK8x7mfBCn8m6elH9GDX3hqG9WobkteKT6avTtmD69Ql2BATmNiE+dnMtWGT\n8o/LtrLQpJhwutjnIIszW3C7XFETcWOWvNnlUHH3BuKtHvpPg6VviSGWbvWm3UwNPM+bTfYOjWT5\nOvO4PSPvTV1JnwNbOpIznSxYsT20m4dd3v5uBZPnxd5p57+fLeU/ny0NU8Be/XI5r365PMobEMRs\nrJi9ZEuUS9FIPCviHwxFhq2UHqMr/6s56zh0QAc+mLaKdyav5KRDu9HjgLKw+opOs7TjDYHB5Aoz\nq2MsN65TYo3FXwYse6nGuBjNpezUVkEFDkBrvVMpVa61rlNKxa9Yuh9RkO929EAEa6ztilE7ymhO\n37yzimVrd5LncYeVsYhk047KhIpFmimgqyISAIyKkFXWUBCjiTpycEpkM/Bde2rCMgPBb20LWtx2\nG+qk2V3VvR7IUPxsZvywz5dj9LlTJs/bQMc2JQzr3RBLEsvtuduiBpxdIq0qjanAQXQwfC7gw5c1\nRVftsGtPtWUQOIS7IFs2Kwiz4JhhGuAewbote+nXtVXcdo1FPOuhGfEUOGgw+pgtPq2s6M++v8j0\neKw5YoMD65GdhKV/faRZvXE3qwL7wprF7j7yv4a6eYnEm0bJ5fMnxJh5DyLjnc3xGyDiYVboe3/C\niRLXUSl1HfA1/p4dHzhWDkRHj+/HFOR72Gmz9MNF938R+tuYxRfJvpp6vpi9lp4HtOD3L8yIq/1b\n7RNnh0hrWTxu+vuUmO/vtXB5QGKWmWXrdoWtRGNxSUQdoFdSqIClgg3bKnn89XmcPLZ76NiH06wT\nTpJxp2YDqVyBNxb1Xl/cQPRs4i+vRNcesyKeAueEWGEdTQ2z59C4VdM+g0IXueAMEmt/2Rc+0pbv\nRfJHi+32Ivlqznp6HhBdYifIkojM52Txen2Wc8P6OErq0rX2r//ZrP0739KJEvd/wKPAHYHXnwMX\nAZ2Bp1MsV05TkOdOqJRCrBWv3WDpVPC6Rd2sRLHaQB2cm/CTJbJid7Zg3LPzw++t9yfcuaea9Vuj\nSy0I6cPndVb8en8l026lbCKZRXQ6MYttMyMy+zoRYnkU4lnP/vSi/aSfTJMzMXFa6/XABJO31gPW\nJqT9kIIYsQ6CEI9Y1f83bKvk13/6vBGlEWrrvVz8x08zLUbWY3dHEGH/4JZ/TIvfqAmQ6bveSZ24\nYuB3wM/xy/0B8HutdfzI2PjnPho4DdgM+LTW90S8XwQ8DKwDegP3a62XBN47FxgG1APLtdb/SFae\nZDFNNBAEISd51GRrJCGaXNgvWhBSTaYtcU60jUfwb6N4K3A7fkXukWQFUEqVAJOA67TWdwODlVJH\nRTS7Flittf5T4JrPBj7bGbgRuFFrPRG4RCnVO1mZkkUscYLQdMiFfZCzgXhZ3YIgpB4nMXF7tda3\nGV6/p5R6NAUyjAZWaa2DmQCTgRPwx9wFOQF/KRO01vOUUkOUUmXAscAsrXVQFZ4KHA9Ypia1alVC\nXl56lazaFG6kLAiCkAvE2lxeEJoqJSWFlJfb32EikmQ+C86UOLMiQNapLvZpBxgj3ysCx+y0sfPZ\nMHYksW2RbSLMq81L8pMuDSEIgiA0fTxul6P9qIXMsmX7XrZssU7ei0V5eXNbn42l6Dlxp/6olJqh\nlHpMKfWoUmomqUlo2AwYJSwLHLPTxs5nG53ImlLlNqqip5vbzxvB5ScPyLQYaePEQPHKdHHWkemp\notO/W/bU1ko3+1MJimzm9CN6xG8k2KK40EObssL4DW1y9RmD+ceN45I6R7rGKifsT8/6srXxi2Gn\nE9tKnNb6MfzxcDVALXBz4FiyTAW6KqWCT8IY4H2lVOuAyxTgffxuV5RSg4AftdYVwMfACKVU8I4Z\nDXyYApmSIrKgbX29j/OOVWm/7sMx9tzs2akFHrfzhIu+XZKvwt6nc4ukzxEPj9uV0F6adhnWx3pj\n52S48axhtvY4bAokcPullFROtlacMLprys/ZvCQ/pecrKsjeLcPSyegB7VN+zqtPH8wd5x/k6DNd\nY2zuPrRX26S39DtsSPRWhkcf1Jm/Xj2WK04ZyPGjunCuzX25E+Wxa8am7dztWmXeKGJkcM82Gb2+\no2FVa/2Z1vrGwL/PlVKnJiuA1roSuAJ4TCn1B2Cu1vpz4BbgykCzR/ErencANwAXBz67Fn/W6iNK\nqT8Dz2itnZfqTjF5Edmp9V4fg3uY/9CRW9V0ad+MZ24en9B1W5cVMfHsYZbvm40N8TJpR/ZvT8tm\nBRw2uGPY8d4OFDOPJ/2zt8ftwhWxFVW7lsVhW9sk8/BbrSzP+Vnig+E1gW3WDjcZdJsiqagCH49Y\nhaqPOyT1ClYkpxzWPX4jhyiT7ayuOGWgZftY218VF3ooKoiOCS4s8HD/r0clJmCOEGubq0TxuN20\naFbIUzeN48azhlJY4Im7mDz18OQsoeOHd4r5fnFhHhPG9wy9/tu1h/Oro/tQVlLAwX3bMWFcL0b2\ni1ZojznYfG/th66wNg5YUVLkfOFh11OU3wjziRNGqPQs8O0Sd0mmlHouxtuHAG8mK4TW+lPg04hj\nEw1/VwFXWXz2ReDFZGVIJZed2J+Jk6aGXnt9PsvVVYfWJSxZ01Cd+ncXHozL5aKowGNa3b5T21LW\nbbWudt03xtY3dSZxFvEmVhfw56vG4HK5WLZuFxu2VXLrucP572fWuvIIVc4s3VCNPK8xlDhPtCUu\nP8/NkF5tmL7I72G/4FhlWYTzspP689S7Cy3PX2dRuPKoEZ156dMlCcncqa1/w+y8GBuHH9K/Pd8v\n3JTQ+S8+oZ/llj+ZoDE8LLGsGAep8oR/q3gcNaIzZaUFtq3dncubsXaLvaLNl588kEseDN95ZGiv\ntgzvU25a9f+ms4dy6YNfmZ7rvGMVeSYynnpYD9q1KrElT2Pyp8tGcetTqak3Fq9qQGG+J1R8/ITR\nXXl/qnXR7RCB2y3P46Z/t9b8/fojAP8eq21bFpmOk0ka2myVsBraqy2vfrkcgJKi6GnebFHatkWR\n6blSbQm2YmS/9kx6e0Hcdk7GkavPGMxjr81NQqr4NMbiNBZ2Rpxu+LfaMvu3Pm2S5TBtI2Lg6uu9\nlrVkWpQWMGZQB8A/mQdviEd+O5bjRnbhN6cNCmv/+4tHMmFcz6jzlBoe1GbF5g+dqTXJxv0XlOn2\n8w7itnNH0LtzSwZaWBYBroywEngiRi2n23pFYhYz4nG7TR8m46Re1szcnTaoRxtGDejAY9ccxggL\nt2lzkz5NxHV2kGHVFrTY9u1irXgnE1vSvlUJRxpW7WeOz2ysjNPBLpF4wVgTZDoH23N+1oeTDu0G\nwFWnWlvJgrRqbs+1W1aSb6qY5ue5+c1pg0xDFTxuNwX54c9Y67JCHrh8NKP6d6CoMFqZycYIpvJW\nxbRvnTrFMp4S19rgbm9eUsB1Zw6Je06rjerPPro3PzvI3LIF6XfBdWxTyu3njeDxaw8zfT9Sj7/m\njMGMG9aJS08ZyLDebcPes1sy69iR4d/33otHcuu5w3nuliPtC24L+3druyyIR083dmbT67XWL5j9\nw1+jTYhDvdcXWg1FbhLtcbtCA3qn8mah44X5Hs48shfD+5Rz0c/7hY67XK4oy9YZ43qGxWXcc9FI\nUzn6d2vFkJ5tuOWc4aFrOlkVlhTl0SswaZw8thu3nzeCob2jlZ7IyfKUw7qHKZZd2jWL/EgYhSbu\nHiNmSqDH7YpSFnt2ahHmQikpjF6RPnXTOK6d4HdrNivOp9Zkj8zjR3WhpCifR347lieuOzzUdwfG\n+R5mGN0MBYFSN+Utixk3zNxFEvmdnBK05rYpK+K4Q7rEdMOlm2qH+6aOGdQxfqMIYim9iehwvzlt\nEH+zmAitGKFiJsgDmLo0zQiGIrS3CAW44Pi+pscjXYfXTRgSSrAqyo9+DrIxDv3p234GwLih4eEG\n/2fxneNRmB97ujv7KEOJUZ/PlqIda2upWFw7Ib6CaMW4oZ249+KRjDLE+JmNmT07taDUwq1pfE6e\nu+VIhvRqS57HzS8O62lpBIjHUSM60+OAMm44ayjgn896d04+phrCF3ROhkSr8TPWHrK5RlwlTmtt\nuQmc1lpKmdug3uujqCCPJ647nBvOGsqo/g0PX+8DW3L4kAPo26WlbUuJccB9/NrD+PmormEr1lbN\nC+nYJnoFW1yYxzUThkTEzCQ2envcbnp2asHtFgqjkS7tm/PYNQ0TYUsLi1iQg2wkEURazDweF+ce\n04fenVtwz0UjueKUgZx9dO8wxa1V80Luu2xUKBZtUI825HnCLXiRqf1XnTqQCeP8v0uL0gKKC/O4\n9ZzhnDm+FwfZmKwjMf52RmvJhHE9Gdkv+nxJJQO4Gvb8LA70w8F929m2AqWSRCyKiSgWR43oHON8\nzk5YkO9meJ/yhOJ74lFsYg2DCEWChgXPHRccxGW/6A+EK2gd25SanueQ/uExT8bQDDMFMtMuITOC\nE/D5x/UNi/HqlWCiVLyEDqN3wYe9kbEuTk3QWArRcSO72LhCuBz3XTaK9q1L6FTejPOPVRQWeDj1\n8B60KCkA7Mf9xvq9vQnuQNCyWSF3nH8QA7q1jnovVshI947N+fUvYsfDGRdGowd2sC1Tu1b+BbLR\nIjdhXM+UPtOZfnSyK0KwiRJUDIoL83C7XFx8Yj/uu2wUf7z0EPp1bUXbFsVM/NXwKCudFUb3itVK\n6/+O70encvMB3kiy91/kwBhpijfLynW5XTGzXmMNIm3K/HEbV5wykL/8ZgyXnNiPstICRvQpp2Ob\nUm49dwQHtmvGwX3bUZjvCSkvQTq0LmFIr7bce/FIfnNatFXKG6HEmZVratuymOMO6WIZf9Wrk/Uk\nY/yEcZVYXJgXZnENkh9RmDqogNrBBVRV+5W4EoPSYOUCSid/vPQQx5+JTFSxQ4sYC4RkY5FSSanF\n5B4ZtH7xiX7FrbQon1H9O3DthMH84ZL4fTlhXC+uP3MIl53UnwHdWoVlQMezdGcjLUv9v2vbFkUJ\nhxg4sTDZ0WNKi/JMk06MmN5zgWNn2iwFctv5I0J/tygtCP1dVJDH368/gpMO7Rbat9auhSnW4tBo\nXAxa1ewQy2swfpj14mrsoI5Ri45YWCVgmOFyuTj/WMWggIJekOfm+FGpTXDKtMtWlLhGIFIx8Ljd\ndGhdYrmKjoedQaxX5xbce7H1YB+sFXV4hKvimYnOM2ODq7+/X39EVAyfMas1GL/TvDif684cSplF\nwGy912fpquwWmIzcbhctmxVy6MCO/PW3Y2leUmDa3iyoF/ym/kgFKXhtI4nsi/fb0wdZv2n47SJX\nw2ar42MjBqwhvdpaKgBmHBpYtR5hcNeePNZeBqWd2C672I1tCsaHgvMVbn6em0P6tbN018ezNkVa\nRuIpkT8PTAaJZBcfWB4to4voZztS8Rjcsy1tLALQjeTnuRkYiPW84axhYSEYZkrcvpq6wPljx2qN\nSkOZDjuM7N+OCeN7cvOvhoethGLFnUViVIDi4QupRX7MlIyHrjw0apEYiSsFKwdjNqbV9RqGKXvX\nizWHBMe8di2LTa1qVsR6vo47xNzqOHZQx7hhE0Mi7slY17FKwjiwvf95G56GUlGZtmLbVuKUUvem\nU5Cmxj9uPILxgYkz0biJIOHDSWrMt4cO7MgzE8dHWY0SqVF078WH8Ng1hwXS68M/b5w8LjmpP+OG\nHsCph/cgP89NsYUV0euDW88dHnasZTP/ANyjk7NYhniDbNS1Iy1xDiqnXzthMLedO8JSoQTzuLwg\nxq77x43jeO6WI8OSZIKrYtuKpctfM+qxaw5j9IAG5eigvvHdwM1L8m3FdqWasQnEwQXJ97gpKcrn\n7otGmk7YkRNXMJMwSKRlJJ5ydvoRPXjm5vFcmECMllmweH6eu1FcM0WGawdds8EdZUbFs4iY3Hod\n25QkHbsZD4/bzfGHdKVNi6KwMWZ4n7YxPhVOmQ0l7tRAiZjBPcPPa+bus7OYTkXRWzvnCI4Jdn+G\nWIpHcCHrZC6IHK8jadW8kD9eegh/v/6IkIeotCiPi07oF/Ys3Ghi+bv85IF0CBgKuneMXVPz1nNH\nmCacjR3UkWsnDOGC4/zPaqZdoKnEiSXuRKXUi0qp/1NKxV8K7ufk53lCA2SyW6j0C2QvBlf+qaqG\n7Xa7GNCtdciSlshkBP7Jx46rom2LYs4/rm+obZ2FW88XiCEM0iaQWXf9L4c4MqWD37JQWpTHeTaL\nW0a6cp3Ehwzu2TYUr3PioeYm+1jy53nc/PLIXlz/yyFhyRvBzOPOAeuNXSUuaEmK/G1KLayTRtI9\nKSeLWeFWY5+ZJb+4XHDXhQ0JQLHcipefPIBfHtWg1PUycZu5XC7LZzFe5nJk9mhRgYdLTxoQNrla\nlXxIloJ8DzedPYz7Lx8dcqsF73PjxH39mUNMx4TjD+kS5rYbPaBDo5QRCmK8kpNdWlo0i6/EnTSm\nO0/dNI5ObUvj2rTsWGCSHasvOE7ZMq6FppgUPLZm94KRTuWlYclzJx7azVYCQ8c2pRQWeOgdMByY\njTH9u7VmYI9w65/b7S+ddd2ZQ7j+l7Hdux1al3D6ET259+KR/P7iBhndbheDe7aJ+czfeYGzos3Z\ngpMn73yt9bnAGuAJpdT9SqnoWhdCiGAJiWQf5LYti3nqpnGcESgt4sR8+7sLD+amGHEN/iKfo3nu\nliNNLQ+DYpQSSRazTFBoKJgaVHh+e/pg8vM8DOzexvGuE6VF+Tx+7eGMH24dk2EkUuFO1Ih62uHm\nj0a8rMRjR3ZhYPfwPr/vslHcecFBIeuSWbed5qCAaJ7HzTMTx3PJidExeEGuPDWGSzhBnLizIPw+\nj4wFvPSkaMuIUXEze+ZcLhfdOtib9Lt1aB52jonnOhvgTz+iZ8h6HEmfzi1QB7YKxXeOGtCeJ68/\nIqpo6J9sFt+9+/8OdvT7gz9Lvl3L4pCiH1wXGL/zwB5tosaEbh2aM2F8L243ZMPX1XtjBq7bwY6C\nFcR4X+TneRjQ3Z7LLzLJyYqgQhrPim9noRMcrqxKF8WjV+eWtvSy4MLOydxw1PDOpovboPfB6utd\nf+ZQOpWXMrRXWy76eT/H9148S1+3qB1s/KW3BvVoYxkDHkmn8mahRa9djCE85x3TJyy+2yo7PBtw\n4msK7tL6E7ATuBQYopTaDDymtZ6VauFynWMOPpAV63dxymHJ71VoXOnasaQESWRLp4lnD+OL2Wu5\n9KT+pnFjdrj5V8PYXlEds41VgH2w1MoZ43py/CFdYgarp5pI92kiMXFBXC7/5GgsyppI/ETzkoIw\nF+2gnm2YtTh8i+ATD+1GWWkBz3+4OOz6VrjdLkYN6EBJYT7fzdsQVTQ2VnKGU4JWpxvOGspdz063\n/Tmj+HZqxhmVOLPvbkf/v/Xc4SxZszOq8G3HtqV069CcVRt3m3kUTbFqd8u5I8Jee0yEbeGgcHCX\n9s3p0r45b3zzk03JGog04HQJxA4ZY+P+eOkhrN60h+LCcIUpz+Omrt5LbZ2XvYEs6ESZMK4nz7zn\nL0x9w1lD2VdtXY7GziN03ZlDcLngL/9rKKDgcrkoLvRQ3qKYuy8ayeUPf0VNjCSf1mVFXH7yALoE\ntsnq07kFS9bu4sErRuNxu225G4NKceQuPkGuOnUgz7y3KFRkOMigHm2Y99M2WjcvZHvFvrjXCf6O\nTgzo51h4J8wU+iDjh3UKKcBXO0iyMjKyX3u+nbuB4y12UPnFmO68N2VV6HW83zvP46Ku3sfxFnF3\ndjF+3/HDO9OtYxk/LN0KwN0XjeSKP3+d1PnThRMl7jmlVBUwFHgOGKq1XqOUKsC/Y8KZ6RAwl2lW\nnM8NZ1lvg5UorcvS683u27VVzJ0f7KBiFLAN0r9bq7CdHSLJ87gbVYEDs+zUxJU4t8tFvc8XVu4l\nFZ7wG88Zwdl3Rm8RfOjADuzcU81b366wLd/Q3m0Z0L01v374q+QFsyBYw9AYi1ValGc68VspuXaU\n37DteALtR/ZrF9qxI3iOP/16lOXWPb07t7R0Dd1xwUH4fD7L3RCiSPDWeeK6wxMqiH34kI50aJ1Y\nslRQi2vXqoQ/XzWGstIGi0fHNqWmSVjlLYvYsK0y6eLd0FAzEYgbTG/nXhjUow0rNlREHX/8msND\n3zU/zx1S4qySeIzbU930q2Hs3VdHWYyY10iCip7X66NXpxYsW7eL9oYFwgjVjk07qnjtq+Vhi/Nr\nJwymptZLYYHHVqbswG6tmTx/o21LcyyCY55ZUkb3jsmff0D31jxx3eGWls48j5vuHZuzYoPfbmSm\nTLZrWczmnVWAP0t3T1Wt6Q5HTgheJphwZ7xuOrZsSxVOlLhOwO+AU7TWtRHHEwumEhIiE3W+0sFF\nP+8XU4nLBNExcfE/U1KYR2V1tEJy1lG9eenTJRzctx1er4/tu6tTEs9olZ2a53HzizHdbStxQfLz\n3PTr2opFq3bgwlz3GNyzDXOXb3MuLA2xfMbJNxnl2AqjMtGrUxmbtlfSqbwZXbZVsnrznpC1qX2C\n20u5XS5HWriZFTc8ls+8D5wm4wS58Hhr97g10TLYHV+uPmMwH09fwzEHd+GdySsTuHYD6bgfunVo\nzjEHH8gnM9aEjhmtZ8H7ZezgjraSeDxutyMFDhpKMOV53Nx09lC2764OFV0OcuTwTqzbsjcsg9Pl\ncoXit+z0zXnHKg7p357+DrJJrQjef2aZnqn6neLd44cNPoAVG7T/hckjd9yoLvzrIx04l4c9VbWh\nckqJ4nK5+OvVY0OLzUSS/DKBk9HiAq112CZ2SqmBWuv5QGJ2VSEhgg9XvJ0Psp1EJ6t0kkiJkb9e\nPdZ0tXzUiM6MG3YAHrc75JIBf5yikxigSOy6ZJ3oizeeNZS6eh9en496Q9DdxLOH8f2iTZx3rOKS\nB76McQZn8thJ9jFOGHaUX6MSd87P+jCwextGqHJOGN2V2jqveQmXkQfy8fQ1UcdjcfOvhtlydZp9\nw6PNSmJkcK4IdnEiNfnatyrhfJM6kLG44DjFi58sifr9k0n+CkrerUNzVm7c3XDc5eLM8b3ClDgj\nQetfOusmXnZSf177ajlnjOtJfp7HdAFRVJDHpSf1T+o6BfmemFshOuGXR/YiP8/NKSaliJIJL3HC\nuGGd+NcnX4bjAAAVKUlEQVTHfiXN7M40jgfFAUXZiRLX44CysEVpsJi0UUmPHC7GDurId/M22L5G\nYxF3FlVKnW/4O9KJfi5wTKqFEmLjcrl48vrDGzUjbH8h6E4tLPDQqllhmDvFili/g9lkn0icYiI4\nGW9dLhf5eUE/U4PrIBWudeM1gliVbrFU9Fz+bMm/vGK9SYwx7qioIC+stpeVO6RFqXOrtp1QAYAh\nPdtGDfqtDVauxpkOYxOKiWskRbJXpxZcdEI/nn53YdhxJ6V8ogjIbqakx/pe+YFYzZra5NxwsWjf\nuoSrTksuSaiR9KYQLZsVmhYeB3ueiVRj9rsGExz6dG4R+pGduFN/PqorB7ZrxuOvzwMwjc+LvO75\nxymOPaQL9/17VtJWv1RixxRyGzDV4j3zDR+FtBNvCxkhMYKKw8F921kOZLlCUhNjDC4/eQCT3l7g\n+HPGMbFbxzKWrd0V3QZzRc+FP1vy9vNGWFptrOLcYpFOy8J5x/bB5/Mxef7G0DGzGM9ErGApo5En\n5bp6n6lVNZl7ddzQTsz/aTtHj+jM0++FK4exrNYFAaXfKks+W4isE5pJGssSF49hfdpyyznDOaBt\nKc8GfvOqGvuKVZ7HzTCTfb+NRHpT8zxuOrUtzaqdX8CeEneX1voVszeUUmekWB5hP+Xu/zuYNZv3\nNJqVyorLTurPPz9YHLfOVy6Q6jijG88aSuW+Og7q2y5BJa5h9PvNqYO49vHvYrY3yh/8bM8YWbOJ\nBNgHz5uq2otG8vM8qC6tQkpcohuLNwaNZYlr37ohIN1IvYN7NVLW4X3KmXTDERTke6KUuFgEM+9r\na7NcicsOvQloXFke+e1Y9lbVmr7ndrlCe4AfNaIzPy7f5riGaDzSMSakg7hKnJUCF+Ag4LXUiSPs\nrwTLJGQa1aUV918+OtNipIRUW+KSDZo2jomW1fMNbZxOGAUJlMM5YugBLF27kxNGd3P8WaecfXT4\n5vbZMDn37FTGwpU7okqqpINnbx4fKJAc/Z4vyXvVbAeMePTt0pIla3amJOMynaQj6SNR0mXdN6NF\naYGt2pIDe7ThHzcekXA5LCusdLhMb7MViZ2YuC+B84FVhBvfg4lst6RHNEEQkiHZnUJSjdOhz+mE\nkYglrrgwj9+enr68rGD1+QnjeoZtfQb++LAZizdzQNsEy4KkgMtPHsicpVsZPTD9e6KaWT1bNS9k\nx+5qR/sBp4oTD+1Gtw5lDOiempjPdNExUDbm8CGJb0mXKrJJoTSSqAJ3zRmDqbSocWilrJ17TJ+E\nPBHpwo479RpgHfCQ1vpm4xtKqQfSIpWw3zB2cEeqkiwUuj8zdlBHy/1ks23AjRwU+xzot4SEtTH8\n7VT+VNQrSzUtmxWGLFCRXHh8X4b1actBGdijNkiz4nzGDk5eObj4hH48+/4iW22N9cduPWc4M/UW\nDlLtuOwkn62FR1lpAQO6t47aGB38E2xkGZCyknx6HBDths/zuBna2/7eq5mipCiPpyeOc7xbTSo5\n+qDOfDZzLX1tJvXkCkN6Wf/+Vga3kf3aU96ymHtfmJkmqZxhx506N/DnzSZvP5VacYT9jVxPHsg0\nQ3q1jdquKUiiW4ali0g32vVnDuHyGFXQ403ol53Un9lLtjB7yVa8Pl9WKnFgvaIvLsxjVP8Opu/l\nGk52+DBuV9W2ZXGoPtqoAfb6wu1ycYPFHppHmmyv98hvx2adC8wpmVTgAM4+qjcnj+1ue9urpkDL\nZoWUFuVx6MDoRU5BFo01jlIclVIHA32AoO1SSowIQgaJNTc1ZvyKPcKFNY1jchATN2pAB0YN6MB1\nj3/Hrr01+9UEk204KXfU2AHjua7AZQMul2u/e77yPG4ev/Zw0/eyacFoW4lTSt2NP5GhGzAD6AKY\n708jCELGybqYOBtzqVWJkVjccNZQvpi1liOHS8WjTJHnsa8oiU4l5DqpTqJIBifqZGut9YnAp1rr\n/9NaHwV8kSa5BEGwQaz5MBtqOvUzFAq2Y4ExNrEbE9e5vBnnH9c3oQxFITVYbfBuhifbCm0JgkNy\n0hIH7Av8b6wD0cWsoSAImWN4n3JmL9lC5yzYlu2McT0bXjicu71eH3decJBlrSghe8hzELMl7k0h\n10mksHi6cKLE9VVKnQrMV0rNAnYBNekRSxAEW5jMh1eeMpCKyhpamuwOkCr+cMkh3PHM93HbhRXs\ndXgNr8+X9TW8BD95eeG/rstlHdOYKxuLC4IVuWqJOxVAa12vlNoEtAb+nczFlVKtgfuBn4DewG1a\n600m7c4FhgH1wHKt9T8CxycBfQ1Nf6u1npeMTIKQ67jdrrQqcID92mZJeHSzLzFDsCLSVZ7vcVNj\nsbF8rlTCFwQrsmkhYluJ01rXG/7+L4BS6jKSKzNyH/CZ1voVpdRJwMPAecYGSqnOwI3AMK21Tyk1\nQyn1hdZ6KbBRa315EtcXhJwmo/tu2sCohnkCwe/G9Pyxgzvy3dyGTeJdroYq4qLD5Q6RLlKPxw1W\nSlz2GDEEIeexs2NDrOSF3iSnxJ0A/DHw92TgBZM2xwKztNbBIX0qcDywFGiulLodqAP2ApO01lI5\nVhCyBYMi5nG7uf/Xo8L2EB3epzxcicOF2+2i3uvLisQMITHyPS6id0j1I5Y4oSlwwuiuUYWlM4Ed\nS9xu4C/4Fa5q4NvA8bHAXKsPBVFKfQyY7elyF9AucH6ACqCVUiovQhEztgm2C5Y4fwmYq7WuU0o9\nCNwK3BtLnlatSsjLovTgpkB5eeb3PN1fadGiOKv7v0XLcPkiZf1ZeXNGDjqAc3/3EQAtW5XgCShx\nhYX5WfXdskmWbMefKdyQkFKQ5w71X2V9g3Ier0+lzxsf6XN7XH6GecFppyTb33aUuCu11uuUUmdp\nrScajn+ilHos3oe11sdavaeU2ow/23UnUAbsMLGkbQZ6GV6XAcsC555tOP4F/l0lYipxO3ZUxhNZ\ncEB5eXO2bNkdv6GQMowP/e7dVVnR/x3blLBhW/SztWNHJVuaxV+tHj+qC59MX0ORG7p2aM7Stbso\nynNlxXcDuc+dEjS2tWhWwLEHd2Fo77ah/ityw8h+7Rjepzxmn0qfNz7S542L3f6OpejFjU7QWq8L\n/NlPKRUajZVShcCg+GLG5H1gdODvMYHXKKXcSqlg+ZKPgRFKqaANfjTwYaDdQ4Zz9Sag3AnC/kK2\nlGs4dmRDtSGjRHZdohPG9eKpm8ZRmO/hqlMHcc7P+jBumBTvzSWuP3NI6O/gDg719T6OO6QLHVqX\nhN5zu1xcfvJARvYzc9AIguAEJ9mprwOrlFIz8Ee6HExDPFui3AY8oJTqA/TEn8AAMBh/5usgrfVa\npdTDwCNKqXrgmUBSA0C5Uup+oBJQwPVJyiMIOUWW6HBhcvzh0kO4/en45Ueiz+E/SVlpAUeNiN4D\nU8huBvZo2JA+WEerPts28BWEJoaT7NTHlVJfAuPxL7bvSLach9Z6O3CpyfE5GKx8WusXgRdN2l2Y\nzPUFQUgNxmD1jm0ayo9IbsL+iSegxNXVyw0gCOnEiSUOrfV8YH6aZBEEwSHZoiRZZRxKhun+SXAv\n1bp6scQJQjqRij2CkMNki47kshhJskQ8oZFpUeoPn86W+1MQmiqixAlCTpMds2SkJe5XR/emVfNC\neh7QIkMSCZng/l+P4uIT+tFNtksThEbBkTtVEITsIlssHZFZskcfdCBHH3RghqQRMkW7ViW0a1XC\nJ9NXZ1oUQdgvEEucIOQwWaLDkUVbCQpZQPcD/Ja4ob3aZlgSQWjaiCVOEHKYbEkcyJZ6dUJ20Ltz\nS+65aCQdWhdnWhRBaNKIEicIOUyW6HB0btcs0yIIWcaBck8IQtoRd6og5DDZosS1aykWF0EQhMZG\nlDhByGmyRIsTBEEQGh1xpwpCDpMtljiAq08fzK691ZkWQxAEYb9BlDhBEJLiprOHATC0t2QiCoIg\nNCaixAlCDpNJQ9xj1xzG3n21tG9VkkEpBEEQ9l9EiROEHCaTJUaaFefTrDg/Y9cXBEHY35HEBkHI\nQS4+oR/tWhYzsHubTIsiCIIgZAixxAlCDjJmUEfGDOqYaTEEQRCEDCKWOEEQBEEQhBxElDhBEARB\nEIQcRJQ4QRAEQRCEHESUOEEQBEEQhBzElckSBYIgCIIgCEJiiCVOEARBEAQhBxElThAEQRAEIQcR\nJU4QBEEQBCEHESVOEARBEAQhBxElThAEQRAEIQcRJU4QBEEQBCEHESVOEARBEAQhBxElThAEQRAE\nIQcRJU6IiVKqr1JqjFJK7pVGQinVJdMy7G8opQ7ItAz7G9LnjY9Sqofhb1cmZdlfUH5OU0rlp+P8\neek4qZD7KKVKgJ8DxwLvAqXA7owK1cRRSjUDfgGcoZRaDXygtf4kw2I1aZRSpcDJwHil1Cpgidb6\nFaWUS2st29mkgcDYciIwQSm1FPhMa/1FhsVq8iiljgeeU0rdqbV+Br8Rpz7DYjVZlFLFwPHAWGAq\n0ALYmurriHVFsOIw/Dfcr4GFQJ1SKg9kBZcOAg/8RKAauArwAG0yKtT+wS/w9/MNwALgJqXUUK21\nT+7z1KOUGgg8AawFrgFKgGFi6U8fhr71Al8AFyilWmit66Xf08pIoFZrfT0wD/8cWgSpnUPlBxRC\nKKU8gf/d+K0TPuAs4HzgQeBmALFQpI5gnwc4D1imtd4A7AR6KKW6Z0aypo1SyhW4z8cDC7TWFfgt\nzp8AD4Hc52liJX6L/nSt9XpgMdBFa+3NqFRNlIBFOdi3vYA38CsUNyqlWuNXooUUopRyB5S0cUCt\nUuo04Ezgd/gXMCkdW0SJE1BKHaCUuhX/g3144KH/Ef9kNlNrfRfwAXCUUmpcBkVtMkT0+RFa6yrg\nReCPSqkXgQL81rjnlVLHZVLWpoJSqrtS6jKlVJnW2he4z9cC9wNoreuAJwGPUmpUJmVtKhj7HEBr\nvQe4K9DXAMuAbwJt22dIzCZF5H1uWChuxb9I+Q7/gnFi4PcQ70qSRPS5N6CkrQceBdZrrX+Pf2wZ\nqZQ6NZXXFiVuP0cp1Q+/++4DYBXwsFLqaPxm957AwYGm3wLTgdpMyNmUsOjz8VrrO4FbgRVa65uB\ne4HPgeYZE7aJoJQqwO+uPg2/lTnIg0AHpdSEwOsdwDSgonElbHpY9bnWeqeh2UjgM6VUb+A3jSth\n08Osz7XWwbi3o4Fzge74x/duSqlBgTZidU6QGGPL80BrYDSA1nop8BIp1rtEiROaAf201j9qrV8G\nPgROAYqAu4G7Au0GAl3wry6E5Ijs8/eBMwMTWR/ggkC70fj7fXFmxGxSFABzgc+A0UE3tdZ6H37F\n+QGlVB9gOHAAosSlAtM+D1p9Au7sA/FPfE8CFRKjlTRWfV4I/ACsAx4IvD8eOFL6PGmsxpZa4Cbg\neqVUR6XUGKA//hjzlOHy+UQB359QSvXFv2L4DJiPf8K6DXhaaz01kIL+APAPrfVnSqmHgX1AJfCC\n1npdhkTPWWz0eXf8rutJ+LOYnsff3z8C/5M+d05Eny/UWu8JuJWGAFcEjj1iaH8JUI4/Y//ZQLyW\n4AAnfR5Q5MbgX8A8j3+8Senktj/gsM+ba613B5KojgIWaa2XZ0r2XCWBseU6/Av3etIwh4oStx8Q\nLJeglLoCKANW4F+FAVyJfxD9Afin1nqXUupxoE5rfV1glVYQsFgINkmwz/dprW8KlGBor7VekQnZ\ncxWLPj8CKNVaX2hodzV+C+cjWutFGRG2iZBMnwcmw0Fa61cbX/LcJdn7XMrnOCcFfe4xuLVTiphR\nmziBFW9x4GVL4COt9SvAHfizTkcC/wEGARcG2s0HvgQIBGmKAueAJPr8WwCtdaUocM6I0ed3Aacr\npY4xNH8VqAH+rJS6KhDTIjgkyT4v0lovFgXOGQn2+cPG+1wUOGekYmxJlwIHosQ1aZRSo4G/4H+I\nB+BfOXQF0Fpvwx/z9rjW+mPgOeBgpdR9+G/YTzMidI4jfd742Ojz3wEPGz7iAdrjt4T+S2td07gS\n5z4p6HNZGDokiT6fg9znCZELY4u4U5sgyl/5/25gKfAK8Az+m2on8Butdd9Au0LgbeBGrfV8pVRb\nwKO13pQRwXMY6fPGx2GfvwncrLWeF+jzIq312owInsNInzc+0ueNTy71uVjimiY+/FlIn2mtdwD3\nACO11n/DXzX62kC7NsCiwD+01ltFmUgY6fPGx0mfLyaQFRboc5nYEkP6vPGRPm98cqbPZe/Upkkl\n8JrWeo3h2NTA/3cCxymlHsJfRmFmOv31+xHS542Pkz6fJX2eEqTPGx/p88YnZ/pclLgmSCBw1Xjz\ndSVg+cFf0+Y+/OUUVgT8+kKSSJ83PtLnjY/0eeMjfd745FKfixK3f9AR2K6U+i/+DdY/0VqvyrBM\nTR3p88ZH+rzxkT5vfKTPG5+s7XNJbGjiKKU6AFPwb3r8itb6pQyL1OSRPm98pM8bH+nzxkf6vPHJ\n9j4XS1zTxws8Czysta7OtDD7CdLnjY/0eeMjfd74SJ83Plnd52KJEwRBEARByEGkxIggCIIgCEIO\nIkqcIAiCIAhCDiJKnCAIgiAIQg4iSpwgCIIgCEIOIkqcIAiCIAhCDiIlRgRBEExQSo0B/gD0x7/J\ndSugGfBPrfVrcT57ITBOa31hmsUUBGE/RixxgiAIJmitJwMv4N9a53Kt9S+BS4A7lVLXZVY6QRAE\nscQJgiDYRmu9QSk1EXhdKfUG8ASwAGgDzNRaT1JK9QbOBToppf4GvKu1/lgpdTXQB6gCWgLXaa33\nZOabCILQFBAlThAEwRkzgFKgHfBnrfWXAEqpuUqpd7TWS5VSL+J3p/4m8N5RwC+01kcHXv8BmAjc\nlZFvIAhCk0CUOEEQhMRwA+OUUmcDlUBroCew3qTt8UBbpdSkwOu2wIZGkVIQhCaLKHGCIAjOOBjY\nCxwJDNNa/wJAKTUU8Fh8xgVM1VpfEWjrAkoaQVZBEJowktggCIJgE6VUB+BB4Hf44+C2B467gc6G\npvsAj1LKpZS6APgQGK+UCi6cTwGubTTBBUFokrh8Pl+mZRAEQcg6lFKjgXuBgcBr+EuMtAD+rbX+\nn1KqC/AysBTYBpwMzAUuBoqB14FlwBda6+eUUtcChwJrgCLgBq31vsb9VoIgNCVEiRMEQRAEQchB\nxJ0qCIIgCIKQg4gSJwiCIAiCkIOIEicIgiAIgpCDiBInCIIgCIKQg4gSJwiCIAiCkIOIEicIgiAI\ngpCDiBInCIIgCIKQg/w/CggVQ1Ie3ysAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x118e93f98>"
]
},
"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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ua+HZvWtIp9IscH5X0YTRFzGsaii7WxrYfmhn0nEk9WMWXlIZW9Gwikw2Qxh9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\nSSVi4SVJklQi/w84f+UlGsg6+QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1197480f0>"
]
},
"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 0x1196ff320>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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iHwFcDOwC5BP8z90PreciWXbccUNYsSI/fNb1hDKETZzMwkRBfgQ1QFCQv5ez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\nRK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1194dc940>"
]
},
"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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G0BIgM8iUbeBm9j7gA/iTALYCU6/0mOc0W1NkvI7uAX5y75bRAe1nrKznA284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\n/x+1kfQDi3aYXQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11962cb38>"
]
},
"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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Gdo7B55wu+2lDcyxor4Qo5kwZQEFZLSajka8ccholFfWcM2twp/RL8I/3e0nv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\nWKa1fquXTZ5WSk0GLgWeHejnCCGGRmOLE6vFQnSUFY8Htu+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ECEmBSkK7jhx8rlLqWa11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\nyc8O/b0xpeoAJW7nxwfky+JJk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bdbVvDlu9dSWZT89cSS5CGUq/4bQohPAq8CgXWCLwMf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\n/T9CVcjP8BYOnwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1196cea20>"
]
},
"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": {},
"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 0x118f76208>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%run es50_imp_vol.py"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\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 10.6 s, sys: 40.8 ms, total: 10.7 s\n",
"Wall time: 10.7 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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1x2E0Gvn6688JC3u+Ssf17NmbuLjfMRgMFBQUkJgYb2lCXh0yJ0yIamrSBG6+We6ACSHq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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1c1c09e898>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_imp_vols(data)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Option Pricing with Python"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some live examples."
]
},
{
"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": {},
"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": {},
"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": {},
"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": {},
"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": {},
"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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5C/q8/BHHD7VF8Hx4Yvg2RVHoe2UvSBJp93902rHoly8n54GPjFtXdTV1UhKWG28m2t+H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v9ICX//5DxiItR8draTH7xSRt0loqvHu4O6MgLChIwhgNMStOu4tAzo9Xv5TcUb9DkHuD1lDSsS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\nRImViIiISIP8P/2DK+4o4dA7AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119622c50>"
]
},
"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": {},
"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 2.46 s, sys: 299 ms, total: 2.76 s\n",
"Wall time: 2.78 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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c0VUrmCr9Yj/SJ/Yk/bI8i4UsWZP1OiiKQmxLkNiWIG+7vZ3OM4OcOdHHxc4R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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119622c18>"
]
},
"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, label='$\\lambda$')\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, label='$\\mu$')\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, label='$\\delta$')\n",
" plt.legend(loc=0)"
]
},
{
"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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dbGpUwjRDM2GDv1TFyHIyErhx+WIWq8C5k7c9sJaqutg+4vRjOyNranBkZmKL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\nAAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x118f4d2e8>"
]
},
"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('http://hilpisch.com/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",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\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": {
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xfXt2drkSgP4lWAErMjF+cJnxA90tBKCPWbwOrMjFBeqTU8dzanYu+/bszMT4AQvXARYR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\nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x113dfbd68>"
]
},
"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 53.3 s, sys: 133 ms, total: 53.4 s\n",
"Wall time: 53.4 s\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 17 s, sys: 36.4 ms, total: 17 s\n",
"Wall time: 17 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": {},
"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": {
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+rIISSXRuNwweXMHixVu49NJyvv8+hbPP9nDZZZn88otuW4mIxFukWzX83Vp7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\nRK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x113dfbd68>"
]
},
"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": {},
"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 0x118f69048>"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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UO3Lq20EHlX6rp/Gizs7OnsbzqrGxJfWivGEzefY0WfYzefY0WfYzeYOxp3ffvZwXX/wj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\nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11975a0f0>"
]
},
"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:team@tpq.io\">team@tpq.io</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>"
]
}
],
"metadata": {
"celltoolbar": "Slideshow",
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
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"nbformat": 4,
"nbformat_minor": 1
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#
# 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('http://hilpisch.com/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()
#
# 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)
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