{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "95JXKOZXC_9R",
    "nbpages": {
     "level": 0,
     "link": "[](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html)",
     "section": ""
    },
    "pycharm": {}
   },
   "source": [
    "<!--NOTEBOOK_HEADER-->\n",
    "*This notebook contains material from [CBE40455-2020](https://jckantor.github.io/CBE40455-2020);\n",
    "content is available [on Github](https://github.com/jckantor/CBE40455-2020.git).*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yniNR0U6C_9T",
    "nbpages": {
     "level": 0,
     "link": "[](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html)",
     "section": ""
    },
    "pycharm": {}
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [7.1 Measuring Return](https://jckantor.github.io/CBE40455-2020/07.01-Measuring-Return.html) | [Contents](toc.html) | [7.3 Binomial Model for Pricing Options](https://jckantor.github.io/CBE40455-2020/07.03-Binomial-Model-for-Pricing-Options.html) ><p><a href=\"https://colab.research.google.com/github/jckantor/CBE40455-2020/blob/master/docs/07.02-Geometric-Brownian-Motion.ipynb\"> <img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open in Google Colaboratory\"></a><p><a href=\"https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.ipynb\"> <img align=\"left\" src=\"https://img.shields.io/badge/Github-Download-blue.svg\" alt=\"Download\" title=\"Download Notebook\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Cj9jZN-5C_9U",
    "nbpages": {
     "level": 1,
     "link": "[7.2 Geometric Brownian Motion](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2-Geometric-Brownian-Motion)",
     "section": "7.2 Geometric Brownian Motion"
    },
    "pycharm": {}
   },
   "source": [
    "# 7.2 Geometric Brownian Motion\n",
    "\n",
    "This notebook presents methods for modeling a financial time series as geometric Brownian motion. The basic outline is to:\n",
    "\n",
    "1. Capture a data series.\n",
    "2. Compute returns (we'll do both linear and log returns).\n",
    "3. Test statistical properties. We need the returns to be independent and identically distributed (iid).\n",
    "4. Fit distribution of returns to a normal distribution.\n",
    "5. Perform simulations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2spMuzM7xKX8",
    "nbpages": {
     "level": 2,
     "link": "[7.2.1 Historical perspectives](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.1-Historical-perspectives)",
     "section": "7.2.1 Historical perspectives"
    }
   },
   "source": [
    "## 7.2.1 Historical perspectives\n",
    "\n",
    "The name [Brownian motion](http://physics.ucsc.edu/~drip/5D/brown/brown.pdf) (or Brownian movement) is a tribute to Sir Robert Brown, the Scottish botanist who, in 1827, reported  the random motion of pollen grains on the surface of water when viewed under a microscope. \n",
    "\n",
    "The explanation of that behavior waited for the genius of Albert Einstein. In the *[Annus mirabilis](https://en.wikipedia.org/wiki/Annus_mirabilis)* of 1905, while employed as a patent clerk and living in a [modest apartment in Bern](https://en.wikipedia.org/wiki/Annus_Mirabilis_papers#/media/File:Albert_einstein_house_bern.JPG), Einstein published papers describing Special Relativity, laid the foundation for quantum theory with a paper on the photoelectric effect, and demonstrated the existence of atoms and molecules with a paper on [Brownian Motion](https://www.zbp.univie.ac.at/dokumente/einstein2.pdf). \n",
    "\n",
    "Remarkably, five earlier [Louis Bachelier](https://en.wikipedia.org/wiki/Louis_Bachelier) published his Master's thesis on the \"Theory of Speculation\". While this study was limited to the dynamics of prices on the Paris Bourse, and therefore didn't have the profound implications for Physics of Einstein's forthcoming work, nevertheless Bachelier should be credited with introducing random motion to describe price dynamics. Unfortunately, this work laid in relative obscurity for decades.\n",
    "\n",
    "Other figures in this intellectual history include the Japanese [Kiyosi Ito](https://en.wikipedia.org/wiki/Kiyosi_It%C3%B4) whose work in the difficult circumstances of the second World War [laid a foundation for stochastic calculus](http://www4.math.sci.osaka-u.ac.jp/shijodanwakai/pdf/1077.pdf). Later, the [eccentric](https://www.theatlantic.com/technology/archive/2014/06/norbert-wiener-the-eccentric-genius-whose-time-may-have-finally-come-again/372607/) [Norbert Weiner](https://en.wikipedia.org/wiki/Norbert_Wiener) established a [theory for random motion -- [the Wiener process](https://en.wikipedia.org/wiki/Wiener_process) -- now widely used in engineering and finance.\n",
    "\n",
    "The colorful history of individual genius and iconclastic research doesn't end there, but it is enough to provide some understanding behind the terminology that will be introduced below.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "aJ9K6S4aC_9U",
    "nbpages": {
     "level": 2,
     "link": "[7.2.2 Python Imports and Utility Functions](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.2-Python-Imports-and-Utility-Functions)",
     "section": "7.2.2 Python Imports and Utility Functions"
    },
    "pycharm": {}
   },
   "source": [
    "## 7.2.2 Python Imports and Utility Functions\n",
    "\n",
    "The [`pandas-datareader`](https://pandas-datareader.readthedocs.io/en/latest/#) package provides a utility for accessing on-line data sources of data. Since the interfaces to those data sources are constantly changing, the next cell updates any current installation of the data reader to the latest available version."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "executionInfo": {
     "elapsed": 430,
     "status": "ok",
     "timestamp": 1604588431403,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "5j6hDBPaC_9V",
    "nbpages": {
     "level": 2,
     "link": "[7.2.2 Python Imports and Utility Functions](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.2-Python-Imports-and-Utility-Functions)",
     "section": "7.2.2 Python Imports and Utility Functions"
    }
   },
   "outputs": [],
   "source": [
    "%%capture\n",
    "#!pip install pandas_datareader --upgrade"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "executionInfo": {
     "elapsed": 402,
     "status": "ok",
     "timestamp": 1604588436232,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "yAi20ohoC_9Y",
    "nbpages": {
     "level": 2,
     "link": "[7.2.2 Python Imports and Utility Functions](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.2-Python-Imports-and-Utility-Functions)",
     "section": "7.2.2 Python Imports and Utility Functions"
    },
    "pycharm": {}
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import datetime\n",
    "\n",
    "import pandas as pd\n",
    "import pandas_datareader as pdr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "executionInfo": {
     "elapsed": 324,
     "status": "ok",
     "timestamp": 1604588449862,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "u22-e3K2Zm32",
    "nbpages": {
     "level": 2,
     "link": "[7.2.2 Python Imports and Utility Functions](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.2-Python-Imports-and-Utility-Functions)",
     "section": "7.2.2 Python Imports and Utility Functions"
    }
   },
   "outputs": [],
   "source": [
    "# python libraray for accessing internet resources\n",
    "import requests\n",
    "\n",
    "def lookup_yahoo(symbol):\n",
    "    \"\"\"Return a list of all matches for a symbol on Yahoo Finance.\"\"\"\n",
    "    url = f\"http://d.yimg.com/autoc.finance.yahoo.com/autoc?query={symbol}&region=1&lang=en\"\n",
    "    return requests.get(url).json()[\"ResultSet\"][\"Result\"]\n",
    "\n",
    "def get_symbol(symbol):\n",
    "    \"\"\"Return exact match for a symbol.\"\"\"\n",
    "    result = [r for r in lookup_yahoo(symbol) if symbol == r['symbol']]\n",
    "    return result[0] if len(result) > 0 else None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KEj5yQDMC_9b",
    "nbpages": {
     "level": 2,
     "link": "[7.2.3 Statistical Properties of Returns](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.3-Statistical-Properties-of-Returns)",
     "section": "7.2.3 Statistical Properties of Returns"
    },
    "pycharm": {}
   },
   "source": [
    "## 7.2.3 Statistical Properties of Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 458
    },
    "executionInfo": {
     "elapsed": 2100,
     "status": "ok",
     "timestamp": 1604589685688,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "jrVe5ZTMC_9c",
    "nbpages": {
     "level": 2,
     "link": "[7.2.3 Statistical Properties of Returns](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.3-Statistical-Properties-of-Returns)",
     "section": "7.2.3 Statistical Properties of Returns"
    },
    "outputId": "6d6703a9-66d2-4901-f6b8-31490fa9a4b2",
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'symbol': 'AAPL', 'name': 'Apple Inc.', 'exch': 'NMS', 'type': 'S', 'exchDisp': 'NASDAQ', 'typeDisp': 'Equity'}\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "symbol = 'AAPL'\n",
    "\n",
    "# get symbol data\n",
    "symbol_data = get_symbol(symbol)\n",
    "print(symbol_data)\n",
    "assert symbol_data, f\"Symbol {symbol} wasn't found.\"\n",
    "\n",
    "# end date is today\n",
    "end = datetime.datetime(2018, 8, 30).date()\n",
    "start = end-datetime.timedelta(3*365)\n",
    "\n",
    "# get stock price data\n",
    "S = pdr.data.DataReader(symbol, \"yahoo\", start, end)['Adj Close']\n",
    "rlin = (S - S.shift(1))/S.shift(1)\n",
    "rlog = np.log(S/S.shift(1))\n",
    "\n",
    "# clean up data\n",
    "rlin = rlin.dropna()\n",
    "rlog = rlog.dropna()\n",
    "\n",
    "# plot data\n",
    "plt.figure(figsize=(10,6))\n",
    "plt.subplot(3,1,1)\n",
    "title = f\"{symbol_data['name']} ({symbol_data['exchDisp']} {symbol_data['typeDisp']} {symbol_data['symbol']})\"\n",
    "S.plot(title=title)\n",
    "plt.ylabel('Adjusted Close')\n",
    "plt.grid()\n",
    "\n",
    "plt.subplot(3,1,2)\n",
    "rlin.plot()\n",
    "plt.title('Linear Returns (daily)')\n",
    "plt.grid()\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.subplot(3,1,3)\n",
    "rlog.plot()\n",
    "plt.title('Log Returns (daily)')\n",
    "plt.grid()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FUNq64DhC_9f",
    "nbpages": {
     "level": 3,
     "link": "[7.2.3.1 Distribution of Returns](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.3.1-Distribution-of-Returns)",
     "section": "7.2.3.1 Distribution of Returns"
    },
    "pycharm": {}
   },
   "source": [
    "### 7.2.3.1 Distribution of Returns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-zBEvBylC_9f",
    "nbpages": {
     "level": 3,
     "link": "[7.2.3.1 Distribution of Returns](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.3.1-Distribution-of-Returns)",
     "section": "7.2.3.1 Distribution of Returns"
    },
    "pycharm": {}
   },
   "source": [
    "A basic assumption in developing developing stochastic price models is that the residuals are indepdendent and identically distributed (i.i.d.) random variates.  Here we show the results of several common statistical tests that would screen out non-i.i.d. random variates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 369
    },
    "executionInfo": {
     "elapsed": 1462,
     "status": "ok",
     "timestamp": 1604589279613,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "b0QdY-M_C_9g",
    "nbpages": {
     "level": 3,
     "link": "[7.2.3.1 Distribution of Returns](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.3.1-Distribution-of-Returns)",
     "section": "7.2.3.1 Distribution of Returns"
    },
    "outputId": "35af3f26-eeef-41f6-e685-0127573099eb",
    "pycharm": {}
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(-0.12,0.10,50)\n",
    "plt.figure(figsize=(10,5))\n",
    "\n",
    "plt.subplot(2,2,1)\n",
    "rlog.hist(bins=bins, density=True, color='b', alpha=0.5)\n",
    "plt.xlim(bins.min(),bins.max())\n",
    "plt.title('Log Returns')\n",
    "\n",
    "plt.subplot(2,2,3)\n",
    "rlog.hist(bins=bins, density=True, cumulative=True, color='b',alpha=0.5)\n",
    "plt.xlim(bins.min(),bins.max())\n",
    "\n",
    "plt.subplot(2,2,2)\n",
    "rlin.hist(bins=bins, density=True, color='y', alpha=0.5)\n",
    "plt.xlim(bins.min(),bins.max())\n",
    "plt.title('Linear Returns')\n",
    "\n",
    "plt.subplot(2,2,4)\n",
    "rlin.hist(bins=bins, density=True, cumulative=True, color='y',alpha=0.5)\n",
    "plt.xlim(bins.min(),bins.max())\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "irLQ-05QC_9j",
    "nbpages": {
     "level": 3,
     "link": "[7.2.3.2 Distribution of First Half versus Second Half of the Data Set](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.3.2-Distribution-of-First-Half-versus-Second-Half-of-the-Data-Set)",
     "section": "7.2.3.2 Distribution of First Half versus Second Half of the Data Set"
    },
    "pycharm": {}
   },
   "source": [
    "### 7.2.3.2 Distribution of First Half versus Second Half of the Data Set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 298
    },
    "executionInfo": {
     "elapsed": 1130,
     "status": "ok",
     "timestamp": 1604589805018,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "41-wccCaC_9k",
    "nbpages": {
     "level": 3,
     "link": "[7.2.3.2 Distribution of First Half versus Second Half of the Data Set](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.3.2-Distribution-of-First-Half-versus-Second-Half-of-the-Data-Set)",
     "section": "7.2.3.2 Distribution of First Half versus Second Half of the Data Set"
    },
    "outputId": "28d8d6d0-7c16-43c5-b206-eccee651122b",
    "pycharm": {}
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Change in Distribution of Log Returns')"
      ]
     },
     "execution_count": 52,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "k = int(len(rlog)/2)\n",
    "r = np.linspace(rlog.min(),rlog.max())\n",
    "\n",
    "plt.figure()\n",
    "\n",
    "param = norm.fit(rlog[:k])\n",
    "rlog[:k].hist(bins=r, density=True, alpha=0.35, color='r')\n",
    "plt.plot(r,norm.pdf(r,loc=param[0],scale=param[1]),'r-',lw=3);\n",
    "\n",
    "rlog[k:].hist(bins=r, density=True, alpha=0.35, color='c')\n",
    "param = norm.fit(rlog[k:])\n",
    "plt.plot(r,norm.pdf(r, loc=param[0], scale=param[1]), 'c-',lw=3);\n",
    "\n",
    "plt.legend(['rLog[:k]', 'rLog[k:]'])\n",
    "plt.title('Change in Distribution of Log Returns')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 321,
     "status": "ok",
     "timestamp": 1604589911997,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "ucQUPNNXC_9n",
    "nbpages": {
     "level": 3,
     "link": "[7.2.3.2 Distribution of First Half versus Second Half of the Data Set](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.3.2-Distribution-of-First-Half-versus-Second-Half-of-the-Data-Set)",
     "section": "7.2.3.2 Distribution of First Half versus Second Half of the Data Set"
    },
    "outputId": "6a382c1b-4b4f-4c53-fa60-4035bc6eba47",
    "pycharm": {}
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0006336699156164701, 0.014878954780728938)"
      ]
     },
     "execution_count": 53,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm.fit(rlog[:k].dropna())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9auPg1Z_C_9r",
    "nbpages": {
     "level": 3,
     "link": "[7.2.3.3 Lag Plot of $r^{log}_{t+1}$ versus $r^{log}_t$](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.3.3-Lag-Plot-of-$r^{log}_{t+1}$-versus-$r^{log}_t$)",
     "section": "7.2.3.3 Lag Plot of $r^{log}_{t+1}$ versus $r^{log}_t$"
    },
    "pycharm": {}
   },
   "source": [
    "### 7.2.3.3 Lag Plot of $r^{log}_{t+1}$ versus $r^{log}_t$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 303
    },
    "executionInfo": {
     "elapsed": 709,
     "status": "ok",
     "timestamp": 1604585784555,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "VoP8k9qvC_9r",
    "nbpages": {
     "level": 3,
     "link": "[7.2.3.3 Lag Plot of $r^{log}_{t+1}$ versus $r^{log}_t$](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.3.3-Lag-Plot-of-$r^{log}_{t+1}$-versus-$r^{log}_t$)",
     "section": "7.2.3.3 Lag Plot of $r^{log}_{t+1}$ versus $r^{log}_t$"
    },
    "outputId": "09e46137-f41c-4eee-fbef-aa2bf431bffd",
    "pycharm": {}
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(rlog[0:-1], rlog[1:],'.')\n",
    "plt.axis('equal');\n",
    "plt.xlabel('$r^{log}_{t}$')\n",
    "plt.ylabel('$r^{log}_{t+1}$')\n",
    "plt.grid()\n",
    "plt.title('Lag Plot for Log Returns');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MT5ybVD-CMEk",
    "nbpages": {
     "level": 3,
     "link": "[7.2.3.3 Lag Plot of $r^{log}_{t+1}$ versus $r^{log}_t$](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.3.3-Lag-Plot-of-$r^{log}_{t+1}$-versus-$r^{log}_t$)",
     "section": "7.2.3.3 Lag Plot of $r^{log}_{t+1}$ versus $r^{log}_t$"
    }
   },
   "source": [
    "i.i.d. ==> Independent and Identically Distributed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "d7PAZk0sC_9u",
    "nbpages": {
     "level": 3,
     "link": "[7.2.3.4 Autocorrelation](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.3.4-Autocorrelation)",
     "section": "7.2.3.4 Autocorrelation"
    },
    "pycharm": {}
   },
   "source": [
    "### 7.2.3.4 Autocorrelation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 573
    },
    "executionInfo": {
     "elapsed": 661,
     "status": "ok",
     "timestamp": 1604590523761,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "SnXaV0pSC_9w",
    "nbpages": {
     "level": 3,
     "link": "[7.2.3.4 Autocorrelation](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.3.4-Autocorrelation)",
     "section": "7.2.3.4 Autocorrelation"
    },
    "outputId": "433b1d47-2808-4b43-e1fe-e4b000a3a4a6",
    "pycharm": {}
   },
   "outputs": [
    {
     "data": {
      "image/png": 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O9obMO5lA37jjFV5+tafsMhpmsA/GPz/1Iiuf2cmrr/UBsLe7l5XP7OTWh57iHbOPf/15B34QB4RCrmUN/00+0g/zYE/PM9+B63i4l1+kvr5g1aZdPL3jFWadcBTzp0+gzV/WLWvi+E7mTD66IfNOJtD3dvcmHeiD+fVzu9mfhXm//a/18evnXmbelGNLqsqK0tcXfOUHa1m/bQ/dPX10drRx0qTxXHPBXIe6HcSDoi1u1glH0dlx4Gbs7Ghj1glHlVSRFWnVpl2s37aH/T19BLC/p4/12/awatOuskuzJuRAb3Hzp0/gpEnjoacboo+x2R7c/OkTyi7NCvD0jlfo7jnwCKy7p4+nd7xSUkXWzJIM9L6+YOXGnXxv5WZWbtxJX1+Tj8yMQFubuOaCuYxf833GPfUz/vTsOSM+HB9Nr1+z8xGYDUcyfej9yuxzLGvwqq1NdO5YDzvWc/rMz41oXu6zbS79R2Crn3kB2jsYO6bDR2A2qOQCvbrPEQ7sczx95nENW24qQdiI12+0naVR5Pr2H4Fd+cnP0Dt+Mld9fPGIX7/Rtj1Gk+QCfag+x0YGellfJEUr+vVL5YsO8gVhI9Y3lSOwor9I/MV0sOQCvb/PcX9VKB2OPseyvkiKVvTrV+YXXZEf+LxB2Oxf7Kkcwaa0o1Ck5AZFG3HWR55BwuEMXjXzoGPRr19ZZ2n0f+BvuP9J7lmxmRvuf5Kv/GDtIb/WeU8fbPazUsqqr+jTL306Z225Al3S+ZLWSVov6eoaj4+VdHf2+COSZhVdaF5Fn/WRNxjyBmHRQVO0ol+/ss7SKPoDnzcIm/2slLLqK/qLpNm/OMtSN9AltQM3AhcA84BFkuYNmOwKYGdEnAR8HfjLogsdjv4+x3EbH+L0mceN6BAsbzDkDcJW2LMo8vUr6zz5oj/weYOw2f8uoKz6ij6CbfYvzrKo3jUvJJ0FXBcR783ufx4gIv6iapp7s2l+IakDeA7oiiFmfvzMuXHuNbcMu+BVj68CYP6p8w9o39vdS0/fGx/gJ9f8CoA589426Lwigj37e3n1tV6OGNPO+LHtSAeG1/aX9/PCnu6Dnts1vpOJR489qL3ecoc7v7zyrG9Z84sIfrN+A7R3MmXKiTVf56K9/GoPW3btO+C6KxJMnTCOo48Y/tBRRPDMi/vYu/81QKhNjBvTzozjxx20LnnXN8/7r19R7+fh1FekvK9f/3T7XuslorLNhpouz/Yoy2DbY0x7G+PGHPrFuZZ8/HdWRMSCWo/leWdPBTZV3d8MnDnYNBHRI+kl4ATgheqJJC0GFgOMP/EtuYofaGCQD6ZeEOV9Qxwxph2Jg4Jh7CAbpN5yhzu/vMGaN3jLmJ8kTp6Tb3vnra/edOPHtjNuTPtBwTB+7KG9zpKYcfw49uzvZP9rvYwdIjDzrO9wA6mo93Pe+voVtT3yvn579ve+vs0q6wX7Xutlz/7eA76Ih7M98q7HcL7o6s1vqO3RSIf1LJeIuAm4CWDBggVx95VnFTbvtc/uZtfe13JPv3LjTm64/0lQW1Zb5VK073/71ANG+8scne/rC66892Z6x0/mfb99XiGnZX3ijs8DcO1nl45oPmXXl2e64ZzlUuTrkkfe919Z8+tX5PbI43srN3PPis0HNgac9eYT+ODp0w55vvXq6/9c9h0xAdo72P7yfo4dN/jnvN78htoe550yeURXW1zy8cEfyxPoW4DpVfenZW21ptmcdbkcC+wYVpWHWd7TDPv7xov+Q5G85zPvmfcBaO/ghvufbKrTspq9Pqi81qfPPK4pThccqOjTXH3a7Mj0j23R0QkMfTpnX1/QfcJJ9I6fzMqNO2t+fssatM1zlsujwBxJsyV1ApcCA7+WlgKXZbc/BNw/VP95MxjOoEp/MHzw9GkjHiTMO78D3mBqa7rB0zLr6/9A7Zv5rqY77TOvogf1Uhkk7B+0HdvRhqDpBtGrd2T2zX7PoGeplbU96gZ6RPQAVwH3AmuBJRGxWtL1ki7KJrsZOEHSeuDTwEGnNjabst44eTX7aVlln19e7wPV7Ip+/5X5fi7yC7b/CPZPz57Dh/7VtEIuNpdH3gDOuyNT1vbI1YceEcuAZQParq26/Srw74otrbGK7kopWlmHnnm1wqFxXnkOoYtWVlde0RrR9VZGV1l/AA8c2xoYwGV11eaV3J/+D0cz97HmfYOVpRH1jbRvciTXmiljLKDo918Z7+dGfMGWIW8AD2dHpoztMaoDvZk1+xFE0fXlDdZGXWum1QOpLK0wGJv3CCxPADf7jpYDvYkV/Q1fdNdCkfXlDdaiP1CtEEjNrNm7Bos+Amv2HS0H+ijR7KcZltU32eyB1OyafY+1EUdgzdxV60AfJZq9a6GsvslmD6Qy5Tmia/Y91tF2BOZAHyWa/Y1dVrA2eyCVZThHdM28xzrajsAc6KNEs7+xywzWZg6ksjT7EV1eo+0ILJlAnzh+LOPHNv/qNPrvZ4M3FvD6BY6A977tTfzk18+z9tnd7H+tj7Fj2ph74jGce8pk2rPQPLi2oYttxLqcd8rkQZdca3lRp8ZDMdR6NWKdD3UdGvle2vrSvppHdFtf2sd7xk484L31Rj35CjrcfwJ23UWn8NgzO3nqhVeYPfEoTptxHG01L7pVbGWDvRztDdxJaf4EzKlrBJeeHS3u+fjv8OC6bazZupt5U45h4cmTGvrmstZ19lsn8U+PbWFvd+/rbeM62zn7rZN4+7TW27t9x6zjyy7hsEgm0K2+9jZxztzJnDN3ctmlWJNbePIk5k+fwKpNu9jX3cu4znbmT5/AwpMnlV2aDcGBbmYHaW8Tt19xpo/oWowD3cxq8hFd68n1I9FmZtb8HOhmZolwoJuZJcKBbmaWCAe6mVkiHOhmZolQWb/lLGk7sPEQnz4ReKHAcsri9WguXo/m4vWobWZEdNV6oLRAHwlJyyNiQdl1jJTXo7l4PZqL12P43OViZpYIB7qZWSJaNdBvKruAgng9movXo7l4PYapJfvQzczsYK26h25mZgM40M3MEtFygS7pfEnrJK2XdHXZ9RwqSU9L+qWkVZKWl11PXpJukbRN0q+q2o6X9GNJT2b/N/2PTg6yHtdJ2pJtk1WSLiyzxnokTZf0gKQ1klZL+mTW3lLbY4j1aLXtcYSkf5b0eLYeX87aZ0t6JMusuyV1NqyGVupDl9QO/AY4F9gMPAosiog1pRZ2CCQ9DSyIiJb6wwlJvwvsAb4VEW/L2v4KeDEi/mv2JXtcRHyuzDrrGWQ9rgP2RMR/L7O2vCSdCJwYESslHQ2sAD4AXE4LbY8h1uMSWmt7CDgqIvZIGgP8HPgk8GngexFxl6S/BR6PiG82ooZW20M/A1gfERsiohu4C7i45JpGlYj4KfDigOaLgduy27dR+TA2tUHWo6VExLMRsTK7/TKwFphKi22PIdajpUTFnuzumOxfAGcD92TtDd0erRboU4FNVfc304IbPhPAjyStkLS47GJGaHJEPJvdfg5o5Z+4uUrSE1mXTFN3VVSTNAs4DXiEFt4eA9YDWmx7SGqXtArYBvwY+BdgV0T0ZJM0NLNaLdBT8u6IOB24APhE1gXQ8qLSh9c6/XgH+ibwFmA+8Czw1XLLyUfSeOC7wKciYnf1Y620PWqsR8ttj4jojYj5wDQqPQpvPZzLb7VA3wJMr7o/LWtrORGxJft/G/BPVDZ+q3o+6wft7w/dVnI9hyQins8+kH3A39MC2yTrq/0u8I8R8b2sueW2R631aMXt0S8idgEPAGcBEyT1/35zQzOr1QL9UWBONmrcCVwKLC25pmGTdFQ2+IOko4DzgF8N/aymthS4LLt9GfC/S6zlkPWHYObf0OTbJBuEuxlYGxFfq3qopbbHYOvRgtujS9KE7PY4KidvrKUS7B/KJmvo9mips1wAslOXvgG0A7dExH8puaRhk/RmKnvlAB3AHa2yHpLuBBZSuSTo88CXgO8DS4AZVC6JfElENPWA4yDrsZDK4X0ATwNXVvVFNx1J7wZ+BvwS6Muar6HS/9wy22OI9VhEa22Pt1MZ9GynsrO8JCKuzz7vdwHHA48BH46I/Q2podUC3czMamu1LhczMxuEA93MLBEOdDOzRDjQzcwS4UA3M0uEA91GHUl76k9l1noc6GZmiXCgmwGS3p9ds/oxST+RNDlr78quKb5a0v+StFHSxLLrNavFgW5W8XPgnRFxGpW/6vts1v4l4P6IOIXKJVBnlFSfWV0d9ScxGxWmAXdn1w/pBJ7K2t9N5ToiRMQPJe0sqT6zuryHblbx18DfRMRvA1cCR5Rcj9mwOdDNKo7ljcuaXlbV/hCVn0JD0nlA0//Igo1evjiXjTqS+oCtVU1fo/LLMl8HdgL3A++IiIWSJgF3UvnVn18A7wNmNepqeWYj4UA3G4KksUBvRPRIOgv4ZvaLNGZNx4OiZkObASyR1AZ0Ax8ruR6zQXkP3cwsER4UNTNLhAPdzCwRDnQzs0Q40M3MEuFANzNLxP8Hv7HjIqIOBuoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n",
    "plot_acf(rlog, lags=min(30, len(rlog)));\n",
    "plt.xlabel('Lag');\n",
    "plot_pacf(rlog, lags=min(30, len(rlog)));\n",
    "plt.xlabel('Lag');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iyssVrq5C_9z",
    "nbpages": {
     "level": 2,
     "link": "[7.2.4 Fitting Returns to a Distribution](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.4-Fitting-Returns-to-a-Distribution)",
     "section": "7.2.4 Fitting Returns to a Distribution"
    },
    "pycharm": {}
   },
   "source": [
    "## 7.2.4 Fitting Returns to a Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "d5cFE2wGC_9z",
    "nbpages": {
     "level": 3,
     "link": "[7.2.4.1 Normal Distribution](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.4.1-Normal-Distribution)",
     "section": "7.2.4.1 Normal Distribution"
    },
    "pycharm": {}
   },
   "source": [
    "### 7.2.4.1 Normal Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 561
    },
    "executionInfo": {
     "elapsed": 754,
     "status": "ok",
     "timestamp": 1604586047732,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "1N01TagwC_90",
    "nbpages": {
     "level": 3,
     "link": "[7.2.4.1 Normal Distribution](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.4.1-Normal-Distribution)",
     "section": "7.2.4.1 Normal Distribution"
    },
    "outputId": "b9a45c93-f95a-49c9-bfc1-91f730a3bf82",
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0009849473520634352 0.01385565341496523\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "from statsmodels.graphics.gofplots import qqplot\n",
    "\n",
    "r = np.linspace(rlog.min(), rlog.max())\n",
    "\n",
    "plt.figure()\n",
    "param = norm.fit(rlog)\n",
    "nu = param[0]\n",
    "sigma = param[1]\n",
    "print(nu, sigma)\n",
    "rlog.hist(bins=int(1.5*np.sqrt(len(rlog))), density=True,alpha=0.4)\n",
    "plt.plot(r, norm.pdf(r, loc=param[0], scale=param[1]), 'r-', lw=3)\n",
    "\n",
    "plt.figure()\n",
    "qqplot(rlog, line='q');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hOqhSaMWzCmm",
    "nbpages": {
     "level": 3,
     "link": "[7.2.4.2 Student's T Distribution](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.4.2-Student's-T-Distribution)",
     "section": "7.2.4.2 Student's T Distribution"
    }
   },
   "source": [
    "### 7.2.4.2 Student's T Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 561
    },
    "executionInfo": {
     "elapsed": 932,
     "status": "ok",
     "timestamp": 1604586307348,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "4ra5Q0olx70T",
    "nbpages": {
     "level": 3,
     "link": "[7.2.4.2 Student's T Distribution](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.4.2-Student's-T-Distribution)",
     "section": "7.2.4.2 Student's T Distribution"
    },
    "outputId": "11f321b1-0d15-47fa-d8dd-1866b20e6923"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3.0986867048737174, 0.001039855273070818, 0.009090875385307088)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import t\n",
    "from statsmodels.graphics.gofplots import qqplot\n",
    "\n",
    "r = np.linspace(rlog.min(), rlog.max())\n",
    "\n",
    "plt.figure()\n",
    "param = t.fit(rlog)\n",
    "print(param)\n",
    "dof = param[0]\n",
    "nu = param[1]\n",
    "sigma = param[2]\n",
    "\n",
    "rlog.hist(bins=int(1.5*np.sqrt(len(rlog))), density=True, alpha=0.4)\n",
    "#plt.plot(r, t.pdf(r, loc=param[0], scale=param[1]), 'r-', lw=3)\n",
    "\n",
    "plt.figure()\n",
    "qqplot(rlog, t,  distargs=(4,), loc=nu,  scale=sigma, line='q');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jj0OC-19C_93",
    "nbpages": {
     "level": 2,
     "link": "[7.2.5 Geometric Brownian Motion](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.5-Geometric-Brownian-Motion)",
     "section": "7.2.5 Geometric Brownian Motion"
    },
    "pycharm": {}
   },
   "source": [
    "## 7.2.5 Geometric Brownian Motion\n",
    "\n",
    "The basic notion behind this class of models is to recognize the return at each point in time, for example,\n",
    "\n",
    "$$\\frac{S_{k+1} - S_k}{S_k} = r^{lin}_{k+1}$$\n",
    "\n",
    "can be expressed as the result of a random process. \n",
    "\n",
    "$$r^{lin}_{k+1} = \\mu\\Delta t + \\sigma \\sqrt{\\Delta t}Z_{k+1}$$\n",
    "\n",
    "where $Z_{k+1}$ comes from a Normal distribution with zero mean and a standard deviation of 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wg92sLuCC_94",
    "nbpages": {
     "level": 3,
     "link": "[7.2.5.1 Linear Returns ](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.5.1-Linear-Returns)",
     "section": "7.2.5.1 Linear Returns "
    },
    "pycharm": {}
   },
   "source": [
    "### 7.2.5.1 Linear Returns \n",
    "\n",
    "A discrete-time model for prices modeled as geometric Brownian motion is given by \n",
    "\n",
    "$$S_{k+1} = S_k + \\mu S_k \\Delta t + \\sigma S_k \\sqrt{\\Delta t} Z_k$$\n",
    "\n",
    "where $Z_k \\sim N(0,1)$ and $\\Delta t$ corresponds to a sampling period, typically a trading period. There are normally 252 trading days in a calendar year, 63 trading days in a quarter, and 21 trading days in a month.\n",
    "\n",
    "Defining the linear return as\n",
    "\n",
    "$$r^{lin}_{k} = \\frac{S_k - S_{k-1}}{S_{k-1}} = \\mu \\Delta t + \\sigma \\sqrt{\\Delta t} Z_k$$\n",
    "\n",
    "then the statistical model for linear returns becomes\n",
    "\n",
    "$$r^{lin}_{k} = \\mu \\Delta t + \\sigma \\sqrt{\\Delta t} Z_k$$\n",
    "\n",
    "This shows, for the case of Geometric Brownian Motion, $r^{lin}_k$ is a random variable drawn from a the normal distribution \n",
    "\n",
    "$$r^{lin}_k \\sim N(\\mu \\Delta t, \\sigma\\sqrt{\\Delta t})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_xo1foAJC_94",
    "nbpages": {
     "level": 3,
     "link": "[7.2.5.2 Log Returns](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.5.2-Log-Returns)",
     "section": "7.2.5.2 Log Returns"
    },
    "pycharm": {}
   },
   "source": [
    "### 7.2.5.2 Log Returns\n",
    "\n",
    "Alternatively, geometric Brownian motion for prices can be modeled using the natural logarithm of price,\n",
    "\n",
    "$$\\ln S_{k+1} = \\ln S_k + \\nu \\Delta t + \\sigma \\sqrt{\\Delta t} Z_k$$\n",
    "\n",
    "where, as for linear returns, $Z_k \\sim N(0,1)$ and $\\Delta t$ corresponds to a sampling period. The relationship between linear and log returns is given by \n",
    "\n",
    "$$\\nu \\approx \\mu - \\frac{\\sigma^2}{2}$$\n",
    "\n",
    "where $\\frac{\\sigma^2}{2}$ is the 'volatility drag' on linear returns. Defining log return as \n",
    "\n",
    "$$r^{log}_k = \\ln S_k - \\ln S_{k-1} = \\nu \\Delta t + \\sigma \\sqrt{\\Delta t} Z_k$$\n",
    "\n",
    "the statistical model for log returns becomes\n",
    "\n",
    "\\begin{align*}\n",
    "r^{log}_{k} & = \\nu \\Delta t + \\sigma \\sqrt{\\Delta t} Z_k \\\\\n",
    "& \\sim N(\\nu \\Delta t, \\sigma\\sqrt{\\Delta t})\n",
    "\\end{align*}\n",
    "\n",
    "This shows, for the case of Geometric Brownian Motion, $r^{log}_k$ is a random variable drawn from a the normal distribution. The following cells is a complete self-contained demonstration of downloading a data series, fitting a GBM price model, and performing simulations. The first cell loads a data series, computes linear and log returns, and estimates values for $\\mu$, $\\nu$, and $\\sigma$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 1026,
     "status": "ok",
     "timestamp": 1604591186333,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "ZsJR145IC_95",
    "nbpages": {
     "level": 3,
     "link": "[7.2.5.2 Log Returns](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.5.2-Log-Returns)",
     "section": "7.2.5.2 Log Returns"
    },
    "outputId": "a94fdf1f-9d78-4dc8-ea08-9a05676ed22a",
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear Returns\n",
      "   mu =  -0.00061601  (annualized = -15.52%)\n",
      "sigma =   0.00000000  (annualized = 1.00%)\n",
      "\n",
      "Log Returns\n",
      "   nu =  -0.00132993  (annualized = -33.51%)\n",
      "sigma =   0.03786823  (annualized = 60.11%)\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import pandas as pd\n",
    "import datetime\n",
    "from pandas_datareader import data, wb\n",
    "\n",
    "import requests\n",
    "\n",
    "def get_symbol(symbol):\n",
    "    \"\"\"\n",
    "    get_symbol(symbol) uses Yahoo to look up a stock trading symbol and \n",
    "    return a description.\n",
    "    \"\"\"\n",
    "    url = \"http://d.yimg.com/autoc.finance.yahoo.com/autoc?query={}&region=1&lang=en\".format(symbol)\n",
    "    result = requests.get(url).json()\n",
    "    for x in result['ResultSet']['Result']:\n",
    "        if x['symbol'] == symbol:\n",
    "            return x['name']\n",
    "\n",
    "symbol = 'X'\n",
    "\n",
    "# end date is today\n",
    "end = datetime.datetime.today().date()\n",
    "start = end-datetime.timedelta(3*365)\n",
    "\n",
    "# get stock price data\n",
    "S = data.DataReader(symbol,\"yahoo\",start,end)['Adj Close']\n",
    "\n",
    "rlin = (S - S.shift(1))/S.shift(1)\n",
    "rlog = np.log(S/S.shift(1))\n",
    "\n",
    "rlin = rlin.dropna()\n",
    "rlog = rlog.dropna()\n",
    "\n",
    "print('Linear Returns')\n",
    "mu,sigma = norm.fit(rlin)\n",
    "print(f'   mu = {mu:12.8f}  (annualized = {100*252*mu:.2f}%)')\n",
    "print(f'sigma = {0:12.8f}  (annualized = {1:.2f}%)'.format(sigma,100*np.sqrt(252)*sigma))\n",
    "print()\n",
    "\n",
    "print('Log Returns')\n",
    "nu,sigma = norm.fit(rlog)\n",
    "print('   nu = {0:12.8f}  (annualized = {1:.2f}%)'.format(nu,100*252*nu))\n",
    "print('sigma = {0:12.8f}  (annualized = {1:.2f}%)'.format(sigma,100*np.sqrt(252)*sigma))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "DZ7L5iZ7C_97",
    "nbpages": {
     "level": 3,
     "link": "[7.2.5.3 Forecasting](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.5.3-Forecasting)",
     "section": "7.2.5.3 Forecasting"
    },
    "pycharm": {}
   },
   "source": [
    "### 7.2.5.3 Forecasting\n",
    "\n",
    "The second cell performs $N$ simulations over a time period $T$, and plots the results with the historical data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 295
    },
    "executionInfo": {
     "elapsed": 4600,
     "status": "ok",
     "timestamp": 1604591246091,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "wRo0VoBuC_98",
    "nbpages": {
     "level": 3,
     "link": "[7.2.5.3 Forecasting](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.5.3-Forecasting)",
     "section": "7.2.5.3 Forecasting"
    },
    "outputId": "58261541-3eee-486a-94a7-ce242ba45242",
    "pycharm": {}
   },
   "outputs": [
    {
     "data": {
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qnWSV1PTYWIUQQghx8k6lqOanwI+UUumYmqh/9syQBq43dp1g1d48IkNsfGXmcKo6CKAcXewDFRVq9sm79429nPX7jym21/fYeIUQQghxcroVQGmtN2itL3E/ztBaz9Naj9Vaf01rfdr/ZPdM3b1zx2KiQmydZ6C6EkCFmPZax93Zp+OShRJCCCH8rqur8ISPnPJa0gqq2JJRQmFlPY9dPQOAL/OrmJMSTUpsGOHBAdQ4XLgadZvbtThd2lvf1JFIdwbKI7O4mtkp0T3zhQghhBDipEgAdRKu+NtnFFU1JdxOlNUwfUQUh/OruGx6EgDh7tqlakcDEcG2VtdwuhoZEtz5tz8iOACrReFqNJsPHyuu7okvQQghhBCnQAKok+AbPAF8nlnG55llAMwcabJDnuLv6vq2AyhHF1fhKaWIDLFRWu0AIL3QfkpjF0IIIcSpk86MPWx+agzQlIGy17Wug8oureFIQRXjE8K7dM2okKYA7IMD+fzz02M9MFIhhBBCnCwJoLqp5ca+M0dGAXD5jCSmDo8kOSYUaAqg2lqJ9+GBfBo1XDtvZJfu6amDCnVv6/LQewdPbvBCCCGE6BEyhddNmSXNa5CevnEOm48Wc9n0JMwWgUZ0mFk9V+aeevNVWu0gwKIYHhXSpXt6Aqfr5o3k2UGafdp8tJjqehfnnpHg76EIIYQQnZIAqpv2nqgA4MpZw7lq9gjihgRx+YzW2wAOiwwGILeirtVz5bVOokJtzQKujty1YjyLxpRy08IUQoMC+Mu6NLTWXX59f6e15hdv7seltQRQQgghBgQJoLppd3Y5Q4ID+MNV07G00Z7AY2h4EAEWRX5FbavnKmqcRIa0Lixvz7zUGOa5a6uCAsysq8PVSFBA520Q+rOCyjqsFkVptYOM4mpsVtVu2wchhBCiP5EaqG7QWrM1o4QZyVEdBk8AVosiISKYvDYzUA6iQgNPagyeAKq+obHbr3W6GnngnQNkdtIKIaukhqo6Z6vj/9l6nO/9bycl9npK7PU0uBr5YH8+T248elLbzMz/9TrmPLyWD/bnu8enya9s/f0SQggh+hvJQHXDp+nFZBRV880lqV06PzEymLzyNgKoGieJEcEnNYYgd/PNemej2dq5E3/7OJ1Aq4VvnzWaTUeKWLk5k4LKOv5xw+w2z39vby53vLCLC6cktjrng/15fJZewvv7TMDz2NXT+eHLewBIK7Dzx69PP6mv6f19eYTYrNQ6XWSX1nS5NkwIIYTwF8lAdZHT1cidL+4ixGbloinDuvSaYZHB5LYxhVde42zVYbyrmjJQrk7ONH7/4Zc88v4hPs8sZX+O2WpmRHT7AYqnz9SXBVXtPufxy7cPeB8H27r3V8nTGBTgcH4V1883KxIziqRRqBBCiP5PAqguqqh1Ulbj5K5zxnlX2HVmdFw42aU1rVofVNQ6vXvcdVd3pvAaXE3nbD9WyoFcUwAfExbU7ms8DTsLK+vRuinIqaxzUlDZvIFoVV0D50xKYHRcGOU1ZspPa016Yevgq6WS6ubXuvOccYweGsY/P83AcRLTk0IIIURfkgCqi6rcDTETItoPPloaFx9Oo26eVXG6GrHXNxB10hkonym8ThT6dEw/kFvBgVyTgeooQPEEUPb6Biprm3pYpRWY7JOn75XHQ1dMZmhYEMV2c6+VmzM550+b2JVV1vHYfIKxn180iYhgG7+4ZBJHi6r5+4b0Tr82IYQQwp8kgOoiT1H1kKCuBz7j3J3G03wyMtmlpti6O4GYryBb21N4hVV1/NXd3sAjt9xMH4YGWll7sJAc9+dOV+cBFEB2WVNh+N4T5QD86esz+Ou1M7lj+Vi2/mwFwyJDiA0P9L5ua0aJ+96ta79yymt5d08u0LQdzv++NZ9vnzUagLMnJrBiYjwvbMtqNsUnhBBC9DcSQHWRJwPVlQ2APVKHhgGQWdwUiOw8bjIzs9x75nVXe1N497y6lz+uOcK+nArvMU/AdPd5E3D4BE2OdgKozOJqNh8t8Ra4e14Ppn1DYkQwqUPDuHR6EvecP4FEd6+rmLBAStwBlGdcNmvrVYoPvHOA77+4ix2Zpd7VdiPdnds9vjJrOIVV9ezILO3sWyGEEEL4jazC66LKWncGqo2NgdsTFGAlLNBKRW1TS4AvssqICA5gTFzX9sFr65rQOoAqcU+h+WZuMoqqUQqumZvMkrFD+TyzlEdXH253Cm/5HzcAJnOWX1nXbNPkfTkVTBsR2ebrYsNMBmrz0WLv1GKts3WRu6cW7KontwAQHWprteJuydihAOzMKmP+6Ng27yeEEEL4m2SguuhkMlAAkSG2ZgHUibJaRseFd9pHqj3eDFSLAKXBZQKnshoHRVX15JTXsju7nPHxQwgLCmBC4hBuWJBCkM3S5hTeaztP4Jn9q65vQCkz3ehq1DQ2ak6U1pIaF9bmmEa5M20PvHPAO7VY1cYmysX25tvaJEQEt/o+RIUGkjo0jN1Z5Z19K4QQQgi/kQxUF2it2XikCICIbnQQ95zvG0BV1DqJPskmmtDULqBlBsrZaD7/xsodzY5fMze52ec2q6VVBkprzT2v7vF+ftHUYWSW1PDUpgye2pTBmeOG4nA1khzdfLrN4/IZw3n582y2HWuadrO32ERZa012aQ0XTU0EzPfhzrPHtXm9qcMjvVOdQgghRH8kAVQH7njhC8prnHxtzghW7csDIDyoe9+yiBAblXXNA6hRsW1ncrqivSk8TwaqpbPGxzX7PDCgdQbKM1U3IjqE1XedSbh7vz2PT9KKAUiOaTuAsloUS8YObR5AtchA5VbUYa9vYE5KDN/opBFpTFhgm53QhRBCiP5CAqgOvLfXBE2+q+i6u09bZIiN7NIaPv6ykCCrxfSAOskWBtA0hXfPq3t4d08uz31jHtC855PHwtGxXDA5sdkxm9WCs0WwlenehuXhK6Z4a7wq25iCS+6gAefI2ObB1RMfp3PmuKHeOqZHVx8mMMDC0glxbb28mWCblboutGkQQggh/EUCqC5o2UCyOyJDbKzJr+LWf38OgFJ0ayPhlnw3EN54pIgL/ryJmSOj2txD7sXbFrQ6Fmi1tMpeZZaYPlVtZca+uP9cfvXuAVbvz2d4BwFU/BCzIu/iacNY5Q48f/bGPi6ZnsQnaUXsz6ngpoWjulQ8H2yz4HA1ysbCQggh+i0JoNrRsns4wC8vOaPb14losWpP61MMoFpsmXI4v4rD+Z13/vawtTGFdyS/CptVNQuQ/nH9LD48kE9MWCB/vnoGj361sVnw1tKC0TH84/pZrJiU4A2gUDSbCvzKzOFdGmOwZ7+/BhehgfJXVAghRP8jP53a4emU/chXppAYEUxyTCjjE4Z0+zptBUvdLUT3FWg9tYWTgVbVLIDSWvPRwQIWjI7F5nPtC6cO48KpZs8/pZQ3qGmPUsp7vkfLfe08jUU7E+yepqxzNnIK9fZCCCFEr5E2Bu0oqDJTYsnRoayYlHBSwRNAZEjrGPVUMlDttT+4dl7TarsHL5/MqjuXtHleYEDTKry9J8pZ/Nv1ZJXWcOm0pJMeU0eGuZttAh1msHyFBJrz2uolJYQQQvQHkoFqR16FCaDiT3LLFY9xbQReUacQQLUnxBbAw1dMQQM3Lkhp9zyb1eJdIfd5Zhm5FXXcvnwMX509osfG8slPlvNlfhWH8io5c3wcV/zts2693pPtamsaVQghhOgPJIBqx66sMoJtFu92LCer5ea70HrFWneNjAklq7Sm2bErZw1nyvC2O4X7slktONyr8Eqr67FaFHefO+GkG3u2JTkmlOSYUM45I8G7yXB3eDJVEkAJIYTor2QKrx1bM0qZnRLd5Wmn9oQGBmC1KEa7u3gnRQYzLLL91Wxdcen05rVGH/zgzC4FT2Cm8A7lVbLlaAml1Q6iQ209Gjy1FOMuYrp+/sguv8bTLFRaGQghhOivJAPVhvyKOg7lVfLj8yf0yPX2PXAeFqUoqqonJuzUq6LvPncCk4ZFcMcLu4CmIKUrPEXo1z6zlfPOSCA27NSmKDtjsSgOPXgBgQFdj9VlCk8IIUR/Jxkotx2ZpXySZrZr+fBAPgDnT07okWuHBgYQbLOSHBNKWDc7mbfFYlFcPHWYN6sV3Y2gLMAn21Ra7eiRgK4zIYHWbvVzCpEASgghRD8nGSigoLKOq57cAsDRX1/EnuxyEiOCGRt/civv+oJSijU/XEpptaNZ+4HOVDuaOoyXVjuYlBTRG8M7JU0ZKJnCE0II0T9JBgrYfLTY+3jbsRJKqh0knOLqu75gtSjihnRvnJW1TQFUSbWD2D7IQHVXUw2UZKCEEEL0T5KBoqlpZlCAhfvf2k9QgHVABFAno6K2+cbG8d0MwPqCJwMlfaCEEEL0V5KBAgqr6gmxWfn5xZM4WlTNwbxKYsP7X2DRE3wDKIAz+vUUngRQQggh+icJoICiqnriI4JI8dlMtz9ObfWElsXcXW1/0Jc8U3gPrzokQZQQQoh+SQIooLCqjrjwIIZHNfVnig0fnAHUszfPYdmEOMAEU/FDgjt5Rd/z3e9vf06FH0cihBBCtE0CKMwUXnxEEElRTcFETC/3R/KXMXHh/PPmufzmyqls/PEyfw+nTUop7lwxDoC0QrufRyOEEEK0dtoHUFprCirqiB8STGhgU019UmT/y8z0FKtFce28kYyIPrUtZXrTD1aMI8RmJa1AAighhBD9z2m/Ci+nvJZqh4txCeEA3Lp4FDarhQWjY/08stObxaIYGx8uU3hCCCH6pdM+A3U4rwqAiYlmNdr/u3Qy9100qVf3hxNdc8GURLZnlrInu7zVc5vTi7ngz5sor5dmm0IIIfpepwGUUipYKbVdKbVHKXVAKfUr9/FUpdQ2pVS6UuplpdSArLo+nF8JwITE/tt1/HR186JRBNssvP7FiWbHG1yNXPfsNg7nV/Hw1jrSpU5KCCFEH+tKBqoeOFtrPR2YAVyglFoAPAo8prUeC5QB3+y9YfaerNIaEiKCCO+BPepEzwoPCmDp+Dg+PJCP1tp7fHtmqfdxca3mnD9t5LzHNpJdWuOPYQohhDgNdRpAacPzK77N/aGBs4HX3MefA67olRH2svzKehIjBm/B+EC3YlICBZX1HPEpJl97sNDbK8rjSIGdL7LKunzdxkbNW7typM+UEEKIk9KltItSygrsBMYCfwOOAuVaa8/GaieA4e289jbgNoCEhAQ2bNhwikPumN1u79Y9MnJriAu19Pq4xMmx1Joap5UfbGV5cgCBVsXH+2oZNQS+PiGYkspaUmJD+cmmWjbvOkhkeVqn16ys1xwpc/HE7nqWfBrAt6YOzpYVg1F3/32LgU3e79PLQHu/uxRAaa1dwAylVBTwJjCxqzfQWj8NPA0wZ84cvWzZspMYZtdt2LCB7tzDvukjlo9OYtmyKb03KHFK/n5wAy8erubTQivv3L6YrI/W8p2lo/nG+RPZsGEDS5cu5f7NHxCZMIJlyyZ1eK3KOifTHvjI+/n2gkaev32pLBoYILr771sMbPJ+n14G2vvdrVV4Wuty4GNgIRCllPIEYCOAnB4eW6+rc7oor3EO2o2DB4vr5o0EILu0lp+9sQ9Xo2ZOSoz3eaUU8RFBFFbWtXuNo0V2/rz2CKv35TU77mhoZPGj63lszZHeGbwQQohBqSur8OLcmSeUUiHAucAhTCB1lfu0m4G3e2uQveWXb+8HIEFqoPq1mxeN4onrZhIRHMCHB/OxWhRzU2OanRMXHsRbu3PZnF7M42vTyKuo9T5XUevk6qe28Oe1afz09X3e43+9diYAeRV1PL0pA1ejRgghhOiKrmSghgEfK6X2Ap8Da7TW7wE/BX6klEoHYoF/9t4we16Dq5H39ppsxJJxQ/08GtERm9XCJdOSGBsfjtYwbURkq1WTh/NNP6/rnt3GY2uP8LeP073PbT9WSrHd4S08D7ZZ+Ozes7lgSqL3nFqni+m/+qjbReXV9Q04GqQXlRBCnG66sgpvr9Z6ptZ6mtZ6itb6QffxDK31PK31WK3117TW9b0/3J6zP7eSGoeLJ66bybDIkM5fIPxuVGwYAAvb6BL/vWVjmn2eU9aUgdqdXYbVorhmrpkKnJIUyfCoEGxWC+vuXsqmHw75IfsAACAASURBVC8HwF7fwJu7uj4T7XQ1Mvn/fcgPX97d7a9FCCHEwHZadSL/YH8+N/9rO65GzaYjRQDMazEVJPqvFE8ANaZ1AHXH2ePY/ctz+dmFE7lwSiJfZJVTUeNEa81n6SVMTBzC5CTTbf5rc0Z4XzcmLpyRsaGkP3IhI2NC2fhlUZfH8/buXABWtairEkIIMfidVt0jf/jybmqdLnYeL+OdPbnMGxVD/BCpfxooVkyKZ39uBXNHtR30RoUG8n9Lx7Ajs5R1hwq57619pMaGsTu7nIcun8yVs0YwPDqkzQxWgNVCSmxos9qpjtQ5Xfz6/UMAxIYNyCb8QgghTsFplYGKCrUB8O3nd5BeaOcrs9psXSX6qSnDI3nmpjkE26wdnjdnVAznTk5g1d48nvg4nTkp0Vw/PwWrRbFozFCUartlQVJkCDnldTzwzgF2Hu+4KeeRgipKqx1MGxFJSbWDGkdDh+cLIYQYXE6bAKrG0UC+e5l7Ra2ToeGBfGWmBFCD1czkKABCA608cd2sLvV5SooKodhez8rNmXzvfzs7PPdokemMfvbEeMBsCSSEEOL0cdpM4a05WIDWsPLWuVTWNTAzOarTTIYYuL42O5njJTX86NzxRHdxim1YVNN0rr2ugXte3cPty8eSOjSs1bnphXYCLIrlE+L589o0jhTYmZgY0WPjF0II0b+dNhmoF7ZlMTImlLPGxXHZ9CSSY0L9PSTRiyJDbTx0xZQuB08Ao30CpWqHi9d2nuCWf29v89yjhdWMjA3ljKQIggIs7M0uP+UxCyGEGDhOiwAqvdDOtmOlXDMvWbbsEO2anRLNW7cvZuWtc73HjpfU8P0Xd7XqD3W0yM6YuHBsVguTkyLYc8IEUOsOFXD/W/vRWppyCiHEYDZoA6i8ilre2WOWma85WADAVbNGdPQScZpTSjEjOYqzxsU1O/7unlw+zyz1ft7gaiSzpJoxceEAzBoZzZ4TFZwoq+Gbz+3gP1uPk15o79OxCyGE6FuDKoB6bnMmj+2sw9HQyMLfrOfOF3dRVu1g5/FSRseFES9btogusFgU6+5eyoZ7lnHfRWbf7OMlTUXi2WW1OF2aMXFmym/R2FgcDY0s/f0G7zlrDxX26ZiFEEL0rUEVQFU7GthT5GLRb9d7j60/XMj2Y6XMTZGGmaLrxsSFM2poGN9aMppAq6XZKjtPdmlMvMlAzR0VQ2CABVejJiEiiOFRIRwpqPLLuIUQQvSNQbUKb567wWKxvWlXmbtf3UOg1cINC1L8NSwxgFksihExIWT5ZKD251RgUTAhYQgAQ4JtfPiDsziUV0lKbCj3vbGPkmqHv4YshBCiDwyqDNTUEZHex2/dvtj7+JXvLGz2nBDdkRITynGfDNTeE+WMix9CmM+GxqlDw7ho6jAmJ0USGx5EiX1AbQ0phBCimwZVABUUYOVXi4LZdf+5zHA3UgSaPRaiuxIjQziUV8nsh9ZQ63CxL6eyw4A8JiyQYns9rkZZiSeEEIPVoAqgAFIirN7eP2/fvpiNP17m3wGJAS8hIgiAkmoHu7PLKbbXMzqudXNNj9jwQAoq61n4m3V9NUQhhBB9bFDVQLU0XTJPogck+Kze/DS9CIBhke2v6BwaZgKuwqp6KuucRATbeneAQggh+tygy0AJ0dPihwR5H286UgxAYkRIu+c3+Ezd7c6SDuVCCDEYSQAlRCd8M1D7ciqAjjNQk5Oa9sTbJQGUEEIMShJACdGJoeFBrY4ldhBAnTU+jj2/PI9RsaEcyqvszaEJIYTwEwmghOhEQkQQP71gIv/71nwARkSHEGyzdviayFAbk4ZFcChfAighhBiMBnURuRA9QSnFd5eNAWDfA+fR4Opae4JJwyJYvT+fGkcDoYHyT00IIbrL4YDAQH+Pom2SgRKiG4YE27xtMjqT6K6dKrFLV3IhhOguux02bzZBVH8kAZQQvSQixGSdKuucfh6JEEIMLA4H7NgBc+ZIBkqI005EiOn/VFnb4OeRGFprymscaC0d0oUQ/VtgICxaBOHh/h5J+ySAEqKXeBpo9ocMVGOj5jv/3cmMB9fwg5d3U+PoH0GdEEK0pT/XPnlIACVEL4n0ZqBMAFVa7b+J/LRCOx8eKGBUbChv787lwsc/8et4hBCiPQ5H/6598pAASohe4slAVdQ6eeXzbGY9tIa0giq/jOV4STUAj18zk6dvnM3xkhpe3J7ll7EIIUR7PJmn/lz75CEBlBC9ZEiwKSJ/fG0aKzdnAnCsuNovY8kqrQEgJTaU8yYnEh1qI6+i1i9jEUKItjidis2bzeq7HTs6zkD1h+yUBFBC9BKLRQFQVd/AQXdH8r6YNjuQW8HhFg08j5fUMCQ4wDutGD8kmILK+l4fixBCdJXNpr2F44sWNc9A+QZMDgds3Oj/IEoCKCH6UF5FXa9ef1tGCRf/5VNueHa791h5jYPPjhYzKjYMpUxQFx8RRGGVBFBCiP4lMLB1YORbE+XvoMmXBFBC9IH7LzkDoNenzd7anQNAsb2ezzNLWfLoemY8uIaMomp+dO5473nxQ4IprOzdYE4IIbrL4YC1a5syTJ6aqEWLzPObN0NpKSxd6v8aKQmghOhFO39xDnv+33l8c0kq05Ojei0D1dioeWtXDqv25nk3P/7uf3dyoswEbF+bPYLlE+O958dHBFFUVU9jo/SEEkL0PwsXmj89mSdPsDR6NDzwgKmT8jcJoIToRbHhQd66o9TYUI4UVPVKI8s3d+Xwg5d3U1nXwG1npaIUFNsdXDV7BOvuXspDV0xpdn5SZDANjZpnPsmQIEoI0a/YbCZg8qzGg6a6p/374Zxz+keDTdnhVIg+MntUDG/tzuVEWS3JMaE9eu139uR6Hy8cPZSgAAt1zkbmpEQzJq71/zSXzxzO+/vy+c3qw0SE2Lh23sgeHY8QQpyMwMCm6TmHA7ZsMceXLjUf/YlkoIToI3NHRQPweWZpj1/7QG7TqrsJiUMIDzK/G01Pjmrz/IhgGy98ez7j4sN5SfpBCSH6Cc90nadYfPbs5vVOnj9lFZ4Qp5Fx8UMItlnYn1PZ+cldVFHj5I8ffUmxvZ5vn5nKO3csJjDAwlM3zuErM4czPmFIu69VSnH+5ET25VTQ4GrssTEJIcTJqKiweovEN26E1avhX/9qKib39Ijyd+DkIVN4QvQRq0UxMTGCA7kVp3Qdp6uRZz7J4Otzknl09WFe3XkCgFkjo5k2wmScZqdEMzslutNrJUYG06ihpNpBQkTwKY1LCCFOlt0Oq1cn8sADsHevyTyFh8OKFU0ZqTlzmqb0Zs+WVXhCnFYmJ0VwMK/ylArJX91xgt998CV///goh3waZqbEhnX7WvFDzIq9QmmqKYTwo8BAGDWqmpgYEyjt3Nl0fO1aePJJ8/nSpWaF3t69/s9ESQAlRB+anhxFVV0DX3ZzT7zCqjre3p1DfYOL178wGafc8loyi2uYnRLNxVOHMTa++8tSPFmnAukJJYTwk6Z6pwrv6juns+n4WWfBN75hMlKBgebP/rBXXqdTeEqpZOB5IAHQwNNa68eVUjHAy8AoIBP4uta6rPeGKsTAt2TsUAA+TStmYmJEl16TUWTnyn9sprzGyf+dNZp9J8wU4PovC3E0NHLJtGHcujj1pMYTH+HOQElXciGEH9jtTdNyTqfZKaHUvc5m0yYTSDmdEBkJU6dCYqJ5fu/e1tu99LWuZKAagLu11mcAC4DblVJnAPcC67TW44B17s+FEB1IigphfEI4D686xM/f3Nfp+fb6Bm7613asSpE6NIynNmXgcDVyzqR4HA2m8HvUSUzdeQwND0IpyUAJIfqew2E2DV640NQ0HTwYQX4+PPQQjB9vMk8A6emQmgr33w9ZWfD88zBxov8zUJ0GUFrrPK31F+7HVcAhYDhwOfCc+7TngCt6a5BCDCbXuXsu/W9bFiX29jM/WmseX3uEE2W1PHnjbL67dIz3uYevmMqclGiWTYhj4ZjYkx6LzWohMSKYY8XV7M+p4Icv7ybNZ3qxosbZK40/hRDCs0VLYKCpebLbrcTEwA9/CO+9Z8658EK44w7zOCUFYmLgppvg8OEBVgOllBoFzAS2AQla6zz3U/mYKT4hRCeum5/CjQtSAPg0vbjd87ZmlPLMJ8e4YkYSc0fFNOvplBgZzGvfXcTKW+cRbLOe0nhmjoxi5/Eynt6UwZu7cvjVuwcByCyuZvqDH/Hi9mzvubuzy9mfc2qrCIUQwsOzwm72bMjJCSE/H06cMEGSp9u43Q533QVXXmnOj4nx//QdgOrqb5dKqXBgI/CI1voNpVS51jrK5/kyrXWrddNKqduA2wASEhJmv/TSSz0z8nbY7XbC+0OPd9EnBur77WrU/HhTLU6XZvgQCzdMCmLEkOa/z2zMdvLvAw7+sDSEoSEWGrXmtjU1XDraxuVje+5/jg8znbx4uOlXuWArPLAohIe21lLthLmJVm6fYYrNb/mgGoCEUMV3pwcxKvLUgrfuGqjvtzg58n4PDk6nwmZrO9aoqbGwatUwzjsvny1bgigvj+bCC/OJjHRRUWHl0KEIJk2q5NVXh5GaWk9YmJNJk6qIjHT1ydiXL1++U2s9p63nutQHSillA14H/qe1fsN9uEApNUxrnaeUGgYUtvVarfXTwNMAc+bM0cuWLevu+Ltlw4YN9PY9RP8xkN/vx5OLuPGf2zlc2khR8AhuWDa+2fOHNx6FA4e5aMVZhAaaf6rpy3t+HGGZpbx42FRxrpgYz7rDhdz7Sa33+THJSSxbNg17fQN88CEABTWaX3/u4PdXTePyGcN7flDtGMjvt+g+eb8HPk8DzPYyRg4HLFgAMTHjCA3dyOzZ8wgPH4fdDk8/DQ0NphfUzJnwwgswfDikpcENN5iCcn/qdApPKaWAfwKHtNZ/8nnqHeBm9+Obgbd7fnhCDF5njovjgUvPAKCuofVvU+U1TgKtFkJOcYquM77dym87azRDw83KvPmpMUBTgflB93Yxz9w0hy/uP5dhkcH8dX16r45NCDGw+dY5teRwmB5PO3eax06nYudO04F861a47Tb43vfMazMy4JZbIDYWrrgCXnrJTO35U1dqoBYDNwJnK6V2uz8uAn4LnKuUSgPOcX8uhOiGWxankhwTQn5F61VwFbUOIkNtmN9hek9kiM37eObIaD74wZmsvutMXv6/hZwzKYG8ijoqap388u39BFotzBwZRUxYIIvGxFJe4+zVsQkhBjenEyZMMAHUwYORzJ7ddDww0LQrABOEeRw71rxGyl86ncLTWn8KtPc/+IqeHY4Qp5/EiOA2A6jyGidRPsFNb4oJC6S02kFggIWh4UHeLNSwyGDWHipg+q8+Akz2yfNcZEgglbVmlV5vB3lCiIGpoyk8TxuDV1+FCy6AujrlXVmnVFP2CiA/H379a3jgAf8HTh6yF54QfpYQEdzmyrbyGidRoX0TQH189zKcja03FJ45Mor/bD3OyJhQrpw1nHPPaFpsGxliw+FqpM7ZSEhg3xaTCyEGhvam8DwbBM+YYf5MTweXS7FyJYwYAcHurTntdjOdt2ULzJ9vgqd162DXLrjnHv8GUxJACeFnwyKD+ehgAXVOV7OWBOW1ToZHhfTJGCLbCdSunDWCr8wc3maGyTP1V1HrlABKCNEuT/DkcDS1LVi9Gg4dgquugpAQmDUL9u0rZerUpn3v5s2DN96ASy6BlSubruF0wpEjA6wPlBCi5y2fYLqKv7c3z9u08kBuBYfyKonuowxUR9qbnvMEUOW1fv5fTAjRb3mCHM9Unt1uHjc0mMaYL70EU6bAPvfGDDExpiZq3DjYv9/0foqJMRmp8eNNxmnePGgjYd7nJAMlhJ8tHBPL2Phw/vnpMf740ZcE26zklps2Ar4r5PobbwZKCsmFEG3wrX8CswHwhx9CQIDJPt10Exw9aqbnhgyBmhorDofJLtXXmyBq716z+u6yy5o2GF63DnJzJQMlxGlPKcWNC1I4lFdJXkUdx4qrqW9o5NGvTuXbZ4329/Da5TuFJ4QQLfkWgW/ebDYBXrMGkpKaNga+5BKTaRo/Hv7971GUlsLkyWC1mtV2kZGwfbvJOm3caIrJP/rIv1+Xh2SghOgHfPeze/amOaTEhjI2vp8sNWmHp8BdAighREcCA032af16uPZaePBBs1HwzJmmENzphK9+FSIi6ti/H5YsMQHTunXw3/+aIGzePLMCz+Ew1xo+3P+r8SSAEqIfGBkT6n08LiGclNgwP46ma6LDTGWop9GmEEL4sttNm4JFi8zjF18003e33AJ33mkCqFtvNdN0b71lsvHjx8Pf/mYyUBMmmHMuu8wUlo8YYYrJ09Jg4UL/T+FJACVEP+C7+i4xMtiPI+m68KAAxsaHs+N4mb+HIoToZzw9nubMMY+3bYORI8HlgqoqM4338MPw97/D5ZebAOu++zQ7d0JWFpx3HixebHpE/eEPoLU5Z/x4M/V34YX+z0BJDZQQ/UxQwMBpCTA/NYYdmWU0uPrBkhghRL/hqX9yOMzUHUBqqjlutZr974YONVN0DodZaXfVVbl85Svw6KMQHW2OV1SYKb0VK6C83BShr1oFr702MLZyEUL0gX9cP4tfXDzJ38PolnmpMdjrGziUV9XpuU4JsoQY9DzTana7KRr/+99NI8xx4+DNN037AaXMnnY//SlkZ5uAaONGsxee3W6CrJISs0fetGlw4oTpG5WWBn/8o2l7UFoqU3hCCLcLpw7z9xC6bX6qKX6/+9XdXDN3JPNSY5gyPLLVec9+ksHDqw6x55fntdu0UwgxsHnaFkybZgInMO0JvvzSBEXf+Iapa8rNNT2g8vLMVF5aGixdCvfeO4w33zTZp717zXUsFjNlt3EjREXBgQNm25e33vJ/ACUZKCHESUuMDGZMXBhHCuw8+N5Brvz7Zo4UtM5GfXggH4C/rk/r6yEKIfqAJ5jxtC2YNMm0KPjgAxP4PPccFBWZrFNUlAm0xo4151ksJmNVUhLM7bebYOuSS8yfBw+a4Km4GDIyICgIXn/d1D+13B6mr0kAJYQ4Jf/55nxW3bmE976/hCCbhd998GWrc5KjzSrD57ZktrlxshBiYPHN/jgcJshZu9YUgD/9NOzebTJNf/2rCapcLhM0BQWZ6bglS8yqvNWrTYbpuecgLKyePXtMwfmaNSZA2r0bQkPN6j2n0wRRdjtcc42pm/InCaCEEKckKSqEyUmRTBkeya2LU1l7qIBvP7+DrJIa7zlV9Q0AOF2ag3mtN04WQgwcnqk6z4bADgfMnm0Kvn/9a7O/3RlnmELx8HDTVfzOO00gFRJiapgWLzbTeY2NZrpuyxbIywshLc1M723fbgrGv/MdSE427QzsdrMFzIwZphDd3ySAEkL0mBvmjyQ2LJA1Bwv4+Vv7vHv72esaSB1qelv5Blb+sD+nghNl/h2DEAOZ7wq7tWvhiSfMSjuLxWSFHA54913zceed8MgjJiBataqpC/nDD5t2BikpUFgIl14KNpsmLs4ER+HhEBdnnqurg8pKk4kqLYXqanjsMZPt8icJoIQQPSY+Ipid95/L/501mk/Sipn2q4949pMMqh0N3mahD7x7kJ+90RRc9aX8ijq+/tQWfvn2AQ7lVfKNlZ9T42jo83EIMRhs2WI6it92mwluqqpg1y7T9DI72/RuOu88uP56+Mc/4N57TeuCnTuhpgY++cRM3+Xnm/Nraiz8619mWi8/3xSTb9pk9svLyDDBVFWVCZxiYqQPlBBiELpsRhIBFkVVXQMPrzpEWoGdIcFNi35f3J5FjnvD5L7029WHqHG4+DyzlO+/uIv1hwvZkSmNQIXoLt8aqMBAM1134gRccYVZeRcXB7W18PbbZu+6iRNNH6err4aICBNYnXmmaXEQGWlqpPLzQ5gwARISzBTfXXeZDFVUlAmezj3XTP8FBpqpP3+TAEoI0eMmJ0Wy74Hz+fieZSgFtU4X4UEBDA1vWjZzKlN5JfZ6CqtMMfrWjBKueXoLZ/5uPW/vzml1rtYaR0MjRwqqeGt3LuMTwqmqayC90HTh+zK/8x5WQogmni7js2ebDNGTTzbVQuXlwcUXm15Pe/aYj6IiE1jl5ppi8aws2LABjhyBzEwoKDC1Ufn5QWzeDOnp5uPVV83rT5wwAdPBg+b6aWnmcX6+f78P0gdKCNErQgKtpA4NY05KNJ9nlhEeFMB73z+T9EI7N/xzG9c9u42vzR7Bo1+dhsWiunXtxY+up87ZyLHfXOSehnMB8NiaI1w+Y3izcx9bm8YzmzI4e2I8gQEWnrlpDt/57xecKKuhqq6BA7lS1C5Edy1aZDJB55xjsk8Oh1kld+yYaXaZlWU2/J040TTF/OMfzYq6M84w511xhaltysszn7/9NoAiIsJkm6qr4dlnISzMBF5VVWbaz+UyH6Gh0sZACDHIjY03hQphQQEkRgazaEys97lXd57gmU8yGHvf+3ywv2u/TroaNXVOk7//NL2YGoeLZRPiuGXRKDJLath+rJSKGqf3/Cc3HKXW6WLVvjwumJxISmwY731/CdvuW8EFkxPZmSVTeEJ0lWcFnq9PPoG//MUETwkJ5qOkxAQ/xcWmFioqymSlwDTCzMgwBeh2uwmWVqwAUAS7twKdOtUEW+Xl5p4ul3l9cLC5XmSk1EAJIQa5+CHmf0TPVi6+2abZKdH8ZvVhGho1v/vwcJeul1bYNOV24z+3A/D4NTO5dHoSgCkSf2c/AIVVdTh8tpC5aGoiAFaLIjQwgIVjYskurSW7VFblCdEVnhV4gYFNe9E5nWblXGysmY679FJTXP7WW5CTY6ba0tNNofiuXSZwWrcOjh83xeChoSYgiourwmIxPZ/KykyGym431wXTDiEkxARQxcXSiVwIMcjFRwQBUFhV7z226cfL2X7fCu5YPtZ7rMHVtVV5u7PKm30eYFFEhtiYmRzFDQtGApBWYP5n35xeAsAL357Pg5dP5pxJCc1eO3+06cS38/jgzkKVVTv4QjJtood4gqdnnzV/hoaaqbz9+82KudtvN4HS5Mkm6ElMNFNw4eEm2MrONudaLKYGqrjYZLDy86NoaDC9nnJyzNRdSIg53yM/3xyrqYFPP/XbtwCQGighRC9bNGYoACsmxnuPjYw1LQ2Ghgd5j+WU11LrcBES2HaHvGPF1dzyQTWjYo8SFWpj689W8N7ePEZEhwAms/XwFVMprnJ4s1SfpBUTFWpjQWqsdxy+UmLCvPcejPadqODlHVmsP1RIbkUdB351PmFB8t++OHXh4fCtb5nHWVmm4NvhMHVPd98NP/qRySpVV8O+fWCzmVV5YFbhaY13ug7Myr26OhM8Wa1myi4vzzzX2GimAGtqzDXCwsyfCc1/H+pzkoESQvSq1KFhpD9yYZubJVssirduX8x3l43B1ajZl9N2QfeB3AqW/2EDAJklNcxIjiLYZuWq2SNYMDq22bnDooLJq6ijvsHF+sMFnDkurt0i9ZBAKxHBARRUDpztZarqnLgaW2frjpdUc/v/vuDnb+4DoMHVyDVPb+G/W7PIdW+fM9gzbaLvOBwmE/Xii+bjggtMJuroUVMLlZho+jh5MkojRpjPwWSewGSpPIqKAFxkZprPlTLdxz2Py8vN/UaNMtcDE5T5k/wqIoTodQHW9n9Xm5EcRXJ0CP/YcJTP0ouZl9p8g6s6p4urn9ra7NjyCfG0JykyhBqHi3te3UtZjZOrZo/ocGyJkcEDZn++fScquPIfnzEmLpx37lhCYID5vpbXOFj6+w3e80JsVq6YOZxqh4t5qTEE26xsOlLE1owS6hsamZcaQ2SIn3/6iAHJU3e0erXp0fTSS2ZarbLS9HTybBx8/LgJfEaONBmq0lJT1wSmLUHbrMTGNmWejh83f6amwqFDZrpw3z6TnQK8wZa/SAZKCOF3seFBnDEsgr+sT2vVVuCpjRnY6xtIiAhibJSFGxekcMOClHavlRhp5gXe3ZOLzapYMrb11J2vhIjgAZGB+jStmEuf+BSnS3M4v4rV+/O8z725q3n/q2c/PcYzn2QA8PurpvH8N+Yxa2QUf99wlG8/v4N7X9/bp2MXg4Nn0+D8fPjPf+DBB02zS4vFBDUNDaYFwfLlMGcOjBljPoemQnAwdVBtUaq2WWG4Z8rPd8sWT/AEptjcnySAEkL0C0/dOJsAi+L1nSYYKKqq55O0Iv637ThnT4xn233n8IsFITx0xRSsHfSNOnPcUM5211vduji1w3MBEiOCyT/FACq90E5aQRVPrE9j5/HSU7pWS7uzy/nhy7t5ZYeppH3je4sYHhXCi9uzuPbprXyWXszGI0WMjQ/n2ZvmeF/39u5cYsMCvVvoTB0e6X1u9f58Kmrb+SkmRAcqK03bghMnTBPN5583Rd6lpXDPPWaabts2k4366CNT1wSmILwzWoc06zDuCaCqq5uO+W4i7O8aKJnCE0L0C8kxoSybEM/7+/L4xcWTeOCdA6zaZ7IsX53V8TScr6jQQP51y1xyymuJHxLU6flJUSEUVdV3WMDemRv/uY089zRgWKCVAw9ecFLXacsPXtpFprtr++SkCGaNjGbx2Fhe2WHmQWLCA9mVVc6FUxK9Pbc8nr15DsrdfOfiaUk8t+U4Ny9M4bktxymsrJNpPNEtDoeZQktNhfPPN0HT0aOQnGwCpj17zHmeqbrw8Kbgx9PyoDNlPmV6AQFN9U4evhmo9jJZfUUCKCFEv3HJtGGsOVjAF1llZJeZoOHS6UmcP7n7v2oOjwrp0nlThkfSqE2h+pxRMZ2/oIUGV6M3eAoKsFDtcPFlfhUTEod0+1ptKahsav/gaUS4eOxQXtlxgpiwQFbtNUHmrJHRjBoaxgvfnk/8kGCGhgcSFdrUqnleagxfPnwBOzPLeG7LcYrs9YxL6JkxitNHbS288orJMpWUmBV11dXNAxuPgoJTrUXeVQAAH0RJREFUu1fL4AlM4bgncKrxc/s2CaCEEP3GikkJ2KyKtYcKOV5Sw7XzkvnNldN69Z7TR5iprc1HS3j582yunT+SWSOju/z6LHcTzj98bTqLxsSy6Lfr+TS9uEcCqDqni1qni++fPZZNR4r47rIxAFw8dRgRITaGhgVxx4tfMCo2jIummVWObbVr8AgKsBLnzsoV2/3chVAMOHa7yTodP26CJzB9ntoKnnqLb9ap/WL0viEBlBCi3wgPCmDSsAg+OmhqdCYNi+j1e8ZHBDMuPpw/rTkCmKX+6+9ZBsCGLwvJq6jjmrnJ3qmwltLcmxKPjQ8nKSqEUbGhbDlazDeXpJ7y2MpqTJCTFBXC23cs8R4PsFq8KxE3/nh5t67p6b1V7NPYVIjO2O3w0EPw2mvN96DzrVny8PRx6m1tZaj6khSRCyH6lanDI8koMoUTExN7P4AC+Petc5s+UeBoMD8Vfv7mfn72xj5Wbs5s83Vaa57aeJTIEBvjE0z90ZThkRwtqm7z/K7allHC5F9+wF/XpwMQHdpzu6ZGhtgIsCiK7RJAia4rLTXTdnV1zYMmT0bIt7i7rzJSI7peGtkrJIASQvQrM5KjvI97qo6oMyOiQ3nw8skAZBRVM/4Xq1l/uMDb8O93H3xJaXXrKa+Cynq+yCrn9uVjCA00Cf34IcEUtrGqL6ukps0GmG1Ze6iAaoeLF7aZ9dsxYT0XQFksitjwQNIK7eRVDM4O7KJn2e2wfr3pz1RXZ7Zeaakvp/E8Xnml7+/pSwIoIUS/crbPli99uUrspoWjeOK6md7P39yVS0FFPWdPjKfW6eLlz7NbveZokZm+m5LU1CIgbkgQ1Q4X1fVN8wv7cyo46/cf8/yWzC6NZXd2OSnu7W4AokN79vswPmEIaw4WcP5jm7ybPAvRFocDPvwQ3nuva60I+tKsWf69vwRQQoh+JTY8iGUT4vj6nL7Pz/sGb4fyKnG4Glk6Po7pIyL5+HBhs3NL7PVc/+w2AMb4tA9oKtJumiJ7392O4VBeZadjqHO62HuiotnGx9E9mIECeOzqGaQODaOyroEvZHsX0QGHA9atg3fe8fdIWjPbv/iPBFBCiH5n5a3z+N1V0/v8vqGBAfzha9MZFhlMurs4fFhkMDNHRrMvp4IGn2yNb12Ub78pTwBVVFXPs59ksOg363h6k+kKXutser3Wmrd353DTv7bzlk8n8S3u7VbOGh/HBZMTAYjq4Uzc0PAg3rljMQEWxZMbj7L4t+vZeMTPP41Ev2S3w/vv+7/nUltq/TwDLavwhBDCx1WzRxBgUfzg5d0ADI8OYUZyFCs3Z/L6Fyc4f3Ii+ZV1vLvHzGfcvnxMsxV6ceFNAdR/th4nt6KOEJuViBAr2aVNjWsO51dx10vmHruyyrhi5nAeeOcAz23JJCzQyvzUGBaNiaXE7uhwL8GTNSTYxgVTEnnP3Ufq7V05WJVizcF8bls6pst9tMTg9tlnTXvS9Tchfv4rKgGUEEK0MHNkUyH7xMQIkiJDiAyx8ciqQ7z0eTa7ssoB+MXFk/jWmaObvTYhwgRQ3/3fFwCcMymeR786jT98dIQP9uexK6uMH7y8m/k+myYPjwqhvsHlzWo9fs1Mgm1mWZNnb7/e8INzxlPnbGTn8VIO51fxq3cPkFZoJ73Izs8unMS2Y6U90o5hIFl/uIDtx8q498KJ/h6K33n2vhNtkyk8IYRoYWRMKEOCA7hl0SisFkV0WCD3nDeeyroGb/AEMCuldcPN2PCgZv2rzkiKJDY8iLmjovn/7d15eFXVufjx75vhZDohIQEyQEIgzFOYxwgIqFFQVBxwuIpArdZqi/Znqd5etcOtVnul2qoXQcWheim1lmpbC0hEBplnCIQ5kEBIICFhSEKyfn/snQFJSA7JOSfD+3kenuxhnb3XcWXD61prv+v0uRJue2M1h3PPVSzFclPfaPafLOSni6wFft+6fyATenlmka8u7ZzMe3Aw00Z2YlfWGdKzC+kW5WTVvlwmvb6SX36+65Jes5Zg+nsbeOvr/Zyu5q3Llqa4GObO9XYtanbsWO1l3KnWAEpE3hGRbBHZUeVYhIgsEZF0+2fd0/YqpVQjJyJse+56nru5V8Wx8mVPRODa7m0Ba2266rz30BCmjUzAR6iYx3TbgPbMvrEHNyfFVqQl8PUR+seFU1Jq+GyLNSToShb0hjLzmk78YGwiPxrflb8/nswjYxKJtXu+vv/BRj5Zd8TjdfK2dYesRaE/3XSUDYcadoHopmLRIivTeGNVXRJPT6pLD9R7wHdXxpwNLDPGdAWW2ftKKdVsiMglc5u62m/aDU2IYN6DQ9j63PUE+FW/+HBUq0Cev6U3B34zkV52kCUiPDImkdfvGUByF2u5lajQAAbYAdPPbuzB4h+Ool0r9w3Z1SQkwI+nU3ow67puBPj5MvvGHqz+2XjuHNSBXVlnePazHXXOYdWUlSdQBSom1T+5cCt3vLXGW1XyqjlzvF2DK0tP9+79aw2gjDErgO+G35OBBfb2AuDWBq6XUko1KpHOAP5jeEeeGN8VXx+pV46q8hxP1tBeBGm/TOH7YxLp1yG8lk961st3JjHn7v6Ulhm+PZDr7eq43aHcygzyX2zLIrvg8oSozU3xxTJ2HMvn4fc3cOpsMcYYDuacxRjD1q3ert2VdfLy9LyrnUQeZYzJsrePAzUO2IvIw8DDAFFRUaSmpl7lLeumsLDQ7fdQjYe2d8vi7fYeHw4lR3NIrecipsEFpUQGCoPCzzf639/S81avzH3z1vK7MUFEBnlu6qyn23vdcSv56cRO/nxxsIS3/vZNxbnG3k5X64NdRSw7Yn3vNelLaBvsw4H8Mlo5BEgAunm4RnVf4C4jYy+pqdm1F3STer+FZ4wxIlJj364xZi4wF2Dw4MFm7Nix9b3lFaWmpuLue6jGQ9u7ZWku7T0WeHSKt2tRd2daHeSFv+9ij4nhmbE9PXZfT7f31qXpiOzljrH9+eLgei6ERAPW/K+RyaNx+DW/965mrfh3xXZBCRTkWwHzmWID+OLZl/UvunS/yMhejB3bq/aCbnK1vw0nRCQGwP7pvRBQKaWUWz00qhOT+sXw8bojFBZdZGtGHjsz88nMO8/tb6xiQTWLLe8/WchbX+9vUnOn0rMLiGsdTGyYlWBo1b7KRd9OVLO+YVNXWmYumfcFcGv/2Cp7nlmL8mp5exL51YaWi4EHgRftn39rsBoppZRqdGZe05nPt2Ux8bVvOJx7jmCHLzOSO7HpSB6bjuTRLSoUP19hcMfWbM7I4/Y3VgOQEBlMSp8YL9e+btJPFNK1nbNi7cHDuedw+PpQXFpGZt554iKCa7lC07IzM5+zxaXMubs/i7dm8lVaNnOmDqh4I7SxB1DeVmsAJSIfY/U4txGRo8BzWIHTQhGZARwG7nJnJZVSSnlX/7hw+rYPY/uxfHwEzhWX8vpX+2gd7M/pcyXc8/a3ADx1XTe+3HWcVoF+nLlwkf9bn9EkAqhzxRdJzy7ghj7RhAdXrj346NhEfr8snePNqAfqwMlC3l11iAM5hYjA6G5tmdQvhot2b2GvmFbsyjpDUv8Qtm7xcmWvIC+v9jLuVGsAZYy5p4ZT4xu4LkoppRqxV+9OYuNha9mZF/+ZxuHcczw7sSefbT7GV2nZBPj58LslewF49qaepGcXsHR3NsaYS1JCNEY7M89QZqBf+7BL5jqN6tKG3y9LJzOvcQZQZWWGWQu3MGVgB0Z3a1unzzy5cCtbMqzoY3jniIq8ZOVZOT6cOYzMvPMcGOnD5MluqXaDKCz07v11KRellFJ10qVdKF3aWcM6z93cu+L4U9d356nru3O+uJSZ76+npNQwZVAHvtiexcINRzmWd54Orb0z/LUyPYduUc5q82vlFhZxKPccA+PD+ef24wD0iwu7pEzv2FaEBvqRle/llWtrsPVoHn/bksmqfTls+M/rqi2TlX+ebw/kcnO/WBasOcyWjDxmJHciwM+HaaMSLisfEeIgIsRBbBAEBsKFxhk7Eu7lrB8aQCmllGoQQQ5fPpo5vGK/v53XanlaNvcMjccA/m5YGPm7ii+WkV1wgdAAf+6fv5b4iGBWPH3tZeXmLE3nT+uOMKJzJCv35TCpXwztQi8NtEIC/IgNCyIrv3FGEUt2nQAgMiSg2vPGGKa8sZrM/Au88uVejuWdZ0LPdjyd0r3GRLDlnE4YMwa+/LLBq90gWlW/EIDHNL93MpVSSjUKfdq3YlDH1ryRup/756/l7v9d45G38uau2E/yS8t5d/VBAI6cOkf+uZLLyq0/dIrSMsPKfTkkRAbz37f3rTg3onNkRfb5mPBA0k8UcCyvbr1QOYVFlFX5nmculLDjWH59vlKNNh4+DUDu2erXXDlZUERm/gX8fARjDLFhgbw0pV+twROAwwF33NGg1W1Qp7y8wo72QCmllHILEWHqkDj+36JtFT04ic/8g7RfphDoX/s/4K46nHuW5xbv5LQdLM1ZWrnWx1d7TnDbgA4A/GN7Ft2jQ9l7ooA2zgByCov4+aRetAqszC7/8cOVPWmjEtuQuuckyS99xZMTuvH4+K411uGN1H389l97uGtwB84Wl+Ijwle7T3C2uJTdv0ghyFH5vYsulvLN3hz2nChgcv9YNh/JY1fWGYL9fbmhTzQFF0pIO17AiTNFPD6uC4UXLpKZf57esdYwY1mZYWfmGQByCovJP19yWYb8nVnW+QXThzLKXkLIFWPHQkgInD1ba1GPczhqL+NOGkAppZRym+Su1j/aPgLlnTI7M/MZ1DGiwe81f+VBUvdYa9gF+vswqV8stw9sz48/2cKSXVYAtXp/Dj/4aBP+vkKZgd/c3pcLJaVc271djdf93ujOpPSJ5nvvb+DDtYf54bgu1U6KzztXzO/toG3hBitdfWiAH2eLSwG4d963fDRzGMEOv4oyP/9sBwAvf7nnkmuVT8Yv99qyymBw1y9uINjhx/6ThRQWXeTmpFj+vjWTLRl5jKkykXz1vhweenc9ULmWo6uio+Gxx2DtWvj666u6hNs4r+4rNRgdwlNKKeU2MWFBPDQqgbfuH8Sq2eMA2JLhnuGsrUcrr3tT3xheuTOJkYltuKZrW9bsz2XP8QKmvWMFFCWlVjQ3rHMENyfF4uNz5bcE4yKCuW94R06cKeL2N1djzOVDkd8eOEXRxTJ+PqkyO/bK2eNY+uRoADYfsSZ8l0uze4fK/fq2Pmz9r+sr9lN6R9M+PIgnr+vGnYM6VBxfsfckxhj+sHwfDl8ffjyhK/6+wpr9uRw4WUjKnBWk7snmiU82A+AM8KNtaPVzpGrjdMKsWTBgAPg0sojhYt1XfXEL7YFSSinlVlXf2GsfHsS6g7nMSG7YlWC3ZOSxNSOPqUPiWLLrBCm9oyvODe3Umr9sOsoTH2+muLSM74/uzP+uOIAzwO+SYbvajEyMBKxA6Fdf7OaH13ahtZ0C4GDOWR75cCMA/zG8I53bhpBTUERYkD9hQf7cNyyej9Ye4R/bs7g5KZZ53xxgeVo2wztH8N5DQzmWd57EtlaXyveu6YSI8MxNPS9JAfHC5N6MeTmVpxZu5YWgXWTlX+CJ8V1JbOtkQHxr/r3zOL4+kHa8gGnvric00I8ls0YTHRZYrzQS0dHw4IMwb573UwdU1ejzQCmllFIN5bpeUfxp3ZFq5+vUx0ffHiY00I//nNSL39ze95KAYXhnK/DZc6KA/nHhzL6xB4ltnbRr5VqvTGJbJ58/nsyk11cyf+XBimCob/swMk6fA+CWpFgcfj6XDQn++ra++PoIn246xq8+38Un6zMAuHNwHIH+vhXBE8CzEyt7sKp+j2CHH395ZCTPfradb9JzuKlvNLMmWPOx7h/ekSc+3swfl+8HYGLfGB4Y0ZGuUQ2TTTwiwgqk9u2DNm0gJ6f2z7ibt4fwNIBSSinlMRP7xfDe6kOsP3iKCb2iXPpsWZnh8KlzpJ8oYHS3tjh8ffCx3y77eu9JRndrizPg8n/WOkaG8NcfjGTj4dMMTohARLhrSNxV1b9P+zBevL0vS3adYFlaNnNXHMDXR+gWFUp8RDCv3TOgxs/2imnF+0WH+WR9BrFhgYzp3o5Hxya6dP/4yGAWPDSUr9NPMtT+LmAFTF/vOclXaSd4YXIfbkmKreVKromPhwUL4KmnoGNH+Otfobi4QW/hsnz3jATXmQZQSimlPKZzmxAA1h06RXLXNnV+G6+ktIw73lxdMc8puUsbtmTkMbBjayJDHGQXFDHuChPBB8S3ZkB86/p/AWDq0HgmJcVy6x9XMWVgBxZuyGB31hkm9r3ykjU9YyoTFy1+PJk2zqubl+TjI5f1cPn6CL+7K+mqrlcXxcXWn/nzrcnk69fD6dPg6+u93qiTJ71z33IaQCmllPKYiBAHPgJzVxwgM+88f7h34BXL550rJizIny+2ZbH1aD4zkzvx541HWbnP+ld7xV7rX9FbkmKZ3L9he12uxBngx9InxwBwz9A4XvxnGrfUcv/u0aG0Dw9ienKnqw6evMXhgMGDYcUKyMiAXr2gqMiayJ2aCtXMqXe7+HjP37MqDaCUUkp5jIhUpDP4fFsWf7i35rJLD5cw7V9LuHdYPH/ZeJQe0aE8c1NP7hvekZe/TKNfh3CC/H3ZdjSfFyb3xs8DWc6rEx7s4MUp/WotF+jvW/EmYlPkdMLo0XD+vDWZPCsLkpJgxw5ruZeCAs/Wx9tDiBpAKaWU8pqyMnNJCgFjDJ9vy2J5WjbfHLISYv5p7REA5k8bgo+P0KlNCG/cN8gr9W3pnE4YNQoWL7bmQhUUQKdOEBoKGzZYgVRoqDWs53S69629zp3dd+260ABKKaWUR00bmcB7qw8B1jIrCfa8KICZCzawLC27Yv/BER1ZsOYwCZHBtA8P8nRVVTWio+HVVyt7gBwOmDIFZs+G1autuVEAwcHuDaASEtx37brQAEoppZRHPX9Lbyb2i+HOt9ZwMPcsIhAW5I+/r88lwZOPwMxrOnPXkDiX8jUp93M44P334YEHrLlR8fEwdap1PCkJPv3Umh+VbTenn1/DJ77MzKy9jDtpAKWUUsrjEiKtXqefLtpGdkERIxMjmT7KSq75wYyhdGnnZP3ab4mLCPZmNVUNnE6YObNyf+VKKCmBsDCYMAHefttaR8/HB86cgago2GwlRiciomEWAvb3ckytAZRSSimPa+O0MnhnFxQBsHp/LmsO5BITFsiQhAgC/X1p5bj67NnK/RyOyvXxzp6FNWusSebdu8OkSdY8KH9/61xRkRVc5edXZhCvb6+Ut9/Ca2Qr2yillGoJqmbY7tPeyo8U5O/LBzOG1Tk3lPIuhwPGjIEbb7TmQD3/POTmwpIlVsAUG2tNKvf1rewtioqClBSrB+u++yqv1b49QJFL6+11atjVgFymPVBKKaW84p1pg7lYasg7X8LTi7bx05QedGnn5fU5lEscjsrt+Hh4+GHYuBFeftk6N2SINXTXrRssX27td+wIycnW23pLl1rpECz+xMfDoUN1u7e31+XTAEoppZRXjOthLeVSWmZoFejH9b2ia/mEauwiIqxeqfLA6s47rWP+/jBsGMydC5GRsG0blJVB164QEGBNPP/iizLKyqweq+Bgq5fq+HEID698sy8mpjLg6t27+jp4ig7hKaWU8ipfHyGlT8wl+aBU01W1V8rptIb4hg+HVatg1ixruO7WW+EnP7EmmV93HfToASkpWbz+OiQmWsNzM2ZYPVd+ftVf29tr4WkApZRSSim3cTisXqgHHoBjx2DgQKuXKTMTpk+33tp75BHo0eMsmzZZ+8HBsH27NQF99Gjr85GRVkAG1ucTXVuHucFpAKWUUkopt3M6rVQHa9dCWpp17JprrOG91athy5ZwuneHxx6zgqinn7Z6oqKioF07azs5GcaNg549IS7Ou99H50AppZRSyu0cDiswAhg/3spk/s470KEDBAXBiBGnufbaDnz4obVYcV4ePPoo3HCDFVR9+KE1pHf8uDXRXCeRK6WUUqpFKJ/DVP5z+nTrrb0RIyA4+BTR0dZwXtW5Tg6H1XuVnGwN/zmd1hp83s4DpQGUUkoppbyi6lt7/v4GqJznVJXDYc2F2rDByiPlcFwaZHmDBlBKKaWU8pq6BkJOJ4wc6f3AqZxOIldKKaVUk9BYgifQAEoppZRSymUaQCmllFJKuUgDKKWUUkopF2kApZRSSinlIg2glFJKKaVcpAGUUkoppZSLNIBSSimllHKRGGM8dzORk8BhN9+mDZDj5nuoxkPbu2XR9m5ZtL1blsbY3h2NMW2rO+HRAMoTRGSDMWawt+uhPEPbu2XR9m5ZtL1blqbW3jqEp5RSSinlIg2glFJKKaVc1BwDqLneroDyKG3vlkXbu2XR9m5ZmlR7N7s5UEoppZRS7tYce6CUUkoppdxKAyillFJKKRc1qwBKRFJEZI+I7BOR2d6uj6ofEYkTkeUisktEdorIj+zjESKyRETS7Z+t7eMiIq/Z7b9NRAZ69xuoqyEiviKyWUQ+t/c7ichau13/T0Qc9vEAe3+ffT7Bm/VWrhORcBFZJCJpIrJbREbo8918icgs++/yHSLysYgENuXnu9kEUCLiC/wRuBHoBdwjIr28WytVTxeBp4wxvYDhwGN2m84GlhljugLL7H2w2r6r/edh4E3PV1k1gB8Bu6vsvwS8aozpApwGZtjHZwCn7eOv2uVU0/J74F/GmB5AEla76/PdDIlIe+AJYLAxpg/gC0ylCT/fzSaAAoYC+4wxB4wxxcAnwGQv10nVgzEmyxizyd4uwPrLtT1Wuy6wiy0AbrW3JwPvG8u3QLiIxHi42qoeRKQDMBGYZ+8LMA5YZBf5bnuX/x4sAsbb5VUTICJhwGhgPoAxptgYk4c+382ZHxAkIn5AMJBFE36+m1MA1R7IqLJ/1D6mmgG7+3YAsBaIMsZk2aeOA1H2tv4ONH1zgKeBMns/Esgzxly096u2aUV72+fz7fKqaegEnATetYds54lICPp8N0vGmGPAK8ARrMApH9hIE36+m1MApZopEXECfwF+bIw5U/WcsfJwaC6OZkBEJgHZxpiN3q6L8gg/YCDwpjFmAHCWyuE6QJ/v5sSeyzYZK3COBUKAFK9Wqp6aUwB1DIirst/BPqaaMBHxxwqePjLGfGofPlHedW//zLaP6+9A0zYKuEVEDmENwY/DmiMTbnf5w6VtWtHe9vkwINeTFVb1chQ4aoxZa+8vwgqo9PluniYAB40xJ40xJcCnWM98k32+m1MAtR7oas/od2BNTlvs5TqperDHu+cDu40x/1Pl1GLgQXv7QeBvVY4/YL+tMxzIrzIUoBo5Y8zPjDEdjDEJWM/vV8aY+4DlwB12se+2d/nvwR12ee2taCKMMceBDBHpbh8aD+xCn+/m6ggwXESC7b/by9u7yT7fzSoTuYjchDWHwhd4xxjzay9XSdWDiCQD3wDbqZwT8wzWPKiFQDxwGLjLGHPKfij/gNUtfA54yBizweMVV/UmImOBnxhjJolIZ6weqQhgM3C/MaZIRAKBD7Dmxp0CphpjDnirzsp1ItIf64UBB3AAeAjrf+z1+W6GROQF4G6sN6w3AzOx5jo1yee7WQVQSimllFKe0JyG8JRSSimlPEIDKKWUUkopF2kApZRSSinlIg2glFJKKaVcpAGUUkoppZSLNIBSStWLiESKyBb7z3EROVZl3+HitVJFZLC9/Q8RCW+A+iWIyHl7uZDdIrJORKbV97pKqZbNr/YiSilVM2NMLtAfQESeBwqNMa+UnxcRvyprXbly3ZsarJKw314uBDuv1KciIsaYdxvwHkqpFkR7oJRSDU5E3hORt0RkLfBbERkqImvsXqDV5dmnRSRIRD6xe4b+CgRVucYhEWlj9yDtFpG3RWSniPxbRILsMkNEZJvd2/WyiOyorW52Mr4ngSfsa9RUtxV2osfy+qwUkSQRGVOlh22ziIQ25H87pVTToAGUUspdOgAjjTFPAmnANXYv0H8B/22XeRQ4Z4zpCTwHDKrhWl2BPxpjegN5wBT7+LvA940x/YFSF+q2Cehhb9dUt/nANAAR6QYEGmO2Aj8BHrPveQ1w3oX7KqWaCQ2glFLu8mdjTHlQEwb82e4hehXobR8fDXwIYIzZBmyr4VoHjTFb7O2NQII9PyrUGLPGPv4nF+omVbZrqtufgUn2gtbTgffs46uA/xGRJ4DwqxmeVEo1fRpAKaXc5WyV7V8Cy40xfYCbgUAXr1VUZbuU+s/fHADsvlLdjDHngCXAZOAu4CP7+ItYa3gFAatEpAdKqRZHAyillCeEAcfs7WlVjq8A7gUQkT5Av7pe0BiTBxSIyDD70NS6fE5EEoBXgNdrqRtYC92+Bqw3xpy2P59ojNlujHkJWE/lUKBSqgXRAEop5Qm/BX4jIpu5tPfoTcApIruBX2ANz7liBvC2iGwBQoD8GsollqcxABYCr1V5A6+mumGM2QicwZprVe7HIrJDRLYBJcA/XayzUqoZEGOMt+uglFJXRUScxphCe3s2EGOM+VEDXj8WSAV6GGPKGuq6SqmmT3uglFJN2UQ7ncAOrDfiftVQFxaRB4C1wLMaPCmlvkt7oJRSSimlXKQ9UEoppZRSLtIASimllFLKRRpAKaWUUkq5SAMopZRSSikXaQCllFJKKeWi/w9/i1XIxGLBXAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "N = 1000\n",
    "T = 63\n",
    "dt = 1\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(S.values)\n",
    "plt.title(get_symbol(symbol))\n",
    "plt.xlabel('Trading Days')\n",
    "\n",
    "Slog = []  # log of final values\n",
    "for n in range(0,N):\n",
    "    P = S[-1]       # returns the last price in the sequence\n",
    "    k = len(S)\n",
    "    Plog = []\n",
    "    tlog = []\n",
    "    for t in range(len(S)+1,len(S)+T+1):\n",
    "        Z = norm.rvs()\n",
    "        P += P*(mu*dt + sigma*np.sqrt(dt)*Z)\n",
    "        Plog.append(P)\n",
    "        tlog.append(t)\n",
    "    plt.plot(tlog,Plog,'b.',ms=0.4,alpha=0.5)\n",
    "    Slog.append(P)\n",
    "\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 312
    },
    "executionInfo": {
     "elapsed": 1047,
     "status": "ok",
     "timestamp": 1604586363449,
     "user": {
      "displayName": "Jeffrey Kantor",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gg_n8V7bVINy02QRuRgOoMo11Ri7NKU3OUKdC1bkQ=s64",
      "userId": "09038942003589296665"
     },
     "user_tz": 300
    },
    "id": "Ji-sFL4HC_9_",
    "nbpages": {
     "level": 3,
     "link": "[7.2.5.3 Forecasting](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.5.3-Forecasting)",
     "section": "7.2.5.3 Forecasting"
    },
    "outputId": "9f5cc74d-4ced-4b1c-9104-bdc66a1df480",
    "pycharm": {}
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.30005648196687873 0.0 8.386063629075824\n"
     ]
    },
    {
     "data": {
      "image/png": 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R2SQLF8K778Izz3Rn/HiYPRs+/BBatIAePaBnz+TH3XeHAw+EkpK4oxYRyW9K3EQkY9XVMHEi/OlP8MILib19Njpv3ryNr+3eHYYPh7POAncwy2qoIiIFSYmbiDRoxQoYOxb+/OdQq7YpFi6E3/42LN26wf77w2GHQZs2TRqqiEhBU+ImInVyD8naNdfA8uU1j7VoAQccAB07fsZhh3Vjl11g553DsU8/hU8+CR/nzYPnnoOvvkpe+9ln8H//F2rtvvtd2G+/cD8REamfEjcRSWvxYjj/fHjmmZr7t9oKLr4YRo6EHXaA8vIPGDSoW41zdt215jXr18PkyfDQQ/DUU7B6ddi/fHmoySsvh1NPhR13zFpxREQKgv7HFZGNlJfDXnvVTNr69IE77oAFC+C220LSlqlWreC44+CRR+DLL+Hss6Fjx+Tx+fPh1lvh3ns3rtkTEZEk1biJyDeqquD668Pintx/5ZXwm99A69ab/4z27eHgg6F/f/jHP0JNXFVVOPaf/4TeqRdfvPnPEREpRErcRASANWvg5JNDMpXQtSs88ECoLctUJoMCQ+iUcNJJIYl74gl4882wf9ky+P3voawMfvxj9T4VEUmlplIRYd268I5ZatI2eDC8/XbjkrZN0bUrXHIJXHEFtGsX9lVXw09/GjouLFuW3eeLiOQTJW4iRa6qCs44A55+Orlv1KjQhNmtW93XNbXdd4err4ZvfSu576mnoF8/mDmz+eIQEcllStxEitiGDXDeeaGpMuHnP4ebbopnloNOnULz6OGHJ/d99BEccgi8+mrzxyMikmuUuIkUqerq0ET58MPJfT/8Idx4Y7zvlbVsCaedBo8/nmw6Xb4cjj46zNogIlLMlLiJFKkf/jAMv5Fw2WWhU0CudAY45RR47TXYdtuwvXo1DB0Kjz0Wb1wiInFS4iZShB54IMyIkHD++fCXv+RO0paw557wr39Br15hu6oqzHc6enSsYYmIxEaJm0iRee89+P73k9vDhsHdd+fulFM77RTeb9ttt7DtDpdeGgYBFhEpNln9VW1mQ8xstpnNMbNRaY4famZvmlmVmQ2rdWyDmc2Ilgkp+3ub2RvRPR8zs9JslkGkkKxaFYb9WLUqbO+6K9x/fzwdERqje3d45RUYMCC573//N8zkICJSTLKWuJlZCXAHcCywGzDczHarddonwHnAI2lusdrd946WE1P23wL8wd13ApYCFzZ58CIF6vLLYdassN6mTc0OALmuSxd48UUYNCi5b+TIMP+piEixyGaN20BgjrvPdfd1wDhgaOoJ7j7f3WcC1Znc0MwMOBwYH+16ADip6UIWKVwPPgj33Zfc/stf4Nvfji+eTdG+fRhvbv/9k/vOOw8mTKjzEhGRgpLNxK078GnK9oJoX6bamNk0M5tiZonkrAvwtbtXbeI9RYrS+++H98ISzjoLLrggvng2R7t2YViQRNK5YUNo/v3nP+ONS0SkOZinziTdlDcO76wNcfeLou2zgf3cfWSac8cCz7j7+JR93d19oZl9C3gJOAJYBkyJmkkxsx7Ac+6+R5p7jgBGAJSVlfUbN25cUxexhsrKStrlS5tTFhRz+eMs++LFDZ/ToYNx6aX9mDcvxNijxypGj57OFltsaPS9unbdeF/t8mdyn0yke1aqiopSLr98Hz77bAsA2rSp4tpr36ZPnxWNvtfm0Pd+cZYdirv8xVx2yH75Bw8ePN3d+6c7ls1J5hcCPVK2t4/2ZcTdF0Yf55pZObAP8ATQ0cxaRrVudd7T3ccAYwD69+/vg1JfjMmC8vJysv2MXFbM5Y+z7JlM6P7eezBvXlhv0waeeaYte+55yCbda9iwjffVLn+mk8xvyrNq23df2Gcf+PprWLOmJTfe2I9Ro2CbbRp/r02l7/1BcYcRm2IufzGXHeItfzabSqcCfaJeoKXA6UBGb6KYWSczax2tdwUOAt7zUD34TyDxa/hc4O9NHrlIgfjyyzB9VcKtt4ax0QpFr15hIOEttwzbK1eGd/dWrow1LBGRrMlajZu7V5nZSGASUALc5+6zzOw6YJq7TzCzAcCTQCfgBDP7tbvvDvQFRptZNSG5vNnd34tu/TNgnJndALwF3IuIbMQdHn0U1q4N2wMG1By/LddlWnO33Xaht+zvfgfr14dkdfRouOKKMH2WiEghyeqvNXefCEyste/alPWphObO2tf9G0jb383d5xJ6rIpIPaZNC50SIAyue9dduT9e26bq3TvM/pBI9mbPhkcegbPPzr3ZIERENkeOjpUuIptj9eowRlvCyJHhfbBC1q9fmMs04bXX4Pnn44tHRCQb1JAgUoCeegqWLw/r220H118fbzzN5dhjYdEieP31sP3kkxt3VBARyWeqcRMpMPPnw8svJ7f/+Efo0CG2cJqVGZx5ZpjfFMJ7fvfeC2+/HW9cIiJNRYmbSAGproaHHw4JC4SJ2U85Jd6YmlurVnDZZbD11mF7/Xo4+WSoqIg3LhGRpqDETaSAvP46fPJJWG/ZEs44ozhfzm/XLrzX16ZN2J43L3wuNmyo/zoRkVynxE2kQKxfH+bxTBgyJFnrVIy23TbMY5owaRJce22dp4uI5AUlbiIF4uWXYenSsN6+PRx1VLzx5IJ99gkdFhJuuil0WBARyVfqVSpSAFavDhOvJxx3XLKZsKmmoMpXJ54Y3v2bNClsn3MOTJ0Ku+4ab1wiIptCNW4iBeCFF5LTPHXpAodsPBVp0WrRIgzG27t32K6shJNOSg6XIiKST5S4ieS5FStg8uTk9gknhJ6VktS5c2gi3WKLsD17Nlx8cbL3rYhIvlDiJpLnnnsuOR9pt26w337xxpOr9toL7r47uf3443DnnfHFIyKyKZS4ieSxJUtqDrY7dGhoGpT0zjwTLrkkuX3llTB9enzxiIg0ln7Fi+SxZ56Bqqqw3rt3qFWS+v3xj7D33mF93bowQPHXX8cbk4hIppS4ieSp999PzskJYXaAYhxst7HatIG//S0MmQJhcN4LLtD7biKSH5S4ieSpm26qObXVLrvEG08+2WknuO++5PaTT8Kf/hRfPCIimVLiJpKH5s2DRx9Nbp94Ynyx5Kthw+Dyy5PbP/0pvPFGfPGIiGRCA/CK5Kj6Bs599NHkvJu77JIco0wa57bbYMqUMCBvVRWcfjrMmAFbbRV3ZCIi6anGTSTPLF8Or72W3B4yJL5Y8l3r1mFYkESiNn8+jBih991EJHdlNXEzsyFmNtvM5pjZqDTHDzWzN82sysyGpezf28xeN7NZZjbTzE5LOTbWzOaZ2Yxo2TubZRDJNS++GCaUB+jZE/r2jTeefNer18bju917b2zhiIjUK2tNpWZWAtwBHAUsAKaa2QR3fy/ltE+A84Cf1Lp8FXCOu39oZt2A6WY2yd0TnfZ/6u7jsxW7SK5avRrKy5Pbxx7bvD1J0zXfdu6c//OhnnJKGN9t9OiwfcUVcMABsPvu8cYlIlJbNmvcBgJz3H2uu68DxgFDU09w9/nuPhOorrX/A3f/MFr/DFgEbJ3FWEXywssvw5o1Yb2sLDkemWy+P/whmaitXg2nnRY+iojkEvMsvcwRNX0OcfeLou2zgf3cfWSac8cCz6SrRTOzgcADwO7uXh2dewCwFngRGOXua9NcNwIYAVBWVtZv3LhxTVW0tCorK2nXrl1Wn5HLirn82Sr74sU1t9eubcEPfrA/y5aVAnDZZf/l8MO/aPLnNlZJSSUbNuT2175r18zOmzevLZdd1o+1a0sAOPHEhVx55Yf1XqPv/eIsOxR3+Yu57JD98g8ePHi6u/dPdyyjplIzOwF41t2rGzy5CZnZdsCDwLkpz/458AVQCowBfgZcV/tadx8THad///4+aNCgrMZaXl5Otp+Ry4q5/Nkqe+3mx5dfhmXLwnqnTrDHHrtSUbFrkz+3sTp3LqeiYlDcYdRr2LCGzwEYNCi8P5iYFmvChO6cfXb3eq/X9/6guMOITTGXv5jLDvGWP9Om0tOAD83sVjPL9C/FQqBHyvb20b6MmFkH4FngKnefktjv7p97sBa4n9AkK1LQNmyA559Pbh95JLTUYD5ZcfHF4Z231O1PPokvHhGRVBklbu5+FrAP8BEwNurxOcLM2tdz2VSgj5n1NrNS4HRgQibPi85/Evhr7ebTqBYOMzPgJODdTO4pks+mT082nW65JRx8cLzxFDKzUNu5ww5h++uv4ayzkuPmiYjEKePOCe6+HBhP6GSwHXAy8KaZXV7H+VXASGAS8D7wuLvPMrPrzOxEADMbYGYLgFOA0WY2K7r8VOBQ4Lw0w348bGbvAO8AXYEbGldkkfziDi+8kNwePDjMtynZ07EjPPIIlIRX3fjXv+DGG+ONSUQEMn/HbShh2I6dgL8CA919kZm1Bd4D/pzuOnefCEyste/alPWphCbU2tc9BDxUxz0PzyRmkUIxdy58/HFYb9kyJG6SfQceCL/8JVwb/cb69a/hiCPgoIPijUtEilumNW7fBf7g7t9299vcfRGAu68CLsxadCLCiy8m1/fbD4q4I1ez+8Uv4NBDw3p1NZxxRmg6FRGJS6avN3/h7q+k7jCzW9z9Z+7+Yl0XicjmWboU3noruX246ps3SSYDBI8YsfG+khJ46CHYc8+QsH3ySehxOm5c8w58LCKSkGmN21Fp9h3blIGIyMbKy0NND8DOO8P2G71YINnWowfcc09y+/HH4f7744tHRIpbvYmbmV0WdQTYNZozNLHMA2Y2T4gixWnduvBSfIJq2+Lzve+FYUESrrgCPvggvnhEpHg1VOP2CHAC8PfoY2LpFw0RIiJZ8p//wMqVYb1LF9hrr3jjKXZ//CPsGo1iuXIlDB8ekmsRkebUUOLm7j4f+AGwImXBzDpnNzSR4uUOL72U3B48GFpkc2ZhaVDbtvDoo1AaZhzjzTfh6qvjjUlEik8mNW4A04Fp0cfpKdsikgXl5bAwmmektDQMTSHx23tvuOWW5PZtt8H06Z3iC0hEik69vUrd/fjoY+/mCUdEAG6/Pbl+wAFhtgTJrkx6nkIY/Hj33WFWNFz4jTeG9tP20Twy6Xqniog0lYY6J+xb39JcQYoUk3nz4O9/T25rwN3c0qIFnHdeMlFburQ1f/1raN4WEcm2hsZx+109xxxQPzeRJnbHHckkYLfdYLvt4o1HNtahQ0je/hzNGTNzZmjeVpItItnWUFOpfg2JNKPVq+G++5LbGgIkd+2xR5gCKzGzxfjxYaw9EZFsaqip9PDo43fTLc0TokjxePzxMFsCQNeu4V0qyV0nnww77FAJQFUV3H03rFoVc1AiUtAa6lV6WPTxhDTL8VmMS6Qo3XVXcv2QQzQESK5r1QquvPK9b4YI+fxz+PGP441JRApbQ02lv4w+nt884YgUrxkzYMqUsN6qFRx0ULzxSGa6d1/FaafBgw+G7bvugqOOgu+qTUJEsiCj/+fNrIuZ3W5mb5rZdDP7k5l1yXZwIsXkzjuT68OGJXstSu476CDo1y+5fdFF8Omn8cUjIoUr04aYccBXwPeAYdH6Y9kKSqTYLF8ODz+c3L7ssvhikcYzg7POClOTQXhP8cwzYcOGeOMSkcKTaeK2nbtf7+7zouUGoCybgYkUk4ceSs5LuvvucPDB8cYjjde2LVxwQfK9xH/9C264Id6YRKTwZJq4PW9mp5tZi2g5FZiUzcBEioV7zU4Jl14aanAk/+y0E/zqV8nt666DV16JLRwRKUD1dk4wsxWEgXYN+CHwUHSoBVAJ/KSB64cAfwJKgHvc/eZaxw8F/gjsCZzu7uNTjp0LJKZwvsHdH4j29wPGAlsAE4H/cdeY5ZJfUqdXmjMH3nknrJeWhua1TKdfktyz9dbQpw98+CFUV8PQoXDNNdCuXc3zNDWWiGyKemvc3L29u3eIPrZw95bR0sLdO9R3rZmVAHcAxwK7AcPNbLdap30CnEdyMvvEtZ2BXwL7AQOBX5pZYibnO4GLgT7RMiSDcorkrJdfTq4PHAhbbBFfLLL5WrSACy9Mzi/79dcwdqymxBKRppHxKFFm1snMBprZoYmlgUsGAnPcfa67ryN0cBiaeoK7z3f3mUB1rWuPASa7e4W7LwUmA0PMbDugg7tPiWrZ/jUgPTkAACAASURBVAqclGkZRHJNZSW8+WZy+7DD6j5X8kenTmFKrIR33oGXXootHBEpIA3NVQqAmV0E/A+wPTAD2B94nfrnKu0OpHaIX0CoQctEumu7R8uCNPvTxTwCGAFQVlZGeXl5ho/eNJWVlVl/Ri4r5vJvStk7dw4f//WvHlRV7QjATjstZ++936znqtxUUlJJ587lcYcRm7rKP2gQzJ+/I88+2wOAJ56oZt9932THHcNMC5l8yyxe3PA5XbtmHmtTK+afeyju8hdz2SHe8meUuBGStgHAFHcfbGa7AjdlL6zN5+5jgDEA/fv390GDBmX1eeXl5WT7GbmsmMu/KWUfMya8//T888l9Bx3UgYqKxt0nF3TuXJ6XcTeV+sp/3HGhtu2TT2DDhhb87nf9ueqq0Bw+bFjD987kXcdM7pMtxfxzD8Vd/mIuO8Rb/kybSte4+xoAM2vt7v8FdmngmoVAj5Tt7aN9majr2oXR+qbcUySnfPABLFoU1tu2hf79441Hml7LlqETQps2Yfurr8J4fXrfTUQ2VaaJ2wIz6wg8BUw2s78DHzdwzVSgj5n1NrNS4HRgQobPmwQcHb1X1wk4Gpjk7p8Dy81sfzMz4Bzg7xneUySnvPpqcn3gQL6Z71IKy9Zbh8F5E6ZOrfm1FxFpjIwSN3c/2d2/dvdfAdcA99JApwB3rwJGEpKw94HH3X2WmV1nZicCmNkAM1sAnAKMNrNZ0bUVwPWE5G8qcF20D+D7wD3AHOAj4LlGlFckJ1RWwltvJbcPbairj+S1AQNqDqo8blyYm1ZEpLEyfccNM9sXOJgwrttrUU/Rern7RMJYa6n7rk1Zn0rNps/U8+4D7kuzfxqwR6Zxi+Si11+Hqqqw3rs3dE/bxUYKyWmnwfz5sGBB+NqfcgpMnw4d6h1YSUSkpkwnmb8WeADoAnQF7jezq+u/SkTScQ/TISUcckh8sUjzKS0N77u1bh2258wJk9HrfTcRaYxM33E7Exjg7r90918ShgM5O3thiRSuV1+FL78M623aqFNCMSkrg7NTfnP+7W/w//5ffPGISP7JNHH7DGiTst0a9eYU2SSpQzwMHJisgZHiMGBAzXcaf/QjmDYtvnhEJL80NFfpnwnvtC0DZpnZ5Gj7KOA/2Q9PpLBUVIRalgQ1kxanU0+FFStCB5V168L29OlhxgURkfo01Dkh8X/gdODJlP3lWYlGpMA99BCsXRvWe/YMixSfVq1CAr/vvrB8OcybF5pQJ0wIc52KiNSl3sTN3R9IrEdjse0cbc529/XZDEyk0LjD3Xcnt1XbVtx23BHuvx++972w/eyzcNNNcLW6fYlIPTLtVToI+BC4A/h/wAcZTDIvIimmTIF33w3rpaXhXScpbt/9LvzkJ8nta6+FSZPii0dEcl+mlfK/A45298Pc/VDgGOAP2QtLpPCk1rYNGBDmqxT5zW/ChPQQamXPOAM+bmheGhEpWpkmbq3cfXZiw90/AFplJySRwrNsGTz2WHJbzaSS0LJlmEmhW7ewXVERJo5fsybeuEQkN2WauE03s3vMbFC03E2y44KINOCRR2DVqrD+7W9Dr16xhiM5pqwsdFZoGb11PG0aXHFFvDGJSG7KNHG7FHgPuCJa3gMuy1ZQIoUmtZl0xAgwiy8WyU0HHgi//31y++67a86wISICGSRuZlYCvO3uv3f370bLH9x9bTPEJ5L3pk9PTijfpg2ceWa88UjuGjkyvOOW8OijYWosEZGEBhM3d98AzDYzjTglsglSa9tOOUWDrErdzMLMGnvtFbY3bIDRo2Hp0njjEpHckWlTaSfCzAkvmtmExJLNwEQKQWVleL8t4eKL44tF8sOWW8JTT0GXLmF7+XK46y5Yr5EzRYSGZ05IuCarUYgUqMceC1MbAey6Kxx8cLzxSH7o1St0VjjySKiuhvnz4eGH4dxz9X6kSLFraK7SNoSOCTsB7wD3untVcwQmkq9SJ5G/+ebk+h571Gw2FanP4MGhaT0xjMzrr0OPHnDEEfHGJSLxaqip9AGgPyFpO5YwEK+IZGDhwjAHJUBJCey/f7zxSP4ZPDj0Nk0YPx7efz++eEQkfg0lbru5+1nuPhoYBjRq2FAzG2Jms81sjpmNSnO8tZk9Fh1/w8x6RfvPNLMZKUu1me0dHSuP7pk4tk1jYhJpLqlDOey9N7RvH18skp/MQi/T3r3DdnV16KzwxRfxxiUi8WkocfvmddjGNpFGw4jcQaip2w0Ybma71TrtQmCpu+9EmELrluhZD7v73u6+N3A2MM/dZ6Rcd2biuLsvakxcIs1h3Tp4443ktmZKkE3VqhVceil07Bi2V6+Gv/wldHwRkeLTUOK2l5ktj5YVwJ6JdTNb3sC1A4E57j7X3dcB44Chtc4ZSmiOBRgPHGG20au3w6NrRfLGm28mZ0ro2hV22SXeeCS/dewIP/gBlJaG7a++gjvvVE9TkWJUb+Lm7iXu3iFa2rt7y5T1Dg3cuzvwacr2gmhf2nOiGr1lQJda55wGPFpr3/1RM+k1aRI9kdi9+mpy/eCDoUWmA++I1KFnT7jwwmSv0jlzQk9T93jjEpHmlelwILEws/2AVe7+bsruM919oZm1B54gNKX+Nc21I4ARAGVlZZSXl2c11srKyqw/I5cVc/lrl3316rZ8+OFAAFq0cI477nU6dVoXU3TZV1JSSefO5XGHEZtNLX8mPy6dO9fcPvxwWLGiBw89tCMQeppeeulHDB/+aZqrs6+Yf+6huMtfzGWHeMufzcRtIdAjZXv7aF+6cxaYWUtgK2BJyvHTqVXb5u4Lo48rzOwRQpPsRombu48BxgD079/fBw0atDllaVB5eTnZfkYuK+by1y77DTckj+25p+F+IBUVzR9Xc+ncuZyKikFxhxGbTS3/sGENn5M6tEzCwQeH3sqvvZY4Z0eOOmrHjO7X1Ir55x6Ku/zFXHaIt/zZbMCZCvQxs95mVkpIwmrPtjABODdaHwa85B4q/s2sBXAqKe+3mVlLM+sarbcCjgfeRSRHrF4dakESDj00vlikMCV6mu68c3LfWWfVbJ4XkcKVtRo3d68ys5HAJKAEuM/dZ5nZdcA0d58A3As8aGZzgApCcpdwKPCpu89N2dcamBQlbSXAC4CGNJWc8be/1eyU0LdvvPFI7kpXm5apli3hkkvg1lvhyy9h7Vo48cRQC6fvOZHCltV33Nx9IjCx1r5rU9bXAKfUcW05sH+tfSuBfk0eqEgTGT06uX7IIeqUINnTrh1cfjncfjssWhQmoj/22FDju912cUcnItmiPysiTeSdd+Df/w7rJSU1R7wXyYatt4aJE8PE9AAffwzHHRcmpheRwpTTvUpF8klqbdvee0OHhgbMEWkC/fqFJvoTToANG2DGjNDx4dlnw+C9mcqk6XbEiE2PU0SahmrcRJrAypXw4IPJ7cMOiy8WKT7HHlsz8Zo8Gc4/P0yRJSKFRYmbSBMYNy7ZPFVWVrPHn0hzuOAC+NWvktsPPwxXXKEBekUKjZpKRZrAXXcl1w85JDm6vUi2pda0bbttGILmlVfC9h13hDHfhtaebFBE8pZq3EQ20+zZ7Zg2Lay3bg0HHBBvPFK8zGD4cOjfP7lv4sTQdCoihUGJm8hmevrpbt+sn3JKGKZBJC4tWoT32/bYI7lv/HgN0CtSKJS4iWyG5cvhxRfLvtm+5JIYgxGJJAbo3Wmn5L6HHoLp0+OLSUSahhI3kc3wwAOwZk0JALvvDgcdFHNAIpHSUhg5Enr2DNvucM898NZb8cYlIptHiZvIJqquhr/8Jbn9/e+rU4Lkli22CD1Lt902bFdXh84MM2bEG5eIbDolbiKbaPJk+OCDsN6hA5xzTrzxiKTTvj1ceSVss03YTiRvb78db1wismmUuIlsoj//Obl+/vnqlCC5q2NH+NGPksnbhg0heXvnnXjjEpHGU+Imsgk++igMs5Dwgx/EF4tIJjp1Csnb1luH7aqqMP7gu+/GG5eINI4SN5FNcMcdyRHp99tvCX36xBuPSCYSyVvXrmG7qgruvFPvvInkEyVuIo1UWQn33ZfcPvnkhfEFI9JInTuH5K1Ll7BdVQWjR8Mbb8Qbl4hkRombSCM9/DAsWxbW+/SBAQMq4g1IpJG6dIGf/KRmh4X7709OlSUiuUtzlYpkaMyY0Dx63XXJffvsAxUVNeeLFMkHnTuH5O2Pf4TPPgvf2w8/DOvWwZFHxh2diNRFNW4ijfDBB+GPHIR5SQ88MN54RDbHVlvBj38MO+yQ3Pe3v8HTTyff4RSR3JLVxM3MhpjZbDObY2aj0hxvbWaPRcffMLNe0f5eZrbazGZEy10p1/Qzs3eia24305Cn0nxeeim5vv/+YYBTkXzWrl0Y5y11eqxnnoFHHw1NqCKSW7KWuJlZCXAHcCywGzDczHarddqFwFJ33wn4A3BLyrGP3H3vaLk0Zf+dwMVAn2gZkq0yiKRasqTmoKWDB8cXi0hTSsyw0Ldvct/LL4dOC+vWxReXiGwsmzVuA4E57j7X3dcB44Chtc4ZCjwQrY8HjqivBs3MtgM6uPsUd3fgr8BJTR+6yMZefDHZfNS3L2y3XbzxiDSl1q3D3KYDBiT3zZgR3oGrrIwvLhGpyTxLLzKY2TBgiLtfFG2fDezn7iNTznk3OmdBtP0RsB/QDpgFfAAsB65293+ZWX/gZnc/Mjr/EOBn7n58muePAEYAlJWV9Rs3blxWyplQWVlJuyIeOr/Qy798eUtOPfUA1q4NE8r/4hcz2Wef0Ju0pKSSDRsKt+wNUfkLq/zV1fDQQ9/i6ad7frOve/eVXHXVTPr2XVvj3EL/uW9IMZe/mMsO2S//4MGDp7t7/3THcrVX6edAT3dfYmb9gKfMbPfG3MDdxwBjAPr37++DBg1q+ihTlJeXk+1n5LJCL/+NN8La6G9Wt27Qs+eeVESjgHTuXE5FxaDYYoubyl945T/+eGjTJnRUAFi4cEtGjTqAyZNh4MDkeYX+c9+QYi5/MZcd4i1/NptKFwI9Ura3j/alPcfMWgJbAUvcfa27LwFw9+nAR8DO0fnbN3BPkSa1ejXcfnty+5hjQF1ipNAdeSRcdBG0jP69X74cDjsMstx4ISINyGbiNhXoY2a9zawUOB2YUOucCcC50fow4CV3dzPbOurcgJl9i9AJYa67fw4sN7P9o3fhzgH+nsUyiPDAA7BoUVjv1KnmO0AihWzAgNBpoW3bsL1mDQwfDr/8pXqcisQla4mbu1cBI4FJwPvA4+4+y8yuM7MTo9PuBbqY2RzgR0BiyJBDgZlmNoPQaeFSd08MT/994B5gDqEm7rlslUFkwwb47W+T20ceCSUl8cUj0tx22QVGjYKysuS+666D006DNWs0FKhIc8vqO27uPhGYWGvftSnra4BT0lz3BPBEHfecBuzRtJGKpPfkk/DRR2G9bVs4+OB44xGJQ1lZSN4mToTJk8O+8ePh7bf3YfLkmgP4ikh26d8lkTq4w623JrcPOyy8sC1SjNq2DYnbyJHJfR9+2J5+/eD55+OLS6TYKHETqUN5OUydGtZbt4bDD481HJHYtWwJf/4z3HlnstPCkiUwZAjccIPeexNpDkrcROqQWtt2/vnQoUN8sYjkkksvDf/YdO0axshxh2uugaFDYenSeGMTKXS5Oo6bSKxmzoR//COsm4WJuFPnKRUpdgcdBKNHT+P22w/i5ZfDvmeegX794LHHGu59PWZMw88YMaLhc5rqPiL5QjVuImn8+tfJ9e99r+YE3CISdO68nhdegJ/+NLlv3jw48MBQY62mU5Gmp8RNpJbp0+H//i+5/YtfxBeLSK5r2TIkaU88Ae3bh31VVfCzn8HRR8Nnn8Ubn0ihUeImUss11yTXhw2DffaJLxaRfPHd74ZJ6ffbL7nvxRdhzz3h6afji0uk0ChxE0nx2mvwXDSks1nNJlMRqd+3vgX/+hdcdVVyWrglS+DEE8N7ZsuXxxufSCFQ4iaSIrW27ayzYLfd4otFJB+1ahWGBnnxRejePbn/7rvh29+GF16ILzaRQqBepSKRF1+Ef/4zrJeUhPkYRSSpdg/Ozp3T9+ocMQIGD4a334ZLLgnvvwF88gkcdVTYt9tuGtBaZFOoxk2EMA7V1Vcnty+4AHbcMb54RApBly7wt7/Bo4+GJC9h9Ogw3+msWfHFJpKvlLiJEKbymTIlrJeW1mwyFZFNZwannx6StJNOSu5fsgRuvz00oS5bFl98IvlGiZsUverqmrVtl14KPXrEF49IIdp22zDMzsMPQ6dOyf3TpsG114aZGDTum0jDlLhJ0Rs/PgxjALDFFvDzn8cbj0ihMoMzzoD33685bMiaNaE59ZZb4OOP44tPJB8ocZOitmpVzVHfr7gi1AyISPaUlYX3SH/4Q9hmm+T++fPhN7+BsWPh66/jik4kt6lXqRS8+uYyfOqp0NMNoGvXMNq7iGyeTOYPBejbNzST/uMfYamqCh2FXn8d3nwzbF95ZagJF5FANW5StL78EiZPTm7fckvNd29EJPtatYITTggJ3F57JfevXRsG8u3bFx55RO+/iSQocZOi5A7jxoX/6CG8b3PeebGGJFLUysrg+98PzafduiX3f/wxnHkm7LsvPPts+NkVKWZZbSo1syHAn4AS4B53v7nW8dbAX4F+wBLgNHefb2ZHATcDpcA64Kfu/lJ0TTmwHbA6us3R7r4om+WQwjNjBrz3Xlg3gyOPhHvuiTcmEQk1bFdfDa++Cs8/D4sXh/1vvw3HHw8HHRTegzvkkHjjFIlL1mrczKwEuAM4FtgNGG5mtScQuhBY6u47AX8Abon2LwZOcPdvA+cCD9a67kx33ztalLRJo6xbB48/ntw+9FDo2TO+eESkppISOOww+PDD0Fzatm3y2GuvhZ/Zo48O86KKFJtsNpUOBOa4+1x3XweMA4bWOmco8EC0Ph44wszM3d9y98+i/bOALaLaOZHNNnEiVFSE9XbtYGjt70oRyQkdO4Z5T+fOhcsvD+/DJUyeHBK43/421J6rCVWKhXmWvtvNbBgwxN0virbPBvZz95Ep57wbnbMg2v4oOmdxrftc6u5HRtvlQBdgA/AEcIOnKYSZjQBGAJSVlfUbN25cVsqZUFlZSbt27bL6jFyWy+VfvDi5/vnnW/CjHw2gqir8z3Lppf/liCO+2Kz7l5RUsmFDbpa9Oaj8xVv+bJe9a9ea21980YaxY3sxeXIZ1dVW49iOOy7nu9/9hH79FlNSUv99mkou/97LtmIuO2S//IMHD57u7v3THcvp4UDMbHdC8+nRKbvPdPeFZtaekLidTXhPrgZ3HwOMAejfv78PGjQoq7GWl5eT7Wfkslwuf2Jogupq+POfkx0SeveGvfbalYqKXTfr/p07l1NRMWjzgsxjKn/xlj/bZR82bON9p58Oc+bAzTfDAw8kf54/+qgDt922B9tsA4cfDgceCK1b132fppDLv/eyrZjLDvGWP5tNpQuB1ImDto/2pT3HzFoCWxE6KWBm2wNPAue4+0eJC9x9YfRxBfAIoUlWpEHPPRfemYHQIWH4cGihftUieWennUJnojlzYNAgaJlSBbFoUegxPmpUmGJr6dLYwhTJimzWuE0F+phZb0KCdjpwRq1zJhA6H7wODANecnc3s47As8Aod38tcXKU3HV098Vm1go4Hnghi2WQAvHRR/DMM8nt44+HHXaILx4R2Xw77BD+ATvuOHjhhdATddWqcGzVKpg0KbwL98YbYQ7iI4+s/5+1TAYOHjGiaWIX2VRZq29w9ypgJDAJeB943N1nmdl1ZnZidNq9QBczmwP8CBgV7R8J7ARca2YzomUboDUwycxmAjMICeHd2SqDFIZVq+Dee5MDeO60U/hFLyKFYaut4HvfC8OEnH56zWm0qqvhySfhmGOgTx+49Vb46qv4YhXZXFl9x83dJwITa+27NmV9DXBKmutuAG6o47b9mjJGKWzu8PDDsGRJ2G7bFi68UE2kIoWoTRsYPDgMJTJzJrz0EsyenTw+d26Y1u7qq+E734Fzzw3/xJWWxhezSGPldOcEkc01dixMm5bcPvts6Nw5tnBEpBm0aAF77x2WL76AV14J858mmlHXrw/zFD/1VBgSaOBAOOAA6NEjvP8qksuUuEnB+uCDMPZTwsEHh2lzRKR4bLstnHoqnHQSTJ8OL78M8+Ylj1dWhpq5l14KTaz9+4ele/f4YhapjxI3KUhLloRf1CtXhu3EL28RKU6lpaFW7YADQi3c66+HTgupvU4XLQoDdE+cCNttFxK4ffYJc6eqJk5yhRI3KTgrV4Zeo++/H7ZbtoSLLkqO6SQi+SGTXp6bYttt4eSTw6wps2eHJG7GDFi7NnnO55/D00+HpWvX0Oy6115w113Jd2Q7d04fo3qeSjYpcZOCsn59qFmbMiVsm8F554V3V0REUrVoESa179s3zGH87rvhndiZM8PvkoTFi8NwIy+8AFtuCbvvHpaDDmpV981FskSJmxQM91CzNjGlH/Of/qSaNhFpWGlpeAd2331DzdvMmfDWWzBrFqxZkzxv5Ur4z3/CMnbsgfTsGZK4vn3DbCytlMtJlilxk4Lxs5/BX1MmP7vqqtA5IVvNLSJSmFq3hgEDwrJ+fejoNGNGSOa+/jp5nrvx8cfw8cfhH8ZWrcI4kRUVYdqtffetOauDSFPQt5TkPfcw8OZttyX3XXQRXH99fDGJSGFo1SrZNDp8OCxYEJpUZ82CuXO9xmT369eHd2t//vOwveWWsP/+oUf7wQeH9SKel12aiBI3yWvr1sH3vx9mRkg46SS48071AhORptWiBfTsGZbjjoPWrV/j3/8+mPfeC7VyixbVPH/lSnjxxbAAlJTAt78N++0Xxo4bODA0sZaUNH9ZJH8pcZO8tXgxHHhgcuJ4gJ13hiOOgPvuiy8uESkOW25ZRb9+0C+az6eiIvRSra6Gf/4TPv205vkbNoQm1xkzYPTosK9du9Ckus8+yY99+6qJVeqmbw3JS++9ByecEKawSdh/fzjrLL0cLCLx6Nw5jBOXGA7kk0/gtdfg1VfDx5kzw6sdqSorw8wOr7yS3Ne6NeyxR6idS13KytSSIErcJA/9/e9wzjmwfHnYNgvNo8cco19qIpI7Es2qw4eH7WXLwuwNb7yRXL74YuPr1q4N502fXnN/ly6hNm7XXcOSWO/ZUzV0xURfaskb8+fDD38YEreE1q3hggvC4JgiIrmgoZ7sXbqEeVLdYeFCePPNsLz1VlhqN7EmLFkSau9efbXm/lat4FvfCj1a+/QJS+/eYenVC9q0aZJiSY5Q4iY5b82a0GP0pptqjqfUowece64G1xWR/GQG228flhNPTO5fvBjeeScs776b/FhZmf4+69eHd+tmz05/vFu3kMTtsEOyFrBHj/Bx++2hUye1VuQTJW6Ss6qqQu3az34GH31U89j558Mtt8CTT8YTm4hItnTtCoMHhyWhujoMRfLf/4YhR95/P6zPnp2+uTXVZ5+F5bXX0h/fYgvo3j25dOsWpgXbdtswZ2tivWPH5HRfEh8lbhKL+poSKipCU8Bbb4VfNqn22QfuuCO8ACwikq8yGRg8dc7T1KFIjj665nm33w5ffRWGI/nyy7C+eHFoWq2o2LhDRG2rV8OcOWGpT8uWsPXWsM020KrVnuy8c0gyay+dOyeXtm03rzavsZ+nYqDETXJCZWX4z3HKlNAsUPsXTceOcOONcMklGvNIRCRVmzah6TPdayMbNoTkLZHE1V6+/jp0hshEVRV8/nlYoDPTpjV8TWlpaIrt1Cn8Hk9dttoKOnRIfuzQAdq3T35s3z68HlNaqpq+VErcpNm5w4oVoflz9uwwcOWCBenPLSsLnQ+uvDL8pyciIpkrKQm/O+v6/ekekqOlS+Ggg0JniS++CMlZ4uPnn4favERP/sZYty7UAn755eaVo7Q0dEZr3TokqqWlyX3//GeYpaJt27BssUXyY+rSpk3yY+qSuGfi/rleOZDVxM3MhgB/AkqAe9z95lrHWwN/BfoBS4DT3H1+dOznwIXABuAKd5+UyT0lXomkLFFNv3hxWObNCwPlfvBBWFLn+0tn113h0ENhr71C9bzeZRORYtMc8yybJRObefPCvkQz5+671zx3/frQiWLRIpg8eSbduu35ze/4xYtDE21FRWhyXbUqzByxfn3TxLluXVhWrNj42NtvN80zElq0CH93ai8lJaEyYYstQme5uGQtcTOzEuAO4ChgATDVzCa4+3spp10ILHX3nczsdOAW4DQz2w04Hdgd6Aa8YGY7R9c0dM9mNWVKaMJbsmQPunSJK4rMpHvPoa597uFl2NT1DRtCVXlVVVhfvz78p7Z6NSxffiDr14f16urGx9aiRejxtOuu4f21srLG30NERLKnVatkk+yKFRUMGpT+vNSEc926kMStWhX+PiQ+rlwJe+4ZxrZbvjx8XLYsJGapy9Kl4R7Nqbo6mSjW9vnn8Q+vks0at4HAHHefC2Bm44ChQGqSNRT4VbQ+HviLmVm0f5y7rwXmmdmc6H5kcM9m9cUX8MwzAF3jCiFHlDbu7NLQc2nnnWGXXcL4Q3H/MIiISNNKNGl27LjxsUw6FYwZk0yk1q6tuSSSq4MOColg7eQw8TFRwZC6vnZtWF+zJrm+alWomGioM0dp4/7cNblsJm7dgdRhBBcA+9V1jrtXmdkyoEu0f0qta7tH6w3dEwAzGwEkvi0qzayOEW6aTFdgcZafkcsaVf5168KAuvPnw/PPZy2m5qKvvcpfrOUv5rJDEZb/kku+Wd3ssqfca7PceWfT3CdTy5fD4MFZ/9rvUNeBgu2c4O5jgGZ4QyAws2nu3r+5npdrirn8xVx2UPmLufzFXHYo7vIXc9kh3vJns4PtQiC1c/L20b6055hZS2ArQieFuq7N5J4iIiIiBSmbidtUoI+Z9TazzQX2pAAAB8lJREFUUkJngwm1zpkAnButDwNecneP9p9uZq3NrDfQB/hPhvcUERERKUhZayqN3lkbCUwiDN1xn7vPMrPrgGnuPgG4F3gw6nxQQUjEiM57nNDpoAr4gbtvAEh3z2yVoZGarVk2RxVz+Yu57KDyF3P5i7nsUNzlL+ayQ4zlN2+o+4SIiIiI5ARNIiEiIiKSJ5S4iYiIiOQJJW6NZGZDzGy2mc0xs1Fpjrc2s8ei42+YWa/mjzI7zKyHmf3TzN4zs1lm9j9pzhlkZsvMbEa0XBtHrNlgZvPN7J2oXBtNr2zB7dHXfqaZ7RtHnNlgZrukfE1nmNlyM/thrXMK6mtvZveZ2SIzezdlX2czm2xmH0YfO9Vx7bnROR+a2bnpzslldZT9NjP7b/S9/aSZpRlSteGfk3xQR/l/ZWYLU76/j6vj2nr/RuS6Osr+WEq555vZjDquLYSvfdq/czn1s+/uWjJcCB0iPgK+RZgq4G1gt1rnfB+4K1o/HXgs7ribsPzbAftG6+2BD9KUfxDwTNyxZqn884Gu9Rw/DngOMGB/4I24Y87S56EE+ALYoZC/9sChwL7Auyn7bgVGReujgFvSXNcZmBt97BStd4q7PE1Q9qOBltH6LenKHh2r9+ckH5Y6yv8r4CcNXNfg34hcX9KVvdbx3wHXFvDXPu3fuVz62VeNW+N8M42Xu68DElNupRoKPBCtjweOMDNrxhizxt0/d/c3o/UVwPskZ7SQ8LX/qwdTgI5mtl3cQWXBEcBH7v5x3IFkk7u/Qujtnir15/sB4KQ0lx4DTHb3CndfCkwGhmQt0CxIV3Z3f97dq6LNKYRxNAtSHV/7TGTyNyKn1Vf26G/ZqcCjzRpUM/r/7d1biFVVHMfx7w8VNBVJArMnsxtUeMOJNIsCGTJKKoqKoIsRGRn5oi+GhG8h9GIXSgshhCTLLmAYBREhpTSoGVkKBhU6WpBiSYX9e1jr0O7MOXPJOXNm7/P7wOEc114zay3XXmf/Z6+99+rnODdqxr4Dt6FptIxXfeDyn2W8gNoyXpWSp4DnAl802LxA0j5JH0i6akQr1loBfCjpS6Ul1eoNZv+ogntp/sVd1b6vmRYRR/PnY8C0Bnk6YT9YRjq73MhA46TMVuSp4teaTJVVve+vB3oj4lCT7ZXq+7rj3KgZ+w7cbMgkTQLeAlZGxKm6zT2kKbTZwAbgnZGuXwstioh5wBLgCUk3tLtCI03pwddLgTcbbK5y3/cRaW6k456nJGkN6fmaW5pkqeo4eQm4BJgDHCVNGXaa++j/bFtl+r6/41y7x74Dt6E5l2W8KkHSONLOvCUi3q7fHhGnIuJ0/rwDGCfpghGuZktExE/5/TiwnTQtUtQJS7ItAXoiord+Q5X7vqC3Nv2d3483yFPZ/UDSQ8CtwP354NXHIMZJKUVEb0ScjYi/gY00bleV+34scCewtVmeqvR9k+PcqBn7DtyG5lyW8Sq9fH3Dq8A3EfFckzwX1q7pk3QNaR8rfeAqaaKkybXPpAu1D9Rlew94QMm1wMnCqfWqaPoXd1X7vk5xfD8IvNsgz06gW9L5eTqtO6eVmqSbgdXA0oj4vUmewYyTUqq7XvUOGreryssyLgYORsSPjTZWpe/7Oc6NnrHf7js4yvYi3Tn4HenOoTU5bR3pywxgPGka6TBpfdWZ7a7zMLZ9Een08H5gb37dAiwHluc8K4CvSXdTfQ4sbHe9h6ntM3Ob9uX21fq+2HYBL+R94ytgfrvrPcz/BxNJgdiUQlpl+54UoB4F/iJdq/II6XrVj4FDwEfA1Jx3PrCp8LPL8nfAYeDhdrdlmNp+mHT9Tm3s1+6evwjYkT83HCdlezVp/+t5XO8nHcSn17c//7vPMaJMr0Ztz+mba2O9kLeKfd/sODdqxr6XvDIzMzMrCU+VmpmZmZWEAzczMzOzknDgZmZmZlYSDtzMzMzMSsKBm5mZmVlJOHAzs0qSdFbS3sJrhqRd5/D7Nku6q0n6kVxGj6QFTX5+naTF/7d8MzOAse2ugJlZi5yJiDl1aQtbVNaqiNgmqRt4GZhV3ChpTESsbVHZZtZBfMbNzDqGpNP5/UZJn0jaJumgpC2FVR/WStoj6YCkV2rpg/QpcGn+Pd9LelZSD3B38YydpC5JuyTtk7Rb0mRJYyStz2Xvl/TYMDffzCrAgZuZVdWEwjTp9gbb5wIrgStJT32/Lqc/HxFdEXE1MIG0Nudg3UZ6un7NLxExLyLeqCXkpZC2Ak9FxGzSUkJnSE/nPxkRXUAX8Kiki4dQtpl1AE+VmllVNZoqLdoded1FSXuBGcBnwE2SVgPnAVNJy/e8P0BZ6yU9DZwgBWA1jRbkvgI4GhF7ACLiVK5DNzCrcB3dFOAy4MgAZZtZB3HgZmad6o/C57PAWEnjgRdJ68z+IOkZ0vrDA1kVEdsapP82hPoIeDIiSr8gvZm1jqdKzcz+VQvSfpY0CehzF+kw+BaYLqkLIF/fNhbYCTwuaVxOv1zSxBaUb2Yl5jNuZmZZRPwqaSNwADgG7GlBGX9KugfYIGkC6fq2xcAm0nRtT74h4gRw+3CXb2blpohodx3MzMzMbBA8VWpmZmZWEg7czMzMzErCgZuZmZlZSThwMzMzMysJB25mZmZmJeHAzczMzKwkHLiZmZmZlcQ/oJg8RQI5ezUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import lognorm\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "nbins = min(100, int(1.5*np.sqrt(N)))\n",
    "plt.hist(Slog, bins=nbins, density=True, alpha=0.4, color='b');\n",
    "\n",
    "shape, loc, scale = lognorm.fit(Slog, floc=0)\n",
    "print(shape, loc, scale)\n",
    "x=np.linspace(0, max(Slog), 100) \n",
    "pdf_fitted = lognorm.pdf(x, shape, loc=loc, scale=scale) # fitted distribution\n",
    "plt.plot(x, pdf_fitted, 'b-', lw=3)\n",
    "plt.xlabel('Final Price')\n",
    "plt.ylabel('Probability');\n",
    "plt.title(get_symbol(symbol))\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KdytQjaeC_-F",
    "nbpages": {
     "level": 3,
     "link": "[7.2.5.3 Forecasting](https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.html#7.2.5.3-Forecasting)",
     "section": "7.2.5.3 Forecasting"
    },
    "pycharm": {}
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [7.1 Measuring Return](https://jckantor.github.io/CBE40455-2020/07.01-Measuring-Return.html) | [Contents](toc.html) | [7.3 Binomial Model for Pricing Options](https://jckantor.github.io/CBE40455-2020/07.03-Binomial-Model-for-Pricing-Options.html) ><p><a href=\"https://colab.research.google.com/github/jckantor/CBE40455-2020/blob/master/docs/07.02-Geometric-Brownian-Motion.ipynb\"> <img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open in Google Colaboratory\"></a><p><a href=\"https://jckantor.github.io/CBE40455-2020/07.02-Geometric-Brownian-Motion.ipynb\"> <img align=\"left\" src=\"https://img.shields.io/badge/Github-Download-blue.svg\" alt=\"Download\" title=\"Download Notebook\"></a>"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "07.02-Geometric-Brownian-Motion.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
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