{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Case1-3: モンテカルロ・シミュレーションをPythonで実装\n",
    "Implement Monte-Carlo Simulation in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-09-17T13:46:45.425234",
     "start_time": "2016-09-17T13:46:44.040168"
    },
    "collapsed": false,
    "hide_input": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-09-17T13:46:45.431169",
     "start_time": "2016-09-17T13:46:45.427205"
    },
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "s, t, r, sigma = 1000, 30 / 365.0, 0.001, 0.2\n",
    "path_of_monte_carlo = 50000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 次の確率微分方程式にしたがう確率過程 Stを求める([幾何ブラウン運動](https://ja.wikipedia.org/wiki/幾何ブラウン運動 \"Wikipedia\"))  \n",
    "it satisfies the following stochastic differential equation  \n",
    "$$dS_t = \\mu S_t\\,dt + \\sigma S_t\\,dB_t$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-09-17T13:46:45.458169",
     "start_time": "2016-09-17T13:46:45.438170"
    },
    "code_folding": [],
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def future_stock_price(s, r, sigma, t):\n",
    "    return s*np.exp(np.random.normal((r - 0.5 * np.power(sigma, 2)) * t, sigma * np.sqrt(t)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 上記の関数を50000回実行\n",
    "run 50000 times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-09-17T13:46:45.960171",
     "start_time": "2016-09-17T13:46:45.462169"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 580 ms, sys: 0 ns, total: 580 ms\n",
      "Wall time: 578 ms\n"
     ]
    }
   ],
   "source": [
    "%time stock_price_results = [future_stock_price(s, r, sigma, t) for _ in range(path_of_monte_carlo)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ヒストグラムを表示\n",
    "plot histgram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2016-09-17T13:46:46.642172",
     "start_time": "2016-09-17T13:46:45.963174"
    },
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 250 ms, sys: 0 ns, total: 250 ms\n",
      "Wall time: 260 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f5750dad2e8>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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t392hzLdPmWM9gSPyVktud3ESKwMw0hF8AQCW03+/ZgCIB9b4AgAAwBYIvgAA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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5742c70cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%time pd.Series(stock_price_results).hist(bins=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  },
  "nav_menu": {},
  "toc": {
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": true,
   "threshold": 6,
   "toc_cell": false,
   "toc_section_display": "block",
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}