MonteCarlo - Black-Scholes-Merton.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas_datareader import data as wb\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "d_1 = \\frac{\\ln(\\frac{S}{K}) + (r + \\frac{stdev^2}{2})t}{s \\cdot \\sqrt{t}}\n",
    "$$\n",
    "\n",
    "$$\n",
    "d_2 = d_1 - s \\cdot \\sqrt{t} = \\frac{\\ln(\\frac{S}{K}) + (r - \\frac{stdev^2}{2})t}{s \\cdot \\sqrt{t}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def d1(S, K, r, stdev, T):\n",
    "    return (np.log(S / K) + (r + stdev ** 2 / 2) * T) / (stdev * np.sqrt(T))\n",
    " \n",
    "def d2(S, K, r, stdev, T):\n",
    "    return (np.log(S / K) + (r - stdev ** 2 / 2) * T) / (stdev * np.sqrt(T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "norm.cdf(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "norm.cdf(0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "norm.cdf(0.75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "norm.cdf(9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\textbf{C} = SN(d_1) - Ke^{-rt}N(d_2) \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def BSM(S, K, r, stdev, T):\n",
    "        return (S * norm.cdf(d1(S, K, r, stdev, T))) - (K * np.exp(-r * T) * norm.cdf(d2(S, K, r, stdev, T)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ticker = 'PG'  \n",
    "data = pd.DataFrame()  \n",
    "data[ticker] = wb.DataReader(ticker, data_source='iex', start='2015-1-1', end='2017-3-21')['close']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "S = data.iloc[-1]\n",
    "S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_returns = np.log(1 + data.pct_change())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "stdev = log_returns.std() * 250 ** 0.5\n",
    "stdev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = 0.025\n",
    "K = 110.0\n",
    "T = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "d1(S, K, r, stdev, T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "d2(S, K, r, stdev, T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "BSM(S, K, r, stdev, T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}