{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Content under Creative Commons Attribution license CC-BY 4.0, code under MIT license (c)2015 C.M. Roberts."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Option Valuation using Numerical Methods:\n",
    "## A Python Programming Approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "There are many different kinds of assets traded in modern financial markets, nearly all falling within one of the five main categories of stock, bond, commodity, currency, or derivative.  Most folks have a basic understanding of stocks (equity in a business) and bonds (financial contracts issued by the government), and those who are more economically savvy may also be familiar with the trade of commodities (goods such as gold, oil, or grain) and currencies (investments in money, both foreign and domestic).  However, few individuals outside of the financial and academic worlds know much about derivatives.  A derivative is a financial instrument whose value is derived from some other asset such as a stock or commodity. In his excellent book, <em>In Pursuit of the Unknown: 17 Equations That Changed the World</em>, the English mathematician, Ian Stewart, states, \n",
    "<br><br>\n",
    "<em style=\"text-align: center;\">“Since the turn of the century the greatest source of growth in the financial sector has been in financial instruments known as derivatives.  Derivatives are not money, nor are they investments in stocks or shares.  They are investments in investments, promises about promises… This is finance in cloud cuckoo land, yet it has become the standard practice of the world’s banking system.”</em>\n",
    "<br><br>\n",
    "Mr. Stewart certainly has a rather sour view on derivatives, but his words also help describe their importance in today’s financial landscape.  One simply can not make it in the financial world without a firm understanding of derivatives and their qualities. \n",
    "In this module,  we will learn about some basic derivatives, how they can be characterized mathematically, and how their value can be estimated using different numerical schemes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Keeping Our Options Open\n",
    "\n",
    "Perhaps the most common derivative is the option, in which the owner of the option has the right to <em>buy </em>the underlying asset at a specific price by some specified date (this is called a <strong>call</strong>) or else the owner has the right to <em>sell</em> the underlying asset at a specific price and date (this is called a <strong>put</strong>).  The price specified in the option contract is called the strike price and the date is simply referred to as the expiration date.  For the time being, we will consider only European options, a style of option whereby the owner may only exercise the option (that is, buy or sell the underlying asset) at the expiration date and no sooner.  Letting $K$ be the strike price and $S$ be the value of the underlying asset, the payoff $V$ of an option at expiration time can be characterized as\n",
    "\n",
    "$$V_{call} =  \\textrm{max}(S - K, 0)$$\n",
    "$$V_{put} =  \\textrm{max}(0, K - S)$$\n",
    "\n",
    "The payoffs are described this way because if the owner does not stand to make money by exercising the option, they will opt to simply let it expire and may choose to buy or sell the asset at the market price, $S$, thereby having a payoff of $0. <br><br>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us put ourselves in the shoes of a trader who is considering whether or not to buy (and thus become the owner of) a certain option.  We know the terms of the contract, that is the strike price and time of expiration.  We also know some facts about the current state of the market including the present value of the asset, the risk-free interest rate (i.e. how much interest money would accrue sitting in a bank), and the level of volatility in the market.  Knowing all of this, what can we calculate to be the fair price of the option? <br>\n",
    "\n",
    "As it turns out, this is no simple task. Luckily for us, in 1973 two economists named Fischer Black and Myron Scholes (with the help of a third economist, Robert Merton) derived an equation describing the price of an option over time.  The equation is\n",
    "\n",
    "$$\\frac{\\partial V}{\\partial t} + \\frac{1}{2}\\sigma^2S^2\\frac{\\partial^2V}{\\partial S^2} + rS\\frac{\\partial V}{\\partial S} - rV = 0$$\n",
    "\n",
    "where $t$ is time, $\\sigma$ is volatility, and $r$ is the risk-free interest rate.  This is pretty exciting stuff and the group was awarded the Nobel Prize in Economics in 1997 for their work.  For our purposes, we must note that the Black-Scholes equation has an analytic solution for European puts and calls, called the Black-Scholes formula and it is as follows:\n",
    "\n",
    "\n",
    "$$V(S,t) = \\epsilon S\\Phi(\\epsilon d1) - \\epsilon Ke^{-r(T-t)}\\Phi(\\epsilon d2)$$\n",
    "where $$ d1 = \\frac{\\ln(S/K)+(T-t)(r+\\sigma^2/2)}{\\sigma\\sqrt{T-t}}$$<br>\n",
    "$$ d2 = \\frac{\\ln(S/K)+(T-t)(r-\\sigma^2/2)}{\\sigma\\sqrt{T-t}}$$<br>\n",
    "$$\\Phi(\\zeta) = \\frac{1}{2\\pi}\\int_{-\\infty}^\\zeta e^{-\\eta^2/2}d\\eta $$<br>\n",
    "$$\\epsilon = \\bigg\\{{1 \\textrm{     for a call} \\atop -1 \\textrm{     for a put}} $$\n",
    "\n",
    "Here, $T$ is the time of expiration and $V(S,t)$ is the value of the option at any time $t$. Armed with this formula, let us return to the issue at hand: valuing an option.  Let us suppose that we know the option has a strike price $K = \\$40$, expiration $T = 0.5 \\textrm{ years}$, and we know the market has a risk-free interest rate $r = 0.1$ and a volatility $\\sigma = 0.25$.  Using Python and the Black-Scholes formula, the fair price for the option can be calculated for a range of possible current asset prices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Import necessary libraries and functions\n",
    "import numpy as np\n",
    "from scipy.stats import norm #Phi() is the normal CDF\n",
    "\n",
    "#Allow plots in notebook and format plots\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as pyplot\n",
    "from matplotlib import rcParams\n",
    "rcParams['figure.dpi'] = 100\n",
    "rcParams['font.size'] = 16\n",
    "rcParams['font.family'] = 'StixGeneral'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def bs_formula(type, S, K, T, r, sigma):\n",
    "    \"\"\"Computes price of European call or put using the Black-Scholes formula\n",
    "    \n",
    "    Parameters:\n",
    "    ----------\n",
    "    type: string\n",
    "        Type of option;\"C\" for a call or \"P\" for a put\n",
    "    S: array of float\n",
    "        Initial asset price or an array of initial asset prices\n",
    "    K: float\n",
    "        Strike price\n",
    "    T: float\n",
    "        Expiration time\n",
    "    r: float\n",
    "        risk-free interest rate, expressed between 0 and 1\n",
    "    sigma: float\n",
    "        market volatility, expressed between 0 and 1\n",
    "    \n",
    "    Returns:\n",
    "    -------\n",
    "    V: array of float\n",
    "        Initial option value or an arrat of initial option values\n",
    "    \"\"\"\n",
    "    \n",
    "    \n",
    "    if type == \"C\":\n",
    "        eps = 1\n",
    "    elif type == \"P\":\n",
    "        eps = -1\n",
    "    d1 = (np.log(S/K) + T*(r + 0.5*sigma**2))/(sigma*np.sqrt(T))\n",
    "    d2 = (np.log(S/K) + T*(r - 0.5*sigma**2))/(sigma*np.sqrt(T))\n",
    "    V = eps*S*norm.cdf(eps*d1) - eps*K*np.exp(-r*T)*norm.cdf(eps*d2)\n",
    "    V = np.clip(V, 0, np.inf)\n",
    "    return V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Parameters\n",
    "K = 40 #strike price\n",
    "T = 0.5 #expiration time\n",
    "r = 0.1 #interest rate\n",
    "sigma = 0.25 #volatility\n",
    "\n",
    "S = np.linspace(1, 100,100) #array of possible current asset prices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we have defined a function that can value a European option, let's go ahead and apply it.  We will assume an initial asset price of \\$45."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exact value of European call given initial asset price of $45 is $7.620\n",
      "Exact value of European put given initial asset price of $45 is $0.669\n"
     ]
    }
   ],
   "source": [
    "V_call = bs_formula(\"C\", S, K, T, r, sigma)\n",
    "print(\"Exact value of European call given initial asset price of $45 is $%.3f\" %V_call[44])\n",
    "V_put = bs_formula(\"P\", S, K, T, r, sigma)\n",
    "print(\"Exact value of European put given initial asset price of $45 is $%.3f\" %V_put[44])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great!  We have our result.  In fact, we calculated a whole array of results, each one based upon a different initial asset price.  If we graph all of these results, we may gain a better understanding of how European options function and how calls and puts differ in their payoffs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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IJDiemjoGZPg5pjSwIQAbDcNIIFThwQfhpZdMbzzc5Bo8ROQeoD5wsaeWlS/l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\nlcdTtALuV9UlqrpcVQfgiix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spPrE55Hq50LTpq6z48CBSJtsGAmDpa2MqOLYMfjiC6ch\n/vHHcPSoa69f39WiuukmSBJ1RaqGD3c7HT7sdipSBK6/3glTtW5tMwINIwtx2+chIsWAQcAqoARQ\nGeinqieJQVjwiB9U3Ujd9993y8aNrr1AAVdS5J57XCUTvyXT//zTDekdP97VVs+kQAFXLvfaa93S\nsCGcdlo4vo5hRC3xHDymA0tU9TnP+lPAeara2c++Fjw8pKSkkJycHGkzAiI93b08fPaZW1at8m6r\nUgXuuMMV4q1cOe/nTJk0ieSdO+HTT50gVeZrC0Dx4k5T5O9/d5qz9etD2bLB+0JRRizeE6HCfOEl\nmMEjah7FROQq4Aagr0/zeOA3EXlaVVf5P9JITU2N+j+OAwdcFZLFi92s78WLT+yiKF0a2raFf/4T\nrrrKDb8NlNQ//iD5gQegVy/3RpKS4mpmzZ3r5o3Mm+eWTCpWdJNELrrITU2vWdPV3ipZ8pS/b6SJ\nhXsiXJgvQkPUBA8gGTisqr9lNqjqGhE5ArTApbIMP+zduzfSJhwnLc1pZ/z2G/z6K6xc6UpYrVzp\n+jN8ueAC1zXRpo17GTjVrNIJfjjzTNdBctNNbn3bNveqs2SJ+/fHH2HLFrfMmHHiiUqWhHPPdUvl\nynDOOW6pUAHOPtstpUtH9fT1aLonIo35IjREU/A4B9jjp303UC28piQWx45BRobL8mRkuLJShw+7\nfw8dcgEhLc29Kfz5p3fZuRO2b3fLli2ur2LnTv/XOO00Nxfjssvc4Kirrz6l+oeBU76860i/5Ra3\nfuwYrFnjSsSvXOmNdKtWwd69rv2HH7I/n4gLUKVLu5mJZ57pprifcYZLkRUr5l2KFvUuRYo4md7C\nhd1SsKBbChVyTjrtNBeUMv/1XZKSvP9mLiLexXfdMEJMNAWPw0C6n/YkwO9fw65dUK1aKE2KflTh\n0KH1vPii/22Z3UKZn32XY8dOfhs4VQoVcg/rF1zgzQLVq+cCR5Eiwb1WVtavX5/3nZOS4Pzz3eKL\nqouG69a55Y8/vMv//ue27djhbr69e90ShawHN+XeN7jAyf/m9Dm3bdntl1fCFOTWHzwIw4aF5VqJ\nRNR0mIvIg8ATqnpmlvZDQH9VfSVLe3QYbhiGEUPE3WgrEakFLAeqqupmT1tN4BegpnWYG4ZhRA9R\nM8NcVVcCc4BOPs3tgJkWOAzDMKKLqHnzABCRM4ChwFpcYKuOmyS4L6KGGUaUIyKFgY5AeeA34FOb\nCJWYiEh5Vd0W8uvE0v0VyAz0eMOTwnsFuBzYD3wIPKKqGQnulzrAV5l9ZYnoCxG5DDcn6lVVHe7T\nnlC+EJGqQG9gNS6I1gDuV9U/E8EXIvJ34BHgHFVt4NOe43fPr2+iJm2VRyYCO1V1hKoOBXYCoyJs\nU8jxvJE9AzwNXAW8CzwIPObZZRKJ6ZeyuDfV4j7NCXWPiMglwALgOd/A4SGhfIH7vpNUdZSqPgts\nAp73bIvrvxFPAFiDG0Gb9Xc9t/sgf/eJqsbEgvvRPAZc4NNWAzgKnB9p+0L83TsCFbK0LQYWAY0S\n0S9AIeBF4HogI1HvESAV+MJPeyL64i+glc96H+CjRPobAcYCy/J6H5zKfRJLbx7J+JmBDmTOQI9b\nVPVDVd2apXkL7kmjKYnpl6eAF4BDPm0J5QsRuRy4GDggIiNEZJmILBaR+iTm38t4YKSIXCki1YEb\ncfdJQt0XWUgm5++e2/ZsiaZJgrlhM9A9iIgA9YB/4HK8CeUXEbkfmKCq2z1DvDOpSGL5oiGgwLOq\nugRARN4GZgBTSCxfANwLFAW+BNYBjVV1q4gk8m9Hbt/99Fy2Z0ssvXkEPAM9jrkbeFlVfybB/CIi\nNwMbVPXHzCafzUdIIF8AxYBDmYHDw4tAWeAKEssXAGfiUjAP4X4UvxORi0mwv5Es5Pbd8+2bWAoe\nmwB/5U5LAxvCbEvEEJHGQGFVHeFpSjS/3AN8ICJpIpIGzALwfL6TxPLFZqCIiPhWaFzr+fc9EssX\nANOB6ar6ElAH97cxGeenRPNFJrn9PuT79yOWgscMoLiIVMps8AxfLejZFveISCPgb6r6qk/zXBLI\nL6p6raqenrngOszxfG5IAvkCWAhkALV92k7HpbKWkkC+EJEyuGHsywFUdTfwAK7z9xsSyBdZyOl3\nc3ou23P0TcwED03wGegi0gxoBSwWkQs8S1vciImE9YsviXaPqOoWYALujSuT64HvVfVLEssXu3AD\nSK7waT4dWK2qi0kcX5ygE5DL38TqU/mbibVJggk5A11EmgKfA1nr0u7FdYgVxo1nTyi/AIjI1cAC\nVS3gWU+oe0REigPDcMNUd+AeJgZ6OorPJIHuCxE5D3gWWIn726gFDFPV1fHuCxEpArTGTSQ+A9cv\nOldVd+b23fP7NxNTwcMwDMOIDmImbWUYhmFEDxY8DMMwjICx4GEYhmEEjAUPwzAMI2AseBiGYRgB\nY1C74kwAAAc8SURBVMHDMAzDCBgLHoZhGEbAWPAwYhoRKeiZKJjwiEhZEakbhuuUzuN+RUTk9FDb\nY0QGCx5GwIhIIxEZLSLHRGSliPwrS3G+7I67TEQ2i0jlU9nHZ9+6wEyckl5eba8hIu/kdf9QIiJN\nRWSFx4/v+5aXF5ECHr8eFJHXPLOEczpXR5z86v0htrkl0Nxnva2IfCki74nI157vMtOz+TDQ1VPZ\n1ogzLHgYAaOqX+Ej76mq41Q1Iw+HrsKVDN+e2SAiNUXkxpz2ycGOH4H382y44yGgo4hUCfC4fCEi\nD2e3TVUXAv/EFTI84qkzlLktA/gM+FFV71XVP3O6jqp+iFMVDBki8g/gclWd6FmvAXwIPKCqnVX1\n70BnoILHJlUnjdtbRM4NpW1G+LHgYeSXTA2Ao3k9QFX3qOrLqnoYwFPJ8zOgVHb75IFjeb2+iJwF\nlMHVgeqX1+Pyi4jcDgzOaR9V/R6YBnQQkQpZNncBXgvgknn2RaB4AsUQXO2oTOrhBOWKZjao6gfA\n11kOHwRM9oiYGXGCBQ8jKIhIRRF50ZOGuUZE5ovILhHp47NPdRHpKyIXeJquAc4DbhSRR7LZBxHp\nLSKDRKS7iEzzlIzOD/fgpGvfArqJSFk/3+N+EblTRHqJyFZP0Tg832mAiHQWkf8TkTae9gIi8qiI\nPCMic0TkIxEp7ukXuMXtIgNE5IYc7BqEK275oI8dgqtuOtGn7UwReVNE7hKRp0Xkrex+kEWkgYhs\nE5ExnvVLRORHEVngs8/5IjJERIaJyPci0jMHGx8AUlTV92HhO9xDxCQRucmn/SnfA1V1M+63pkMO\n5zdijXALtNsSHwtQFfek+4RPW0/cj8m1nvW+QBpOG6A0LmV0DGjic8wx4A7P55P2AcrjNCsu9KwP\nxaXKMo//F5CRB3uLAJM9nyvgtM+fy7JPCZwkZ5JnvQNwhufzd0ADz+dzgJaez08BzTyfC+HSba8F\nYptn31nAPqCUZ7018HSWfR4BvvVZ3wa08llfCIzJYX0srgIxnv+TmcBpnvVbPH6vn41924Deftpv\nALZ4jk0BLs7m+DHA1Ejft7YEb7E3DyOYHMT98M71rP+Ae6Iup06cZ1JOB/vbR1W34bSoV3hSJzVw\nQSZQugLjPOfcisvV9xaRElns/wv43JOjn6DestSrgfdF5GpV/QP3wwvuifwyEekP9MH9gBbKh32D\ngOJ4O7x7AW9m2ectoLOIJInINbin+fz4AlxwOhvo67G9LjAP91BwAp4RU2fjdK1PQFVn4ikDD1wK\nfC8i//Zzvd2AdZzHEadF2gAjrsnMwZ/qQ8pREXkJ+BT4GQhoaK4ntdMNWC4it3iaS+F0D3rhUlmo\n6lERuRYXWFYCL4rIE6p6DOgOvA0sFJGPgZ4ikoR7W3lFVQ+eyhdU1cUi8iXwbxGZDvzpCXK+7MF1\nSP8DeBc4QP41uM/DCSW9kId9M0d6ndC/JSIFVDVDVQ8Az4nI+7ig+pKILFDVFT67H8J+b+IKe/Mw\nohoRaYB7mh+kqovyeZpbcOmbrqrazbPcDHwBPCAihTzXKgbsVNVLgbuAe3FpNICzVLU90Ainjz0e\n9zSdATTLYnNdyd/8hkG4N4mpwOt+tv8XaK6qg9X1IwSKb6DZDjQSkYIn7OCkjrOyAzfsNutbzjDf\nFVVdDzyO+12pkWXfksD6gC02ohYLHkZ+Kez51/fHJ+tcj9NwP1iSZbvvfXcAKCcip3lGQ2XdJ9lz\nnoKeH/kGQCnxzivJcX6J562jD/COn80v4fpU7vasn4ULGqjqeM8xmU/dj3javwYGAGeqG077MTBK\nRFqLm6TXEuisqmnAfo8NZ/sZSXUSnnTfUmCrqi7xs8u1eHwpIn8DygKlfXyRxIkBYgdwkbiJlBVw\nQS8zTTfD83mKiNQSkQoi8jROujWrXUdxgbZ6lk2FxM1B8f3/PA/YCXyVZd9KgL/vZMQqke50sSX2\nFuAyYBTuqXsFrmP5HGCKp60LLiU01rP+OO7H42nP+ptARc+5/oP7kXsRKJd1H9yP0Urgf55r3oqT\nGP0PUBuY7dn/bqBYFjtLAiNw6Z52WbaV8tiVAewC2v9/e/erEkEUBWD8uwaTRus+gcVk2WJXDAsW\nQQzCgsU3EHwCk2jYIoJd8C0UBFHYpGAxWuzXcC6sLChzQFlYvh9Mmbkz9w8Dh7nnXoaY7/8Ejokc\nyQWThPlLq38POKMlhttzrlof3onfgC5+q/+JyP3sdBzbTWD/h2uHre8PwBAYAa/ABrEy6wN4Bvqt\n/BowBt6IZbYnwDWTxQh94I7I8zwCg1/atQXcT507auM3Bs5be26B1alyC8SXTm/W767H3x3+hlZS\nJyV25l/W2NyYue8AWK61nv5LwzQTTltJ6moI7GZ255dS1oEVA8f88ctDUkopZbvWetOh3BIxvWeu\nYw4ZPCRJaU5bSZLSDB6SpDSDhyQpzeAhSUozeEiS0gwekqS0L/vFiNyPV5BgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x72b9b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(S,V_call,color='blue', lw=2, label=\"European Call\")\n",
    "pyplot.plot(S,V_put,color='red', lw=2, label=\"European Put\")\n",
    "pyplot.xlabel('Initial Asset Value (S)')\n",
    "pyplot.ylabel('Value of Option (V)')\n",
    "pyplot.grid()\n",
    "pyplot.legend(loc='upper left',prop={'size':15});\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## No solution? There's a solution for that!\n",
    "\n",
    "The Black-Scholes formula is a godsend, but sometimes it doesn't work.  One such case is when volatility is not constant over the lifetime of an option. In such an instance, the Black-Scholes equation (recall the difference between the <em>equation</em> and the <em>formula</em>) still applies, but a neat, analytic solution just doesn't exist.  To value an option under these circumstances, we have to use a numerical scheme which will provide an estimate of the option's value.  Several numerical schemes exist that are capable of doing this, but here we choose to focus on the Crank-Nicolson method due to its accuracy and stability.\n",
    "\n",
    "To implement the Crank-Nicolson scheme, we first construct a two-dimensional grid of asset price versus time and we then discretize the Black-Scholes equation using a forward difference in time and central difference in asset price. A key feature of the Crank-Nicolson method is that for asset price, we actually average the central difference of the current time step with the central difference of the next time step.  This approach yields the following terms: \n",
    "\n",
    "$$\\frac{\\partial V}{\\partial t} \\approx \\frac{V^{n+1}_m - V^{n}_m }{\\Delta t}$$\n",
    "\n",
    "$$\\frac{\\partial V}{\\partial S} \\approx \\frac{V^{n}_{m+1} - V^{n}_{m-1} + V^{n+1}_{m+1} - V^{n+1}_{m-1}}{4 \\Delta S}$$\n",
    "\n",
    "$$ \\frac{\\partial^2 V}{\\partial S^2} \\approx \\frac{V^{n}_{m+1} - 2 V^{n}_{m} + V^{n}_{m-1} + V^{n+1}_{m+1} - 2 V^{n+1}_{m} + V^{n+1}_{m-1}}{2 \\Delta S^2}$$\n",
    "\n",
    "where $n$ is the index in time and $m$ is the index in asset price.  By taking into account that $S = m\\Delta S$, substituting the above terms into the Black-Scholes equation, and then separating those terms which are known (with time index $n$) from those that are unknown (with time index $n+1$), we get \n",
    "\n",
    "$$\\frac{\\Delta t}{4}(rm - \\sigma^2m^2)V^{n+1}_{m-1} + (1 + \\frac{\\Delta t}{2}(r + \\sigma^2m^2))V^{n+1}_{m} + (-\\frac{\\Delta t}{4}(rm + \\sigma^2m^2))V^{n+1}_{m+1} = \\\\ \\frac{\\Delta t}{4}(-rm + \\sigma^2m^2)V^{n}_{m-1} + (1 + \\frac{\\Delta t}{2}(r + \\sigma^2m^2))V^{n}_{m} + (\\frac{\\Delta t}{4}(rm + \\sigma^2m^2))V^{n}_{m+1}$$ \n",
    "\n",
    "or, if we define $a = \\frac{\\Delta t}{4}(rm - \\sigma^2m^2)$, $b = \\frac{\\Delta t}{2}(r + \\sigma^2m^2)$, and $c = -\\frac{\\Delta t}{4}(rm + \\sigma^2m^2)$, we get \n",
    "\n",
    "$$ aV^{n+1}_{m-1} + (1+b)V^{n+1}_{m} + cV^{n+1}_{m+1} = -aV^{n}_{m-1} + (1-b)V^{n}_{m} -cV^{n}_{m+1} $$\n",
    "\n",
    "which is a bit easier to handle.  This equation only takes into account one time step into the future and a total of three asset prices.  To solve for a number of asset prices at once, we can create a system of linear equations where each equation applies to a different subset of the set of asset prices (for example, if the first equation deals with $m-1$, $m$, and $m+1$, the second will deal with $m$, $m+1$, and $m+2$). Such a system will be in the form \n",
    "\n",
    "$$[A_1][V^{n+1}_{int}] = [A_2][V^{n}_{int}] + [B.C.] $$\n",
    "\n",
    "where $[B.C]$ is a column vector containing appropriate boundary conditions. To determine these boundary conditions, we first have to determine if we are valuing a call or put. If we are concerned with a call, we know the payoff is $V(S,t) = \\max(S - K, 0)$.  Given a set of asset prices ranging from $0$ to some $S_{max}$, we know that $V(0,t) = 0$.  This is our first of two boundary conditions. Our second boundary condition is derived from our knowledge that $V(S_{max},t) = S_{max} - K$.  Letting the largest possible asset price $S_{max}$ have the index $M$, we can arrive at the equation:\n",
    "\n",
    "$$ aV^{n+1}_{M-2} + (1+b)V^{n+1}_{M-1} + cV^{n+1}_{M} = -aV^{n}_{M-2} + (1-b)V^{n}_{M-1} -cV^{n}_{M} $$\n",
    "\n",
    "Substituting those terms having index $M$ with $S_{max} - K$ and once again moving all known values to the right side of the equation, we get\n",
    "\n",
    "$$ aV^{n+1}_{M-2} + (1+b)V^{n+1}_{M-1} = -aV^{n}_{M-2} + (1-b)V^{n}_{M-1} - 2c(S_{max} - K)$$\n",
    "\n",
    "Thus, $$ [B.C.] =  \\left[ \\begin{array}{c} 0 \\\\ \\vdots \\\\ \\\\ 0 \\\\ - 2c(S_{max} - K) \\end{array} \\right]$$ \n",
    "\n",
    "With $[B.C.]$ now determined and $[A_1]$ and $[A_2]$ easily determined from our discretization of the Black-Scholes equation, we can now construct a linear system of equations for a European call. Given a set of asset prices of size $M$, ranging from 0 to $S_{max}$, such a system can be characterized by\n",
    "\n",
    "$$ \\left[ \\begin{array}{cccccc} (1+b) & c & 0 & \\cdots & & 0 \\\\ a & (1+b) & c & 0 & \\cdots & 0 \\\\ 0 & & \\ddots & & & \\vdots \\\\ \\vdots & & & a & (1+b) & c  \\\\ 0 & \\cdots & & 0  & a & (1+b) \\end{array} \\right] \\left[ \\begin{array}{c}V^{n+1}_{1}\\\\V^{n+1}_{2}\\\\ \\vdots \\\\ V^{n+1}_{M-1}\\\\ V^{n+1}_{M} \\end{array} \\right] = \\\\ \\left[ \\begin{array}{cccccc} (1-b) & -c & 0 & \\cdots & & 0 \\\\ -a & (1-b) & -c & 0 & \\cdots & 0 \\\\ 0 & & \\ddots & & & \\vdots \\\\ \\vdots & & & -a & (1-b) & -c  \\\\ 0 & \\cdots & & 0  & -a & (1-b) \\end{array} \\right] \\left[ \\begin{array}{c}V^{n}_{1}\\\\V^{n}_{2}\\\\ \\vdots \\\\ V^{n}_{M-1}\\\\ V^{n}_{M} \\end{array} \\right] +  \\left[ \\begin{array}{c} 0 \\\\ \\vdots \\\\ \\\\ 0 \\\\ - 2c(S_{max} - K) \\end{array} \\right]$$\n",
    "\n",
    "This system applies only to one time step, so in order to succesfully value an option, we must solve this system repeatedly for each time step from the initial time to the time the option expires.  \n",
    "\n",
    "Now that we have derived the Crank-Nicolson scheme for valuing European calls, let's define a Python function to implement it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#import function to solve matrices\n",
    "from scipy.linalg import solve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cn_call(V, N, r, dt, sigma, S_max, K):\n",
    "    \"\"\"Solves for value of European call using Crank-Nicolson scheme\n",
    "    \n",
    "    Parameters:\n",
    "    ----------\n",
    "    V: array of float\n",
    "        option values if call expired immediately\n",
    "    N: integer\n",
    "        number of time steps\n",
    "    r: float\n",
    "        risk-free interest rate\n",
    "    dt: float\n",
    "        time step length\n",
    "    sigma: array of floats\n",
    "        volatility over asset lifetime\n",
    "    S_max: float\n",
    "        maxmum asset value\n",
    "    K: float\n",
    "        strike price\n",
    "        \n",
    "    Returns:\n",
    "    -------\n",
    "    Vn: array of float\n",
    "        option values given parameters\n",
    "    \"\"\"\n",
    "    \n",
    "    \n",
    "    M = np.shape(V)[0] - 1 #number of initial values\n",
    "    i = np.arange(1,M) #array of indexes\n",
    "    Vn = np.copy(V) \n",
    "    \n",
    "    for t in range(N):  \n",
    "        a = dt/4 * (r*i - sigma[t]**2*i**2)\n",
    "        b = dt/2 * (r + sigma[t]**2*i**2)\n",
    "        c = -dt/4 * (r*i + sigma[t]**2*i**2)\n",
    "        \n",
    "        #create LHS of Ax = b\n",
    "        A = np.diag(1+b) + np.diag(c[:-1], 1) + np.diag(a[1:],-1)\n",
    "        \n",
    "        #create RHS of Ax = b\n",
    "        B = np.diag(1-b) + np.diag(-c[:-1], 1) + np.diag(-a[1:],-1) #create matrix of RHS coefficients\n",
    "        B = np.dot(B,Vn[1:-1]) #multiply coeff's by current option values\n",
    "        B[-1] += -2*c[-1] * (S_max - K) #apply boundary condition\n",
    "        \n",
    "        #solve Ax = b\n",
    "        Vn[1:-1] = solve(A,B)\n",
    "    \n",
    "    return Vn\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Parameters\n",
    "N = 100 #number of time steps\n",
    "T = 0.5 #expiration time\n",
    "dt = T/N #timestep size\n",
    "K = 40 #strike price\n",
    "r = 0.1 #interest rate\n",
    "\n",
    "S_max = 4*K #arbitrary maximum asset value of four times strike price\n",
    "S = np.linspace(0, S_max, 161) #array of some possible current asset prices\n",
    "V0 = np.clip(S - K, 0, S_max-K) #initial payoff value of option\n",
    "\n",
    "#constant volatility of 0.25\n",
    "sigma_const = np.zeros(N)[:] + 0.25 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us proceed by computing option values for the same initial asset price as before using the Crank-Nicolson function we have just defined.  Then, we can graphically compare the Crank-Nicolson results to the analytic results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CN estimated value of European call given initial asset price of $45 is $7.616\n"
     ]
    }
   ],
   "source": [
    "#apply CN for constant volatility\n",
    "V_cn = cn_call(V0, N, r, dt, sigma_const, S_max, K)\n",
    "\n",
    "print(\"CN estimated value of European call given initial asset price of $45 is $%.3f\" %V_cn[45])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\croberts94\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:30: RuntimeWarning: divide by zero encountered in log\n",
      "C:\\Users\\croberts94\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:31: RuntimeWarning: divide by zero encountered in log\n"
     ]
    }
   ],
   "source": [
    "#recalculate analytic solution with new S array\n",
    "V_call = bs_formula(\"C\", S, K, T, r, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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3U0lgpw/Pb4wJRrt306T7C9y12VmsJCVY9sjP9LvlScRqLEEp0x76ItIPuB64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\nQhSOjIsQQojC+QF4/saaRiSyZAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x75acd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(S,V_cn,color='red', lw = 2,label='CN')\n",
    "pyplot.plot(S,V_call,color='green', ls='--', lw = 3, label='Analytic Solution')\n",
    "pyplot.xlabel('Initial Asset Value (S)')\n",
    "pyplot.ylabel('Value of Option (V)')\n",
    "pyplot.legend(loc='upper left',prop={'size':15});"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That looks pretty great! Clearly, some error exists, but we can get pretty near to the exact, analytic result using the Crank-Nicolson scheme. We will now move on to pricing an option under a non-constant volatility."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#volatilty stepping from 0.0 to 0.8\n",
    "sigma_step = np.zeros(N)\n",
    "sigma_step[int(N/2):]+= 0.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CN estimated value of European call given initial asset price of $45 is $10.616\n"
     ]
    }
   ],
   "source": [
    "#apply CN for  non-contstant volatility\n",
    "V_cn_step = cn_call(V0, N, r, dt, sigma_step, S_max, K)\n",
    "\n",
    "print(\"CN estimated value of European call given initial asset price of $45 is $%.3f\" %V_cn_step[45])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 35)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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F5CcROSMiHwM/AQ8qfAxFrwwvApwSkRMicj+ee2UbP/30Ew0bNmTw4MFs3LjR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\neS7EnQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x75bbc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(S,V_cn_step,color='blue', lw=2, label='CN, step-sigma')\n",
    "pyplot.plot(S,V_cn,color='red', lw = 2,label='CN, constant-sigma')\n",
    "pyplot.plot(S,V_call,color='green', ls='--', lw = 3, label='Analytic Solution')\n",
    "pyplot.xlabel('Initial Asset Value (S)')\n",
    "pyplot.ylabel('Value of Option (V)')\n",
    "pyplot.legend(loc='upper left',prop={'size':15});\n",
    "pyplot.xlim(20,70)\n",
    "pyplot.ylim(0,35)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well would you look at that.  Having a non-constant volatility can completely shift our valuation for an option!  Perhaps it's unrealistic to expect anyone to know precisely how market volatility will change over a given period of time (an old joke comes to mind about how weathermen and economists are the only people who can consistently be wrong and still keep their jobs), but the point is that as factors in the market change, the analytic solution starts to become irrelevant.  A strong numerical scheme such as the Crank-Nicolson method is an indispensable tool for traders in an ever-shifting financial landscape."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Life, Liberty, and the Freedom to Exercise Early\n",
    "\n",
    "So far, we have focused only on European options where the owner may exercise the option only at the time of expiration. We now move on to American options, a style in which the option can be exercised at any time during its lifetime.  It should be noted that these names merely denote the option style and have nothing to do with where these options are actually traded.<br>\n",
    "\n",
    "Due to the nature of American options, it is necessary to check at every time step for the possibility of early exercise, making a Black-Scholes approach insufficient. Instead, a popular method for tackling the valuation of American options is the binomial model, proposed by Cox, Ross, and Rubinstein in 1979.  In the binomial model, we start with the knowledge that over the course of one time step, the stock price $S$ can move up to some value $Su$ with probability $p$ or down to some value $Sd$ with probability $1-p$. For a call option, then, we can define the value of the option after one up-tick to be <br>\n",
    "\n",
    "$$V_u = \\max(Su - K,0)$$ <br>and the value after a down-tick to be <br>\n",
    "\n",
    "$$V_d = \\max(Sd - K,0)$$.\n",
    "\n",
    "Building from this, the current value of the option can be taken to be the expected value of its possible future values, discounted by the interest that would be accrued between now and said future values. This can be expressed as\n",
    "\n",
    "$$ V = e^{-rdt}[pV_u + (1-p)V_d] $$\n",
    "\n",
    "and we shall note here that \n",
    "\n",
    "$$ u = e^{\\sigma\\sqrt{dt}} $$ <br>\n",
    "$$ d = 1/u = e^{-\\sigma\\sqrt{dt}} $$ <br>\n",
    "$$p = \\frac{e^{rdt}-d}{u - d}$$\n",
    "\n",
    "We won't be troubled over the derivation of $u$,$d$, and $p$ for the purposes of this lesson, but the <a href=\"https://www.researchgate.net/profile/Stephen_Ross3/publication/4978679_Option_pricing_A_simplified_approach/links/09e4151363b7910ad9000000.pdf\">Cox, Ross, Rubenstein paper</a> is actually quite interesting and is worth the read.\n",
    "\n",
    "So at every time step, the value of the asset (and, correspondingly, the option) has the possibility of moving up or down.  Over the course of many time steps, the possibilities spread out, forming what is known as a binomial tree (pictured below).\n",
    "\n",
    "<img src=\"./figures/bintree.PNG\">\n",
    "<em style = \"text-align: left; font-size: 0.8em\">Image source: https://upload.wikimedia.org/wikipedia/commons/2/2e/Arbre_Binomial_Options_Reelles.png</em>\n",
    "\n",
    "Each box in the tree is referred to as a leaf.  The easiest and most common way of finding an option's value using the binomial method is to use given information to find the asset values at all of the final leaves (that is, the leaves existing at the time of expiration), and then working backwards towards a fair value for the option at the beginning of its lifetime. The first step is to use the time of expiration $T$, the number of time steps $N$, the risk-free interest rate $r$, and the market volatility $\\sigma$ (we once again assume this to be constant over the lifetime of the option) to find $u$,$d$, and $p$.  Next, we can express the leaves at the expiration time as a list of the form\n",
    "\n",
    "$$ S_0d^Nu^0,\\ S_0d^{N-1}u^1,\\ S_0d^{N-2}u^2,...,S_0d^2u^{N-2},\\ S_0d^1u^{N-1},\\ S_0d^0u^{N} $$\n",
    "\n",
    "where $S_0$ is the initial asset value.  Using the formulae mentioned earlier in this section, we can then use these final asset values to make a list of final option values. These final option values can then be used to determine the option values at the preceding time step, and then these option values can be used to solve for the previous option values, and so on and so forth until we have arrived at the initial value of the option. If the option is American, at each iteration we must also compare the value of holding the option longer versus the value of exercising it early.  If the option has a higher value if exercised early, then we assume that the owner of the option would do so and we replace the recursively calculated value at that leaf with the early exercise value. To perform this scheme using Python, we can write a function such as the one below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def binomial(type, S0, k, r, sigma, T, N ,american=\"false\"):\n",
    "    \"\"\" Computes option value for European or American options using the binomial method\n",
    "    \n",
    "    Paramters:\n",
    "    ---------\n",
    "    type: string\n",
    "        type of option; \"C\" for call, \"P\" for put\n",
    "    S0: float\n",
    "        initial asset price\n",
    "    k: float\n",
    "        strike price\n",
    "    r: float\n",
    "        risk-free interest rate\n",
    "    sigma:float\n",
    "        volatility\n",
    "    T: float\n",
    "        Expiration time\n",
    "    N: integer\n",
    "        number of time steps\n",
    "    american: string (Boolean input)\n",
    "        american=\"true\" for American option, american=\"false\" for European option \n",
    "    \n",
    "    Returns:\n",
    "    -------\n",
    "    V[0]: float\n",
    "        option value given parameters\n",
    "    \"\"\"\n",
    "    \n",
    "    dt = T/N #time step\n",
    "    u = np.exp(sigma * np.sqrt(dt))\n",
    "    d = 1/u\n",
    "    K = np.ones(N+1)*k #strike price array\n",
    "    p = (np.exp(r * dt) - d)/ (u - d)\n",
    "    V =  np.zeros(N+1) #initialize option value array\n",
    "    \n",
    "    #expiration asset prices (S)\n",
    "    S = np.asarray([(S0 * u**j * d**(N - j)) for j in range(N + 1)])  \n",
    "    \n",
    "    #expiration option values (V)\n",
    "    if type ==\"C\":\n",
    "        V = np.clip(S - K, 0, np.inf)\n",
    "    elif type ==\"P\":\n",
    "        V = np.clip(K - S, 0, np.inf)\n",
    "   \n",
    "    #calculate backwards the option prices\n",
    "    for i in range(N-1, -1, -1):\n",
    "        #Current Option Value: V = e^(-r*dt)(pVu + (1-p)Vd)\n",
    "        V[:-1]=np.exp(-r * dt) * (p * V[1:] + (1-p) * V[:-1])\n",
    "        #Current Assett Values\n",
    "        S[:-1] = S[:-1]*u\n",
    "\n",
    "        if american=='true':\n",
    "        #Check if current exercise value is greater than exercise at expiration. If so, exercise early.\n",
    "            if type ==\"C\":\n",
    "                V = np.maximum(V, S - K)\n",
    "            elif type ==\"P\":\n",
    "                V = np.maximum(V, K - S)\n",
    "    \n",
    "    #Return value of option at t=0\n",
    "    return V[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<em style=\"font-size: 0.8em\">Please note that while the above code is the original work of the author, it owes much of its overall structure to a code found <a href = \"http://gosmej1977.blogspot.be/2013/02/american-options.html\">here</a>. I would be remiss not to say thank you to one Julien Gosme for providing the framework for this code on his/her blog.</em>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now define our parameters once again and use the binomial function to estimate the value of different options."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Parameters\n",
    "N = 100 #number of time steps\n",
    "T = 0.5 #expiration time\n",
    "K = 40 #strike price\n",
    "r = 0.1 #interest rate\n",
    "sigma = 0.25 #volatility\n",
    "S0 = 45 #initial asset price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Given an initial asset price of $45:\n",
      "The value of a European Call is $7.623\n",
      "The value of a European Put is $0.672\n",
      "The value of an American Call is $7.623\n",
      "The value of an American Put is $0.723\n"
     ]
    }
   ],
   "source": [
    "print(\"Given an initial asset price of $45:\")\n",
    "V_bin_EC = binomial(\"C\", S0, K, r, sigma, T, N ,american=\"false\")\n",
    "print(\"The value of a European Call is $%.3f\" %V_bin_EC)\n",
    "V_bin_EC = binomial(\"P\", S0, K, r, sigma, T, N ,american=\"false\")\n",
    "print(\"The value of a European Put is $%.3f\" %V_bin_EC)\n",
    "V_bin_EC = binomial(\"C\", S0, K, r, sigma, T, N ,american=\"true\")\n",
    "print(\"The value of an American Call is $%.3f\" %V_bin_EC)\n",
    "V_bin_EC = binomial(\"P\", S0, K, r, sigma, T, N ,american=\"true\")\n",
    "print(\"The value of an American Put is $%.3f\" %V_bin_EC)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we compare our analytic values for a European call/put to those estimated above, we see that the binomial model does a pretty good job of estimating an option's value. Also, notice how the values for the European and American calls are identical, while the value of the American put is greater than its European counterpart. This is because under the assumptions of our model (i.e. no <a href=\"http://www.investopedia.com/terms/d/dividend.asp\">dividends</a> and no <a href=\"http://www.investopedia.com/terms/a/arbitrage.asp\">arbitrage</a>), it is never optimal for the owner of an American call to exercise early.  However, there do exist some circumstances where the owner of an American put would exercise early, thus raising its value compared to a plain old European put. For a mathematical proof of why this is the case, check out this <a href=\"http://www.math.nyu.edu/~cai/Courses/Derivatives/lecture8.pdf\">lecture outline</a> from NYU.\n",
    "\n",
    "Also, it may seem like we've wandered off pretty far from the realm of partial differential equations, but in fact we never left.  If we were to shorten the length of the time step used in the binomial model to an infinitesimally tiny size, effectively migrating from discrete to continuous time, we would observe that the binomial model <a href = \"http://www.bus.lsu.edu/academics/finance/faculty/dchance/Instructional/TN00-08.pdf\">converges to the Black-Scholes model</a> (for European options, at least).  We are still looking at the very same problem governed by the same PDE, but whereas the analytic and finite-difference (e.g. Crank-Nicolson) methods take a careful, highbrow approach, the binomial method trades elegance for elbow grease to get the job done.  It's the quintessential American way!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tokyo Royale\n",
    "\n",
    "Okay, so that title is a pretty lame joke, but it fits because what we are going to be looking at in this section is valuing an Asian option using the Monte Carlo method. Again, the name of the option has nothing to do with where it is traded, rather a couple of English financial analysts happened to be in Tokyo when they devised it.  The Asian option is different from other options because its payoff is derived from the average asset price over the option's lifetime, making it path-dependent. These options have an advantage of being less susceptible to volatility than European or American options, but they also pose a challenge for estimating their value, as there are a huge number of possible paths an asset's price can take over even a relatively small period of time.\n",
    "\n",
    "This challenge can be met using the Monte Carlo method, which owes its name to the fact that its underlying principle is akin to rolling a dice over and over, as in a casino.  To use this method, we start by simulating a single path that the price of the asset may take between the time the option is created to the time of expiration. The asset price is assumed to follow \n",
    "\n",
    "$$ dS = \\mu Sdt + \\sigma SdW(t) $$\n",
    "\n",
    "where $dW(t)$ is a Wiener (i.e. Brownian) process and $\\mu$ is the expected return on the asset in a risk-neutral world.  The assumption that an asset price follows a random walk underpins both the Black-Scholes and binomial models and by invoking it here, we are maintaining consistency with the work we have done so far in this module. If we let $dS$ be the change in asset price over some very small time step $dt$ and substitute $r$ for $\\mu$ (because they are synonymous in this context), we can rearrange this equation to be\n",
    "\n",
    "$$ S(t + dt) - S(t) = rS(t)dt + \\sigma S(t)Z\\sqrt{dt} $$\n",
    "\n",
    "where $Z\\sim N(0,1)$.  It is more accurate to simulate $\\ln S(t)$ than $S(t)$, so we use <a href=\"https://en.wikipedia.org/wiki/It%C3%B4%27s_lemma\">Ito's lemma</a> to transform our equation, yielding\n",
    "\n",
    "$$\\ln S(t + dt) - \\ln S(t) = (r - \\frac{\\sigma^2}{2})dt + \\sigma Z\\sqrt{dt}$$\n",
    "\n",
    "which is equivalent to\n",
    "\n",
    "$$S(t + dt) = S(t)e^{(r - \\frac{\\sigma^2}{2})dt + \\sigma Z\\sqrt{dt}}$$\n",
    "\n",
    "A Python function has been defined below that simulates the path of an asset based on this equation.\n",
    "\n",
    "\n",
    "\n",
    "<br><em style=\"font-size: 0.8em\">Please note that the author first encountered this derivation in <a href=\"http://www.scienpress.com/Upload/CMF/Vol%201_1_3.pdf\">this paper</a> and most of the steps presented in this section of the module follow those presented in it. If any concepts used in this section are unclear, you may consider going to this paper and reading the Monte Carlo section.  However, it would probably be even better to check out <a href=\"http://www.math.umn.edu/~adams005/Financial/Materials/bemis5.pdf\"> this presentation</a> on the derivation of the Black-Scholes equation in order to understand why Brownian motion factors into our analysis at all and gain a better understanding of how we have handled the stochastic elements of our equations and why.  These topics are too involved to be covered in this module but are certainly worth appreciating.</em>\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from random import gauss\n",
    "\n",
    "def asset_path(St, sigma, r, dt):\n",
    "    \"\"\"Simulates next step in potential path an asset price might take\n",
    "    \n",
    "    Parameters:\n",
    "    ----------\n",
    "    St: float\n",
    "        current asset price\n",
    "    sigma: float\n",
    "        volatility\n",
    "    r: float\n",
    "        risk-free interest rate\n",
    "    dt:float\n",
    "        length of time step\n",
    "    \n",
    "    Returns:\n",
    "    -------\n",
    "    St: float\n",
    "        next time step asset price    \n",
    "    \"\"\"\n",
    "    \n",
    "    St = St * np.exp((r - 0.5 * sigma**2)*dt + sigma * gauss(0,1.0) * np.sqrt(dt))\n",
    "    return St"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step of the Monte Carlo method is to simulate many of these paths.  The law of large numbers tells us that the more paths we simulate, the closer the average of these paths will be to the true mean path. Let us try this for a European call using the same parameters as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#parameters\n",
    "S0 = 45 #initial asset price\n",
    "K = 40 #strike price\n",
    "sigma = 0.25 #volatility\n",
    "r = 0.1 #risk-free interest rate\n",
    "T = 0.5 #time of expiration\n",
    "N = 100 #number of time steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def monte_carlo(sims, N, T, S0, sigma, r):\n",
    "    \"\"\"Performs a number of monte-carlo simulations of asset price\n",
    "    \n",
    "    Parameters:\n",
    "    ----------\n",
    "    sims: integer\n",
    "        number of simulations to be performed\n",
    "    N: integer\n",
    "        number of time steps in each simulations\n",
    "    T: float\n",
    "        expiration time of option\n",
    "    S0: float\n",
    "        intiial asset price\n",
    "    sigma: float\n",
    "        volatility\n",
    "    r: float\n",
    "        risk-free interest rate\n",
    "    \n",
    "    Returns:\n",
    "    -------\n",
    "    all_paths: 2D array of float\n",
    "        simulated asset price paths with each row being a seperate simulation\n",
    "        \n",
    "    Also, the function outputs a plot of its simulations    \n",
    "    \"\"\"\n",
    "    \n",
    "    dt = T/N\n",
    "    all_paths = np.zeros(N)\n",
    "\n",
    "    for trial in range (0,sims):\n",
    "        prices = [S0]    \n",
    "        St = S0\n",
    "        for t in range(1,N):\n",
    "            St = asset_path(St, sigma, r, dt)\n",
    "            prices.append(St)\n",
    "\n",
    "        if trial < 1:\n",
    "            all_paths += prices\n",
    "        else:\n",
    "            all_paths = np.vstack((all_paths, prices))\n",
    "\n",
    "        t = range(0,N)\n",
    "        pyplot.plot(t,prices)\n",
    "        pyplot.xlabel('Time Step (N)')\n",
    "        pyplot.ylabel('Asset Price ( S(t) )')\n",
    "    \n",
    "    return all_paths\n",
    "    pyplot.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Time to test our simulation function! We'll stick to 10 simulations just to make sure it works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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zMGiQvPrQEa3KQxCEOoIgrAUwHMAXAFoBaAqgAQBLAP0ABAP4VRCE9jUrqoyMTFUpKiqC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\nwZ7ADusAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x95b2b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sims = 10\n",
    "test = monte_carlo(sims, N, T, S0, sigma, r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hey, not too shabby!  This looks pretty believable, so let's move on to something more rigorous. How about 1,000 simulations?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PKFOmDL2q96JDpQ7UcKyBVpvJ4QdH+WjPYKxXWVOhXAUiOkcwue4cRjTrwuzZYGEB5ubg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uB377ArsrBnjEizR42oia8ib08ejZ424mlGBoNGjqSmsJo9BT9jve1HDhvLuFQ0DkvBFSQXbiIO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oswzQqRic35MDsmAK5k9jTcpE6F1Cv7P9MYcUsr4jlscFfRBdLMgcOhhTYOBNsQyLAC8l9uwh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/AmkUIg1rkf8/qjL7Eg+CnOPXeJbYKCVl0QWqXE6dxCRDkBoTWCHr1+R3PnZ4yCyP0xg8iN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\nGEaD/T+XsbvnrmnXTAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9c137b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sims = 1000\n",
    "MC_sim = monte_carlo(sims, N, T, S0, sigma, r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wow, look at all those lines and colors! Sometimes math really can be art. For our final step, we estimate the value of a European call by taking the average of the final asset prices for each simulated path and subtracting the strike price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Monte-Carlo estimated value of European call is $7.582\n"
     ]
    }
   ],
   "source": [
    "print(\"Monte-Carlo estimated value of European call is $%.3f\" %(np.max((np.average(MC_sim[:,-1]) - K),0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That result is not quite perfect, but we're certainly in the ballpark. Perhaps with more simulations and a more powerful computer, the answer would be even closer to the analytic result. Let's move on to valuing an Asian option.  Since we already performed the Monte-Carlo simulations, the only thing we need to change is how we process the results.  The first step will be to iteratively go through the matrix of resulting asset prices, averaging each column, which will yield an array characterizing the expected - or mean - path.  We will then apply the payoff equation for an Asian call which is\n",
    "\n",
    "$$V_{call} = \\textrm{max}(\\ \\textrm{avg}(\\ S(t)\\ )-K,0) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Monte-Carlo estimated value of Asian call is $6.225\n"
     ]
    }
   ],
   "source": [
    "mean_path = np.zeros(N)\n",
    "for i in range(N):\n",
    "    mean_path[i] = np.average(MC_sim[:,i])\n",
    "\n",
    "print(\"Monte-Carlo estimated value of Asian call is $%.3f\" %(np.average(mean_path) - K))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There you have it! We have successfully estimated the value of an Asian call, something that could not have been achieved analytically, nor with the Crank-Nicolson or binomial methods.  There isn't any great way to check the accuracy of this estimate, besides maybe adding more and more simulations, but we do expect an Asian call to be valued below a European call due to the averaged nature of its payoff.  Our result here at least meets that rather basic criterion."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion"
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    "In this module, we have explored three different styles of options and four different methods for valuing them.  The most basic style, the European option, can be valued analytically using the Black-Scholes formula under known, constant market conditions.  If we have reason to believe that those conditions are non-constant, we can use the Crank-Nicolson method to estimate the option's value.  In the case of an American option, which is similar to the European style but allows for early exercise, we can employ the binomial model and work our way backwards from the set of all possible option payoffs to accurately value the option.  For a path dependent option such as that described by the Asian style, the Monte-Carlo method gives us the ability to extract an option's value estimate by analyzing a large number of simulated paths.  In conclusion, a number of financial derivative styles exist, each with unique mathematical properties.  It is crucial that traders and academics alike keep an equally diverse set of numerical schemes in their tool sets and apply them appropriately in order to determine an option's value.\n",
    "\n",
    "<strong> Special thanks to:</strong>\n",
    "<ul>\n",
    "<li> Dr. Lorena Barba and her TA's, Naty Clementi and Gil Forsyth, for their patience and assistance and for putting on an <a href=\"http://openedx.seas.gwu.edu/courses/GW/MAE6286/2014_fall/about\"> excellent course</a>.</li>\n",
    "<li> Dr. Hugo Junghenn for his course \"Mathematics of Finance\" where I first came into contact with many of the concepts presented in this module. His book on option valuation can be found <a href=\"http://www.amazon.com/Option-Valuation-Financial-Mathematics-Chapman/dp/1439889112\">here</a>.</li>\n",
    "<li>Tingyu Wang for their <a href=\"http://nbviewer.ipython.org/github/numerical-mooc/assignment-bank/blob/705c3e47e5fd441c30a38c1ab17a80a75441e7d5/Black-Scholes-Equation/Black-Scholes-Equation.ipynb\">MAE 6286 project</a> completed in 2014 that helped provide a jumping-off point for this module.</li>\n",
    "<li>C.R. Nwozo and S.E. Fadugba whose <a href=\"http://www.scienpress.com/Upload/CMF/Vol%201_1_3.pdf\">paper</a> was a source of inspiration and guidance for the creation of this module.</li>\n",
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