{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parallel Monto-Carlo options pricing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook shows how to use `IPython.parallel` to do Monte-Carlo options pricing in parallel. We will compute the price of a large number of options for different strike prices and volatilities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "import time\n",
    "from IPython.parallel import Client\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the basic parameters for our computation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "price = 100.0  # Initial price\n",
    "rate = 0.05  # Interest rate\n",
    "days = 260  # Days to expiration\n",
    "paths = 10000  # Number of MC paths\n",
    "n_strikes = 6  # Number of strike values\n",
    "min_strike = 90.0  # Min strike price\n",
    "max_strike = 110.0  # Max strike price\n",
    "n_sigmas = 5  # Number of volatility values\n",
    "min_sigma = 0.1  # Min volatility\n",
    "max_sigma = 0.4  # Max volatility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "strike_vals = np.linspace(min_strike, max_strike, n_strikes)\n",
    "sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Strike prices:  [  90.   94.   98.  102.  106.  110.]\n",
      "Volatilities:  [ 0.1    0.175  0.25   0.325  0.4  ]\n"
     ]
    }
   ],
   "source": [
    "print \"Strike prices: \", strike_vals\n",
    "print \"Volatilities: \", sigma_vals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Monte-Carlo option pricing function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function computes the price of a single option.  It returns the call and put prices for both European and Asian style options."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def price_option(S=100.0, K=100.0, sigma=0.25, r=0.05, days=260, paths=10000):\n",
    "    \"\"\"\n",
    "    Price European and Asian options using a Monte Carlo method.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    S : float\n",
    "        The initial price of the stock.\n",
    "    K : float\n",
    "        The strike price of the option.\n",
    "    sigma : float\n",
    "        The volatility of the stock.\n",
    "    r : float\n",
    "        The risk free interest rate.\n",
    "    days : int\n",
    "        The number of days until the option expires.\n",
    "    paths : int\n",
    "        The number of Monte Carlo paths used to price the option.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    A tuple of (E. call, E. put, A. call, A. put) option prices.\n",
    "    \"\"\"\n",
    "    import numpy as np\n",
    "    from math import exp,sqrt\n",
    "    \n",
    "    h = 1.0/days\n",
    "    const1 = exp((r-0.5*sigma**2)*h)\n",
    "    const2 = sigma*sqrt(h)\n",
    "    stock_price = S*np.ones(paths, dtype='float64')\n",
    "    stock_price_sum = np.zeros(paths, dtype='float64')\n",
    "    for j in range(days):\n",
    "        growth_factor = const1*np.exp(const2*np.random.standard_normal(paths))\n",
    "        stock_price = stock_price*growth_factor\n",
    "        stock_price_sum = stock_price_sum + stock_price\n",
    "    stock_price_avg = stock_price_sum/days\n",
    "    zeros = np.zeros(paths, dtype='float64')\n",
    "    r_factor = exp(-r*h*days)\n",
    "    euro_put = r_factor*np.mean(np.maximum(zeros, K-stock_price))\n",
    "    asian_put = r_factor*np.mean(np.maximum(zeros, K-stock_price_avg))\n",
    "    euro_call = r_factor*np.mean(np.maximum(zeros, stock_price-K))\n",
    "    asian_call = r_factor*np.mean(np.maximum(zeros, stock_price_avg-K))\n",
    "    return (euro_call, euro_put, asian_call, asian_put)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can time a single call of this function using the `%timeit` magic:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(12.478072469211625, 7.5692079226372924, 6.9498346596114704, 4.5592719279729934)\n",
      "1 loops, best of 1: 111 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit -n1 -r1 print price_option(S=100.0, K=100.0, sigma=0.25, r=0.05, days=260, paths=10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parallel computation across strike prices and volatilities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Client is used to setup the calculation and works with all engines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rc = Client()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A `LoadBalancedView` is an interface to the engines that provides dynamic load\n",
    "balancing at the expense of not knowing which engine will execute the code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "view = rc.load_balanced_view()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Submit tasks for each (strike, sigma) pair. Again, we use the `%%timeit` magic to time the entire computation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "async_results = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loops, best of 1: 810 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit -n1 -r1\n",
    "\n",
    "for strike in strike_vals:\n",
    "    for sigma in sigma_vals:\n",
    "        # This line submits the tasks for parallel computation.\n",
    "        ar = view.apply_async(price_option, price, strike, sigma, rate, days, paths)\n",
    "        async_results.append(ar)\n",
    "\n",
    "rc.wait(async_results)  # Wait until all tasks are done."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(async_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Process and visualize results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Retrieve the results using the `get` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "results = [ar.get() for ar in async_results]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assemble the result into a structured NumPy array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "prices = np.empty(n_strikes*n_sigmas,\n",
    "    dtype=[('ecall',float),('eput',float),('acall',float),('aput',float)]\n",
    ")\n",
    "\n",
    "for i, price in enumerate(results):\n",
    "    prices[i] = tuple(price)\n",
    "\n",
    "prices.shape = (n_strikes, n_sigmas)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the value of the European call in (volatility, strike) space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1100a3290>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABGcAAAMvCAYAAAB/e73nAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAAAAAAAAAAAAAAAAAAAAAAAYnv8LTrFLgrpADnoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ffc7c10>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 407,
       "width": 563
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.contourf(sigma_vals, strike_vals, prices['ecall'])\n",
    "plt.axis('tight')\n",
    "plt.colorbar()\n",
    "plt.title('European Call')\n",
    "plt.xlabel(\"Volatility\")\n",
    "plt.ylabel(\"Strike Price\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the value of the Asian call in (volatility, strike) space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11009b3d0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABGUAAAMvCAYAAAB7jm3aAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ffc7210>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 407,
       "width": 562
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.contourf(sigma_vals, strike_vals, prices['acall'])\n",
    "plt.axis('tight')\n",
    "plt.colorbar()\n",
    "plt.title(\"Asian Call\")\n",
    "plt.xlabel(\"Volatility\")\n",
    "plt.ylabel(\"Strike Price\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the value of the European put in (volatility, strike) space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1109ef450>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABHoAAAMvCAYAAACtK7e/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1109e0310>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 407,
       "width": 573
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.contourf(sigma_vals, strike_vals, prices['eput'])\n",
    "plt.axis('tight')\n",
    "plt.colorbar()\n",
    "plt.title(\"European Put\")\n",
    "plt.xlabel(\"Volatility\")\n",
    "plt.ylabel(\"Strike Price\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the value of the Asian put in (volatility, strike) space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1109e3b10>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABGUAAAMvCAYAAAB7jm3aAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110dd2c50>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 407,
       "width": 562
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.contourf(sigma_vals, strike_vals, prices['aput'])\n",
    "plt.axis('tight')\n",
    "plt.colorbar()\n",
    "plt.title(\"Asian Put\")\n",
    "plt.xlabel(\"Volatility\")\n",
    "plt.ylabel(\"Strike Price\")"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 0
}