{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parallel Monto-Carlo options pricing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook shows how to use `ipyparallel` 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": {},
   "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",
    "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": {},
   "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": [
    "from __future__ import print_function # legacy Python support\n",
    "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": {},
   "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": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 174 ms, sys: 5.96 ms, total: 180 ms\n",
      "Wall time: 211 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(12.166236181100073,\n",
       " 7.6440122060909745,\n",
       " 6.8409606562778666,\n",
       " 4.4639448434953621)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time result = price_option(S=100.0, K=100.0, sigma=0.25, r=0.05, days=260, paths=10000)\n",
    "result"
   ]
  },
  {
   "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": [
    "import ipyparallel as ipp\n",
    "rc = ipp.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": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "async_results = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 127 ms, sys: 15.7 ms, total: 143 ms\n",
      "Wall time: 1.97 s\n"
     ]
    }
   ],
   "source": [
    "%%time\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": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30"
      ]
     },
     "execution_count": 12,
     "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": 13,
   "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": 14,
   "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": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x106036470>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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vq7U+rNa6161JF0/y1d0bSynXSPIr6d5yuTKTizO11q/UWs+b89h5Xsd5rXS3SO31+U+n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\nluj/AnN6nnqCXKW/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10601c978>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 410,
       "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": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1062d27f0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AByLMAGN22hfOE2aAqQkzLEKt9cIkd0ryjHSv1H5Tkmen26P2ZrXWD856j6ZtR/f2q7Wx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\nALBC4gwAAADACv1/Z26P1/NPQ6AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1060fca20>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 410,
       "width": 563
      }
     },
     "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": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x106c0c748>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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YeKQJM/KoNEYe5cjII/Vm5FEJ3LKlaWHgkaaAkUelMfIoR0YeqTfP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\nAEDP/V96nEbDO4df8wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1060fccc0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 410,
       "width": 572
      }
     },
     "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": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1078690b8>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GmJc2DfSPLU/AJhDOADtPWAPMSpsG+kmbBlgX4QzQO3thjZAGmIY2DfSPNg2wasIZoLdG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\nSJwBAAAAGJA4AwAAADCg/w9Eb0cSCPNO6wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10603c9e8>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 410,
       "width": 563
      }
     },
     "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": {
  "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"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
