{
 "metadata": {
  "name": "mcpricer"
 }, 
 "nbformat": 2, 
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown", 
     "source": [
      "# Parallel Monto-Carlo options pricing"
     ]
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "## Problem setup"
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "import sys", 
      "import time", 
      "from IPython.parallel import Client", 
      "import numpy as np", 
      "from mckernel import price_options", 
      "from matplotlib import pyplot as plt"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 1
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "cluster_profile = \"default\"", 
      "price = 100.0  # Initial price", 
      "rate = 0.05  # Interest rate", 
      "days = 260  # Days to expiration", 
      "paths = 10000  # Number of MC paths", 
      "n_strikes = 6  # Number of strike values", 
      "min_strike = 90.0  # Min strike price", 
      "max_strike = 110.0  # Max strike price", 
      "n_sigmas = 5  # Number of volatility values", 
      "min_sigma = 0.1  # Min volatility", 
      "max_sigma = 0.4  # Max volatility"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 2
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "strike_vals = np.linspace(min_strike, max_strike, n_strikes)", 
      "sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 3
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "## Parallel computation across strike prices and volatilities"
     ]
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "The Client is used to setup the calculation and works with all engines."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "c = Client(profile=cluster_profile)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 4
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "A LoadBalancedView is an interface to the engines that provides dynamic load", 
      "balancing at the expense of not knowing which engine will execute the code."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "view = c.load_balanced_view()"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 5
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "print \"Strike prices: \", strike_vals", 
      "print \"Volatilities: \", sigma_vals"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "stream", 
       "stream": "stdout", 
       "text": [
        "Strike prices:  [  90.   94.   98.  102.  106.  110.]", 
        "Volatilities:  [ 0.1    0.175  0.25   0.325  0.4  ]"
       ]
      }
     ], 
     "prompt_number": 6
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "Submit tasks for each (strike, sigma) pair."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "t1 = time.time()", 
      "async_results = []", 
      "for strike in strike_vals:", 
      "    for sigma in sigma_vals:", 
      "        ar = view.apply_async(price_options, price, strike, sigma, rate, days, paths)", 
      "        async_results.append(ar)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 7
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "print \"Submitted tasks: \", len(async_results)"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "stream", 
       "stream": "stdout", 
       "text": [
        "Submitted tasks:  30"
       ]
      }
     ], 
     "prompt_number": 8
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "Block until all tasks are completed."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "c.wait(async_results)", 
      "t2 = time.time()", 
      "t = t2-t1", 
      "", 
      "print \"Parallel calculation completed, time = %s s\" % t"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "stream", 
       "stream": "stdout", 
       "text": [
        "Parallel calculation completed, time = 4.46057891846 s"
       ]
      }
     ], 
     "prompt_number": 9
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "## Process and visualize results"
     ]
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "Get the results using the `get` method:"
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "results = [ar.get() for ar in async_results]"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 10
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "Assemble the result into a structured NumPy array."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "prices = np.empty(n_strikes*n_sigmas,", 
      "    dtype=[('ecall',float),('eput',float),('acall',float),('aput',float)]", 
      ")", 
      "", 
      "for i, price in enumerate(results):", 
      "    prices[i] = tuple(price)", 
      "", 
      "prices.shape = (n_strikes, n_sigmas)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 11
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "Plot the value of the European call in (volatility, strike) space."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plt.figure()", 
      "plt.contourf(sigma_vals, strike_vals, prices['ecall'])", 
      "plt.axis('tight')", 
      "plt.colorbar()", 
      "plt.title('European Call')", 
      "plt.xlabel(\"Volatility\")", 
      "plt.ylabel(\"Strike Price\")"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "pyout", 
       "prompt_number": 12, 
       "text": [
        "<matplotlib.text.Text at 0x106b618d0>"
       ]
      }, 
      {
       "output_type": "display_data", 
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Vw5WxC2CE5cUIG8EIq44rY41jiOXFEBvBEGsCV8YaxQjLjyHuhBHWFMZYYxhh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\nxkREGvD/vLHqAgUOcYsAAAAASUVORK5CYII=\n"
      }
     ], 
     "prompt_number": 12
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "Plot the value of the Asian call in (volatility, strike) space."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plt.figure()", 
      "plt.contourf(sigma_vals, strike_vals, prices['acall'])", 
      "plt.axis('tight')", 
      "plt.colorbar()", 
      "plt.title(\"Asian Call\")", 
      "plt.xlabel(\"Volatility\")", 
      "plt.ylabel(\"Strike Price\")"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "pyout", 
       "prompt_number": 13, 
       "text": [
        "<matplotlib.text.Text at 0x106bd90d0>"
       ]
      }, 
      {
       "output_type": "display_data", 
       "png": 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      }
     ], 
     "prompt_number": 13
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "Plot the value of the European put in (volatility, strike) space."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plt.figure()", 
      "plt.contourf(sigma_vals, strike_vals, prices['eput'])", 
      "plt.axis('tight')", 
      "plt.colorbar()", 
      "plt.title(\"European Put\")", 
      "plt.xlabel(\"Volatility\")", 
      "plt.ylabel(\"Strike Price\")"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "pyout", 
       "prompt_number": 14, 
       "text": [
        "<matplotlib.text.Text at 0x106d34150>"
       ]
      }, 
      {
       "output_type": "display_data", 
       "png": 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lypUrhIWFUVBQQFRUFA6Hg7S0NABSUlIoKiri/PnztGjRouYJOijaFKZgidD+JP1+079b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\n2Gbc2udPP6Yd42z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      }
     ], 
     "prompt_number": 14
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "Plot the value of the Asian put in (volatility, strike) space."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plt.figure()", 
      "plt.contourf(sigma_vals, strike_vals, prices['aput'])", 
      "plt.axis('tight')", 
      "plt.colorbar()", 
      "plt.title(\"Asian Put\")", 
      "plt.xlabel(\"Volatility\")", 
      "plt.ylabel(\"Strike Price\")"
     ], 
     "language": "python", 
     "outputs": [
      {
       "output_type": "display_data", 
       "png": 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eHq72MkhtHFW4HEcVnkP1HXF5eTlGjRqF4uJi+Pv7Y/v27Th16hQWLlyIVq1a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\nAeyS/5wqC8i5AAAAAElFTkSuQmCC\n"
      }
     ], 
     "prompt_number": 15
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "plt.show()"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 16
    }
   ]
  }
 ]
}