IPythonParallenIn15min.ipynb

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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "from IPython import parallel in 15 min"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Based on the [Parallel Monto-Carlo options pricing](http://nbviewer.ipython.org/github/ipython/ipython/blob/master/examples/Parallel%20Computing/Monte%20Carlo%20Options.ipynb) from [IPython.parallel examples](http://nbviewer.ipython.org/github/ipython/ipython/tree/master/examples/Parallel%20Computing/).\n",
      "\n",
      "This notebook shows how to use `IPython.parallel` to do Monte-Carlo options pricing in parallel.  \n",
      "We will compute the price of a large number of options for different strike prices and volatilities."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Few words about IPython ecosystem"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import HTML\n",
      "HTML('<iframe src=http://ipython.org/index.html width=1024 height=350></iframe>')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<iframe src=http://ipython.org/index.html width=1024 height=350></iframe>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "<IPython.core.display.HTML at 0x1069e0f10>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HTML('<iframe src=http://nbviewer.ipython.org/ width=1024 height=350></iframe>')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<iframe src=http://nbviewer.ipython.org/ width=1024 height=350></iframe>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "<IPython.core.display.HTML at 0x103fd6ed0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HTML('<iframe src=http://continuum.io/downloads width=1024 height=350></iframe>')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<iframe src=http://continuum.io/downloads width=1024 height=350></iframe>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<IPython.core.display.HTML at 0x10634fa90>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Have we got a cluster running?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![IPython parallel cluster](http://ipython.org/ipython-doc/stable/_images/wideView.png)\n",
      "\n",
      "First we my need to create a profile (default will be there by default)  \n",
      "`ipython profile create --parallel --profile=yourProfileName`  \n",
      "\n",
      "You can start it by using the IPython Notebook's [Clusters tab](http://127.0.0.1:8888/tree#clusters)  \n",
      "  \n",
      "Or by calling (of it form):  \n",
      "`ipcluster start -n 4`  \n",
      "\n",
      "Or the combination of  \n",
      "`ipcontroller --ip=192.169.X.Y` and `ipengine`  \n",
      "Where you want really want your controller to start up first, whilst engines will checks the ipcontroller-engine.json file it generates (you will copy it from say .ipython/profile_default/security/ipcontroller-engine.json to location from where engine will read it).\n",
      "\n",
      "If you are on restricted network, don't worry there is support for [SSH tunneling](http://ipython.org/ipython-doc/dev/parallel/parallel_process.html#ssh-tunnels)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.parallel import Client\n",
      "c = Client()\n",
      "c.history, c.ids"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "([], [0, 1, 2, 3, 4, 5, 6, 7])"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dv = c[:]\n",
      "print(type(dv))\n",
      "\n",
      "lv = c.load_balanced_view()\n",
      "print(type(lv))\n",
      "\n",
      "dv.results.items()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<class 'IPython.parallel.client.view.DirectView'>\n",
        "<class 'IPython.parallel.client.view.LoadBalancedView'>\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "[]"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Passing data around"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ar = dv.scatter('x', range(64),block=True)\n",
      "print(type(ar))\n",
      "\n",
      "ar = dv.scatter('x', range(1024*1024*30),block=False)\n",
      "ar.get(), ar.progress, ar.elapsed, ar.ready(), ar.serial_time, ar.wall_time"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "<type 'NoneType'>\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "([None, None, None, None, None, None, None, None],\n",
        " 8,\n",
        " 1.509833,\n",
        " True,\n",
        " 1.4056050000000002,\n",
        " 1.509833)"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l = c[4]['x']\n",
      "print(4, min(l), max(l), len(l))\n",
      "l = c[6]['x']\n",
      "print(6, min(l), max(l), len(l))\n",
      "\n",
      "c[0].push(dict(x=[0]))\n",
      "l= dv.pull('x',targets=0,block=True)\n",
      "print(0, min(l), max(l), len(l))\n",
      "\n",
      "l = c[7].pull('x').get()\n",
      "print(7, min(l), max(l), len(l))\n",
      "\n",
      "dv.push(dict(x=[1]))\n",
      "dv.gather('x').get()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(4, 15728640, 19660799, 3932160)\n",
        "(6, 23592960, 27525119, 3932160)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "(0, 0, 0, 1)\n",
        "(7, 27525120, 31457279, 3932160)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "[1, 1, 1, 1, 1, 1, 1, 1]"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import gc\n",
      "gc.collect()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "0"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with c[:].sync_imports():\n",
      "    import gc\n",
      "\n",
      "%px gc.collect()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "importing gc on engine(s)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\u001b[0;31mOut[0:1]: \u001b[0m35"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\u001b[0;31mOut[1:1]: \u001b[0m32"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\u001b[0;31mOut[2:1]: \u001b[0m32"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\u001b[0;31mOut[3:1]: \u001b[0m32"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\u001b[0;31mOut[4:1]: \u001b[0m32"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\u001b[0;31mOut[5:1]: \u001b[0m32"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\u001b[0;31mOut[6:1]: \u001b[0m32"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\u001b[0;31mOut[7:1]: \u001b[0m32"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "with c[:].sync_imports():\n",
      "    import numpy\n",
      "    \n",
      "%px x = numpy.random.randint(0,1024,10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "importing numpy on engine(s)\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%px --targets ::2\n",
      "x.sort()\n",
      "print(x, numpy.average(x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[stdout:0] (array([ 46,  84, 249, 303, 435, 554, 632, 663, 854, 926]), 474.60000000000002)\n",
        "[stdout:2] (array([ 71,  89, 298, 367, 500, 528, 619, 676, 870, 901]), 491.89999999999998)\n",
        "[stdout:4] (array([ 61,  77,  93, 144, 215, 282, 418, 512, 714, 813]), 332.89999999999998)\n",
        "[stdout:6] (array([  4,  72, 201, 201, 444, 542, 820, 824, 842, 928]), 487.80000000000001)\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pxconfig --noblock --targets [0,1,2,3]\n",
      "%px print (x, numpy.average(x))\n",
      "%pxresult"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[stdout:0] (array([ 46,  84, 249, 303, 435, 554, 632, 663, 854, 926]), 474.60000000000002)\n",
        "[stdout:1] (array([668, 983, 168, 522, 232, 540, 547, 673, 310, 842]), 548.5)\n",
        "[stdout:2] (array([ 71,  89, 298, 367, 500, 528, 619, 676, 870, 901]), 491.89999999999998)\n",
        "[stdout:3] (array([1010,  793,  265,  869,  427,  757,  181,  732,  466,  966]), 646.60000000000002)\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Debugging"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.parallel import CompositeError\n",
      "import random\n",
      "\n",
      "print( c[0].pull('x').get() )\n",
      "c[0].execute('numpy.append(x,[1,2,3])')\n",
      "print( c[0].pull('x').get() )\n",
      "\n",
      "i = random.choice(c.ids)\n",
      "c[i].execute('x = numpy.append(x,[0])')\n",
      "print( i, c[i].pull('x').get() )\n",
      "\n",
      "try:\n",
      "    dv.execute('y = int(numpy.max(x)) / int(numpy.min(x))', block=True)\n",
      "except CompositeError, e:\n",
      "    print e\n",
      "\n",
      "%px print y\n",
      "%pxresult"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 46  84 249 303 435 554 632 663 854 926]\n",
        "[ 46  84 249 303 435 554 632 663 854 926]\n",
        "(7, array([791, 497, 459, 970,  29, 860,   1, 547, 445,  51,   0]))\n",
        "one or more exceptions from call to method: execute\n",
        "[7:execute]: ZeroDivisionError: integer division or modulo by zero\n",
        "[stdout:0] 20\n",
        "[stdout:1] 5\n",
        "[stdout:2] 12\n",
        "[stdout:3] 5\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%px --targets 7\n",
      "from IPython import parallel\n",
      "parallel.bind_kernel()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "<AsyncResult: execute>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c[7].execute(\"%qtconsole\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "<AsyncResult: execute>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Just one more word on AsyncResult"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import time, os\n",
      "\n",
      "def getFewDetailsWithDelay(delay):\n",
      "    time.sleep(delay)\n",
      "    return os.getpid()\n",
      "\n",
      "getFewDetailsWithDelay(0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "1003"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dv.apply_sync(getFewDetailsWithDelay,3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "CompositeError",
       "evalue": "one or more exceptions from call to method: getFewDetailsWithDelay\n[0:apply]: NameError: global name 'time' is not defined\n[1:apply]: NameError: global name 'time' is not defined\n[2:apply]: NameError: global name 'time' is not defined\n[3:apply]: NameError: global name 'time' is not defined\n.... 4 more exceptions ...",
       "output_type": "pyerr",
       "traceback": [
        "[0:apply]: ",
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
        "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)\u001b[0;32m<string>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m",
        "\u001b[0;32m<ipython-input-15-94d42fdec29e>\u001b[0m in \u001b[0;36mgetFewDetailsWithDelay\u001b[0;34m(delay)\u001b[0m",
        "\u001b[0;31mNameError\u001b[0m: global name 'time' is not defined",
        "",
        "[1:apply]: ",
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
        "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)\u001b[0;32m<string>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m",
        "\u001b[0;32m<ipython-input-15-94d42fdec29e>\u001b[0m in \u001b[0;36mgetFewDetailsWithDelay\u001b[0;34m(delay)\u001b[0m",
        "\u001b[0;31mNameError\u001b[0m: global name 'time' is not defined",
        "",
        "[2:apply]: ",
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
        "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)\u001b[0;32m<string>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m",
        "\u001b[0;32m<ipython-input-15-94d42fdec29e>\u001b[0m in \u001b[0;36mgetFewDetailsWithDelay\u001b[0;34m(delay)\u001b[0m",
        "\u001b[0;31mNameError\u001b[0m: global name 'time' is not defined",
        "",
        "[3:apply]: ",
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
        "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)\u001b[0;32m<string>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m",
        "\u001b[0;32m<ipython-input-15-94d42fdec29e>\u001b[0m in \u001b[0;36mgetFewDetailsWithDelay\u001b[0;34m(delay)\u001b[0m",
        "\u001b[0;31mNameError\u001b[0m: global name 'time' is not defined",
        "",
        "... 4 more exceptions ..."
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import random, time, os\n",
      "from IPython.parallel import require\n",
      "\n",
      "@require(random, os,time)\n",
      "def getFewDetails():\n",
      "    delay = random.randint(0,10)\n",
      "    time.sleep(delay)\n",
      "    return os.getpid()\n",
      "\n",
      "ar = dv.apply_async(getFewDetails)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ar.progress"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "6"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ar.progress, ar.get(), ar.wall_time, ar.serial_time"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "(8, [958, 959, 960, 962, 964, 966, 968, 970], 11.804897, 42.011956)"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ar.metadata"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "[{'after': [],\n",
        "  'completed': datetime.datetime(2014, 5, 10, 15, 3, 58, 285200),\n",
        "  'data': {},\n",
        "  'engine_id': 0,\n",
        "  'engine_uuid': u'ba31eb76-1217-44df-82af-8870c8c17d15',\n",
        "  'follow': [],\n",
        "  'msg_id': u'fe78a315-1bf9-4f82-aebc-31ebcd093e57',\n",
        "  'outputs': [],\n",
        "  'outputs_ready': True,\n",
        "  'pyerr': None,\n",
        "  'pyin': None,\n",
        "  'pyout': None,\n",
        "  'received': datetime.datetime(2014, 5, 10, 15, 4, 2, 240695),\n",
        "  'started': datetime.datetime(2014, 5, 10, 15, 3, 53, 283631),\n",
        "  'status': u'ok',\n",
        "  'stderr': '',\n",
        "  'stdout': '',\n",
        "  'submitted': datetime.datetime(2014, 5, 10, 15, 3, 53, 282470)},\n",
        " {'after': [],\n",
        "  'completed': datetime.datetime(2014, 5, 10, 15, 4, 0, 286009),\n",
        "  'data': {},\n",
        "  'engine_id': 1,\n",
        "  'engine_uuid': u'05f0a6ff-7715-4062-b575-627f95e29f8a',\n",
        "  'follow': [],\n",
        "  'msg_id': u'6a995734-8df7-474e-8433-ad7b9137c7a4',\n",
        "  'outputs': [],\n",
        "  'outputs_ready': True,\n",
        "  'pyerr': None,\n",
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      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Let's run a simple simulation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "import sys\n",
      "import time\n",
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here are the basic parameters for our computation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "price = 100.0  # Initial price\n",
      "rate = 0.05  # Interest rate\n",
      "days = 260  # Days to expiration\n",
      "paths = 100000  # 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"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "strike_vals = np.linspace(min_strike, max_strike, n_strikes)\n",
      "sigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Strike prices: \", strike_vals\n",
      "print \"Volatilities: \", sigma_vals"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Strike prices:  [  90.   94.   98.  102.  106.  110.]\n",
        "Volatilities:  [ 0.1    0.175  0.25   0.325  0.4  ]\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "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",
     "collapsed": false,
     "input": [
      "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)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can time a single call of this function using the `%timeit` magic:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit -n1 -r1 print price_option(S=100.0, K=100.0, sigma=0.25, r=0.05, days=260, paths=100000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(12.374451344147433, 7.4518010512618824, 6.8561124933571236, 4.4580879409633019)\n",
        "1 loops, best of 1: 1.06 s per loop\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "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",
     "collapsed": true,
     "input": [
      "rc = Client()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "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",
     "collapsed": true,
     "input": [
      "view = rc.load_balanced_view()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "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",
     "collapsed": false,
     "input": [
      "async_results = []"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "%%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."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 1: 6.82 s per loop\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len(async_results)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "30"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Process and visualize results"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Retrieve the results using the `get` method:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "results = [ar.get() for ar in async_results]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Assemble the result into a structured NumPy array."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "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)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot the value of the European call in (volatility, strike) space."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "<matplotlib.text.Text at 0x10844f990>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/zN7fp08fvPHGGxgzZgxat24NnU4HHx+rb00xYvHqjiNHjuDChQv6gwDA6dOn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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105325f90>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot the value of the Asian call in (volatility, strike) space."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<matplotlib.text.Text at 0x108948a10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Vwjg3wEjrHIOsPcZZJYyzWYy0zjDK+sAwq4RhtoqR1hCDrD+Ms0oYZ5tpEuns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\nTUSkY4w0EZGOMdJERDrGSBMR6dj/AzIVq1SjmkE+AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10893e0d0>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot the value of the European put in (volatility, strike) space."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "<matplotlib.text.Text at 0x1089b1a90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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fpJqFPTXvnwOqjDntoROlMHlp4tixY7Flyxamf+NIioKuOhR0ogQmY7527VpM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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108976c10>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot the value of the Asian put in (volatility, strike) space."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "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\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "<matplotlib.text.Text at 0x108f42050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10898ae50>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Using dill to pickle (especially closure)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HTML('<iframe src=http://nbviewer.ipython.org/gist/minrk/5241793 width=1024 height=550></iframe>')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<iframe src=http://nbviewer.ipython.org/gist/minrk/5241793 width=1024 height=550></iframe>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 149,
       "text": [
        "<IPython.core.display.HTML at 0x1080b9f50>"
       ]
      }
     ],
     "prompt_number": 149
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "CPU affinity and numpy"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HTML('<iframe src=http://nbviewer.ipython.org/gist/minrk/5500077 width=1024 height=550></iframe>')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<iframe src=http://nbviewer.ipython.org/gist/minrk/5500077 width=1024 height=550></iframe>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 148,
       "text": [
        "<IPython.core.display.HTML at 0x1080b9a50>"
       ]
      }
     ],
     "prompt_number": 148
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "IPython slated"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[Daniel Rodriguez](https://github.com/danielfrg) covers an handly way of deploying clusters with [salt](http://www.saltstack.com/)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HTML('<iframe src=http://danielfrg.com/blog/2014/04/20/ipython-parallel-cluster-salt/ width=1024 height=550></iframe>')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<iframe src=http://danielfrg.com/blog/2014/04/20/ipython-parallel-cluster-salt/ width=1024 height=550></iframe>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 154,
       "text": [
        "<IPython.core.display.HTML at 0x1080b9810>"
       ]
      }
     ],
     "prompt_number": 154
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "StarCluster (for AWS):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HTML('<iframe src=http://star.mit.edu/cluster/docs/latest/plugins/ipython.html width=1024 height=550></iframe>')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<iframe src=http://star.mit.edu/cluster/docs/latest/plugins/ipython.html width=1024 height=550></iframe>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 150,
       "text": [
        "<IPython.core.display.HTML at 0x1080b9610>"
       ]
      }
     ],
     "prompt_number": 150
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HTML('<iframe src=http://badhessian.org/2013/11/cluster-computing-for-027hr-using-amazon-ec2-and-ipython-notebook/ width=1024 height=550></iframe>')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<iframe src=http://badhessian.org/2013/11/cluster-computing-for-027hr-using-amazon-ec2-and-ipython-notebook/ width=1024 height=550></iframe>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 152,
       "text": [
        "<IPython.core.display.HTML at 0x1080b9750>"
       ]
      }
     ],
     "prompt_number": 152
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "... and it works on Azure as well"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is quite extensive walk-through at Microsoft Research [webpage](http://research.microsoft.com/en-us/projects/azure/technical-papers.aspx).  \n",
      "However, for few details you might want to check the [MATLAB Distributed Computing Server with HPC Cluster in Microsoft Azure](http://research.microsoft.com/en-US/projects/azure/mdcs-with-hpc-cluster-on-microsoft-azure.pdf)  \n",
      "[Wenming Ye](https://github.com/wenming) shared a link to materials from an [Azure lab](http://research.microsoft.com/en-us/UM/redmond/projects/azure/Azure-training-course-0.51.zip) (which cover IPython as well)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HTML('<iframe src=http://azure.microsoft.com/en-us/documentation/articles/virtual-machines-python-ipython-notebook/ width=1024 height=550></iframe>')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<iframe src=http://azure.microsoft.com/en-us/documentation/articles/virtual-machines-python-ipython-notebook/ width=1024 height=550></iframe>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 153,
       "text": [
        "<IPython.core.display.HTML at 0x1080b9a90>"
       ]
      }
     ],
     "prompt_number": 153
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[IPython cluster helper](https://github.com/roryk/ipython-cluster-helper)\n",
      "\n",
      "ipython-cluster-helper creates a throwaway parallel IPython profile, launches a cluster and returns a view. \n",
      "On program exit it shuts the cluster down and deletes the throwaway profile. Schedulers supported: Platform LSF (\"lsf\"), Sun Grid Engine (\"sge\"), Torque (\"torque\") and SLURM (\"slurm\")."
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Learning materials:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "1. IPython.parallel documentation [http://ipython.org/ipython-doc/stable/parallel/parallel_intro.html](http://ipython.org/ipython-doc/stable/parallel/parallel_intro.html) and [parallel computing examples](https://github.com/ipython/ipython/tree/master/examples/Parallel%20Computing)\n",
      "\n",
      "2. The [IPython in-depth: high-productivity interactive and parallel python](https://github.com/ipython/ipython-in-depth) tutorial by [Brian E. Granger](http://brianegranger.com) , [Fernando P\u00e9rez](http://fperez.org) and [Min Ragan-Kelley](https://github.com/minrk) featuring from time to time at Python conferences. As far as I know IPython.parallel was covered last time at [PyCon US 2013](https://us.pycon.org/2013/schedule/presentation/20/).\n",
      "[![IPython in-depth: high-productivity interactive and parallel python](http://img.youtube.com/vi/bP8ydKBCZiY/0.jpg)](http://www.youtube.com/watch?v=bP8ydKBCZiY)\n",
      "\n",
      "4. University of Colorado Boulder's [presentation](https://www.rc.colorado.edu/node/217) on IPython.parallel\n",
      "\n",
      "3. Min RK's recent (24th April 2014) [talk at BayPiggies](https://github.com/minrk/baypiggies-2014-04-24)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import YouTubeVideo\n",
      "YouTubeVideo('z1DQzrpXN_U')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "        <iframe\n",
        "            width=\"400\"\n",
        "            height=300\"\n",
        "            src=\"https://www.youtube.com/embed/z1DQzrpXN_U\"\n",
        "            frameborder=\"0\"\n",
        "            allowfullscreen\n",
        "        ></iframe>\n",
        "        "
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "<IPython.lib.display.YouTubeVideo at 0x1094620d0>"
       ]
      }
     ],
     "prompt_number": 25
    }
   ],
   "metadata": {}
  }
 ]
}