diff --git a/docs/examples/parallel/options/mcpricer.ipynb b/docs/examples/parallel/options/mcpricer.ipynb index 5c1d26d..6ae3dba 100644 --- a/docs/examples/parallel/options/mcpricer.ipynb +++ b/docs/examples/parallel/options/mcpricer.ipynb @@ -1,243 +1,380 @@ { - "nbformat": 2, - "metadata": { - "name": "mcpricer" - }, - "worksheets": [ - { - "cells": [ - { - "source": "# Parallel Monto-Carlo options pricing", - "cell_type": "markdown" - }, - { - "source": "## Problem setup", - "cell_type": "markdown" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [], - "collapsed": true, - "prompt_number": 1, - "input": "import sys\nimport time\nfrom IPython.parallel import Client\nimport numpy as np\nfrom mckernel import price_options\nfrom matplotlib import pyplot as plt" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [], - "collapsed": true, - "prompt_number": 2, - "input": "cluster_profile = \"default\"\nprice = 100.0 # Initial price\nrate = 0.05 # Interest rate\ndays = 260 # Days to expiration\npaths = 10000 # Number of MC paths\nn_strikes = 5 # Number of strike values\nmin_strike = 90.0 # Min strike price\nmax_strike = 110.0 # Max strike price\nn_sigmas = 5 # Number of volatility values\nmin_sigma = 0.1 # Min volatility\nmax_sigma = 0.4 # Max volatility" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [], - "collapsed": true, - "prompt_number": 3, - "input": "strike_vals = np.linspace(min_strike, max_strike, n_strikes)\nsigma_vals = np.linspace(min_sigma, max_sigma, n_sigmas)" - }, - { - "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": "markdown" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [], - "collapsed": true, - "prompt_number": 4, - "input": "c = Client(profile=cluster_profile)" - }, - { - "source": "A LoadBalancedView is an interface to the engines that provides dynamic load \nbalancing at the expense of not knowing which engine will execute the code.", - "cell_type": "markdown" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [], - "collapsed": true, - "prompt_number": 5, - "input": "view = c.load_balanced_view()" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [ - { - "output_type": "stream", - "text": "Strike prices: [ 90. 95. 100. 105. 110.]\nVolatilities: [ 0.1 0.175 0.25 0.325 0.4 ]" - } - ], - "collapsed": false, - "prompt_number": 6, - "input": "print \"Strike prices: \", strike_vals\nprint \"Volatilities: \", sigma_vals" - }, - { - "source": "Submit tasks for each (strike, sigma) pair.", - "cell_type": "markdown" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [], - "collapsed": true, - "prompt_number": 7, - "input": "t1 = time.time()\nasync_results = []\nfor strike in strike_vals:\n for sigma in sigma_vals:\n ar = view.apply_async(price_options, price, strike, sigma, rate, days, paths)\n async_results.append(ar)" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [ - { - "output_type": "stream", - "text": "Submitted tasks: 25" - } - ], - "collapsed": false, - "prompt_number": 8, - "input": "print \"Submitted tasks: \", len(async_results)" - }, - { - "source": "Block until all tasks are completed.", - "cell_type": "markdown" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [ - { - "output_type": "stream", - "text": "Parallel calculation completed, time = 2.57819604874 s" - } - ], - "collapsed": false, - "prompt_number": 9, - "input": "c.wait(async_results)\nt2 = time.time()\nt = t2-t1\n\nprint \"Parallel calculation completed, time = %s s\" % t" - }, - { - "source": "## Process and visualize results", - "cell_type": "markdown" - }, - { - "source": "Get the results using the `get` method:", - "cell_type": "markdown" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [], - "collapsed": true, - "prompt_number": 10, - "input": "results = [ar.get() for ar in async_results]\n" - }, - { - "source": "Assemble the result into a structured NumPy array.", - "cell_type": "markdown" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [], - "collapsed": true, - "prompt_number": 11, - "input": "prices = np.empty(n_strikes*n_sigmas,\n dtype=[('ecall',float),('eput',float),('acall',float),('aput',float)]\n)\n\nfor i, price in enumerate(results):\n prices[i] = tuple(price)\n \nprices.shape = (n_strikes, n_sigmas)\nstrike_mesh, sigma_mesh = np.meshgrid(strike_vals, sigma_vals)" - }, - { - "source": "Plot the value of the European call in (volatility, strike) space.", - "cell_type": "markdown" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 12, - "text": "<matplotlib.text.Text at 0x2c54750>" - }, - { - "output_type": "display_data", - "png": 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4UFlTU8O9997Lq6++iouLi8Gvb/PhfH0hVUexkKq+BsTDmNPguEfpSmyeLDlwISCPIv9a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\npdh+TwWtrKby2DC2V9jHJwR9JElw/A0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- } - ], - "collapsed": false, - "prompt_number": 12, - "input": "plt.contourf(sigma_mesh, strike_mesh, prices['ecall'])\nplt.axis('tight')\nplt.colorbar()\nplt.title('European Call')\nplt.xlabel(\"Volatility\")\nplt.ylabel(\"Strike Price\")" - }, - { - "source": "Plot the value of the Asian call in (volatility, strike) space.", - "cell_type": "markdown" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 13, - "text": "<matplotlib.text.Text at 0x2e14610>" - }, - { - "output_type": "display_data", - "png": 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ebtVCtksyoi8YjotW0SWqRzQbY4xAu8VjtYoHQ1lBiGgZDkdm/1nGU4Ghu6Ho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\nzVv3sbGyRrQUSSfoc0MwIh6MYr5+qUY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2ljFjxjB58mT+/Oc/8+abb15Tm+Jms+2EhASe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\nRU5ErkJggg==\n" - } - ], - "collapsed": false, - "prompt_number": 13, - "input": "plt.contourf(sigma_mesh, strike_mesh, prices['acall'])\nplt.axis('tight')\nplt.colorbar()\nplt.title(\"Asian Call\")\nplt.xlabel(\"Volatility\")\nplt.ylabel(\"Strike Price\")" - }, - { - "source": "Plot the value of the European put in (volatility, strike) space.", - "cell_type": "markdown" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 14, - "text": "<matplotlib.text.Text at 0x32ee190>" - }, - { - "output_type": "display_data", - "png": 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Sk9ylGKXZlDOc/aiplrsU2Zk3mzK5SMuAGwfkLsWwZE+FPSfA8OOgQ+UWwTj+PV3W7dlW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\nhjghhLgxGuKEEOLGaIgTQogb+z9RrMAdh+sfRQAAAABJRU5ErkJggg==\n" - } - ], - "collapsed": false, - "prompt_number": 14, - "input": "plt.contourf(sigma_mesh, strike_mesh, prices['eput'])\nplt.axis('tight')\nplt.colorbar()\nplt.title(\"European Put\")\nplt.xlabel(\"Volatility\")\nplt.ylabel(\"Strike Price\")" - }, - { - "source": "Plot the value of the Asian put in (volatility, strike) space.", - "cell_type": "markdown" - }, - { - "cell_type": "code", - "language": "python", - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 15, - "text": "<matplotlib.text.Text at 0x3487c50>" - }, - { - "output_type": "display_data", - "png": 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AHMWw/9Yh3UGGLv5JfQYd1d+zjtF6lOIFMRUuyGadpGWUwmtNb5Bz5v+s38lh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\nJIgXZ47jOAnixZnjOE6C/g98ZDDk0wdCzQAAAABJRU5ErkJggg==\n" - } - ], - "collapsed": false, - "prompt_number": 15, - "input": "plt.contourf(sigma_mesh, strike_mesh, prices['aput'])\nplt.axis('tight')\nplt.colorbar()\nplt.title(\"Asian Put\")\nplt.xlabel(\"Volatility\")\nplt.ylabel(\"Strike Price\")\n" - } - ] - } - ] + "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", + "png": 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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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ewHwYYfEYYTFchvjq1av44x//iNOnT2Ps2LH45S9/qe+nLlNjiuwBzIcRFosBFsvl22DO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\n6zyQVarBwoqT2y9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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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95UvNs2bN4s9//jOhoaGMGDGCY8eOBaJUF081l5eXM3HiRFq1asXs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\nQmCC\n" + } + ], + "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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+ } + ], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": true, + "input": [ + "plt.show()" + ], + "language": "python", + "outputs": [], + "prompt_number": 16 + } + ] + } + ] } \ No newline at end of file diff --git a/docs/examples/parallel/options/mcpricer.py b/docs/examples/parallel/options/mcpricer.py index 4f2e751..65282e1 100644 --- a/docs/examples/parallel/options/mcpricer.py +++ b/docs/examples/parallel/options/mcpricer.py @@ -14,7 +14,7 @@ import sys import time from IPython.parallel import Client import numpy as np -from mcpricer import price_options +from mckernel import price_options from matplotlib import pyplot as plt # @@ -24,7 +24,7 @@ price = 100.0 # Initial price rate = 0.05 # Interest rate days = 260 # Days to expiration paths = 10000 # Number of MC paths -n_strikes = 5 # Number of strike values +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 @@ -117,7 +117,6 @@ for i, price in enumerate(results): prices[i] = tuple(price) prices.shape = (n_strikes, n_sigmas) -strike_mesh, sigma_mesh = np.meshgrid(strike_vals, sigma_vals) # @@ -125,7 +124,8 @@ strike_mesh, sigma_mesh = np.meshgrid(strike_vals, sigma_vals) # -plt.contourf(sigma_mesh, strike_mesh, prices['ecall']) +plt.figure() +plt.contourf(sigma_vals, strike_vals, prices['ecall']) plt.axis('tight') plt.colorbar() plt.title('European Call') @@ -138,7 +138,8 @@ plt.ylabel("Strike Price") # -plt.contourf(sigma_mesh, strike_mesh, prices['acall']) +plt.figure() +plt.contourf(sigma_vals, strike_vals, prices['acall']) plt.axis('tight') plt.colorbar() plt.title("Asian Call") @@ -151,7 +152,8 @@ plt.ylabel("Strike Price") # -plt.contourf(sigma_mesh, strike_mesh, prices['eput']) +plt.figure() +plt.contourf(sigma_vals, strike_vals, prices['eput']) plt.axis('tight') plt.colorbar() plt.title("European Put") @@ -164,10 +166,15 @@ plt.ylabel("Strike Price") # 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