{ "metadata": { "name": "BS_Hedging", "zanadu": { "authors": [ "Antoine Jacquier" ], "category": "1", "clearance": "Private", "group_name": "Imperial College", "md5": "ab0de3f9eb057e901e5a94e13fc2f707", "notebook_id": "68A158E6-9380-459F-B3BD-A2AC71DC0D65", "python_name": null, "reviewer_id": null, "status": "WIP" } }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "Hedging strategy in the Black-Scholes model\n======\n***" }, { "cell_type": "code", "collapsed": false, "input": "import matplotlib.pyplot as plt\nimport numpy as np\nfrom scipy.stats import norm\nfrom scipy.optimize import bisect\nfrom math import isnan", "language": "python", "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [], "prompt_number": 26 }, { "cell_type": "heading", "level": 2, "metadata": { "zanadu": {} }, "source": "Black-Scholes functions" }, { "cell_type": "code", "collapsed": false, "input": "def phi(x): ## Gaussian density\n return np.exp(-0.5*x*x) / np.sqrt(2.*np.pi)\n \n#### Black Sholes Function\ndef BlackScholesCore(CallPutFlag,DF,F,X,T,v):\n\tvsqrt=v*np.sqrt(T)\n\ttry:\n\t\td1 = (np.log(F/X)+(vsqrt*vsqrt/2.))/vsqrt\n\texcept:\n\t\td1 = 0.\n\td2 = d1-vsqrt\n\tif CallPutFlag:\n\t\treturn DF*(F*norm.cdf(d1)-X*norm.cdf(d2))\n\telse:\n\t\treturn DF*(X*norm.cdf(-d2)-F*norm.cdf(-d1))\n \n#### Black Sholes Vega\ndef BlackScholesVegaCore(DF,F,X,T,v):\n\tvsqrt=v*np.sqrt(T)\n\td1 = (np.log(F/X)+(vsqrt*vsqrt/2.))/vsqrt\n\treturn F*phi(d1)*np.sqrt(T)/DF\n\n#### Black Sholes Delta\ndef BlackScholesDelta(CallPutFlag,S,X,T,r,d,v):\n\tvsqrt=v*np.sqrt(T)\n\tF = np.exp((r-d)*T)*S\n\ttry:\n\t\td1 = (np.log(F/X)+(vsqrt*vsqrt/2.))/vsqrt\n\texcept:\n\t\td1 = 0.\n\td2 = d1-vsqrt\n\tif CallPutFlag:\n\t\treturn norm.cdf(d1)\n\telse:\n\t\treturn norm.cdf(d1)-1. \n\ndef BlackScholes(CallPutFlag,S,X,T,r,d,v):\n\treturn BlackScholesCore(CallPutFlag,np.exp(-r*T),np.exp((r-d)*T)*S,X,T,v)", "language": "python", "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [], "prompt_number": 27 }, { "cell_type": "heading", "level": 3, "metadata": { "zanadu": {} }, "source": "Hedging strategy" }, { "cell_type": "code", "collapsed": false, "input": "def hedgingStrategy(CallPutFlag,S,X,T,r,d,v,n):\n\ttt = np.linspace(0, T, n)\n\tdt = T / (n-1.)\n\texpDrift = np.exp((r-0.5*v*v)*dt)\n\tdiff = v*np.sqrt(dt)\n\tSS, bank, strategyS, BSDelta, value, profit = [], [], [], [], [], []\n\t##nS = np.random.normal(0., 1., len(tt))\n\n\t##initialisation step\n\ttau = T\n\tSS.append(S)\n\tBSValue = BlackScholes(CallPutFlag,S,X,tau,r,d,v)\n\tBSDelta.append(BlackScholesDelta(CallPutFlag,S,X,tau,r,d,v))\n\tstrategyS.append(BSDelta[-1]*S)\n\tvalue.append(BSValue)\n\tbank.append(BSValue - strategyS[-1])\n\tprofit.append(value[-1] - BSValue)\n \n ## Evolution over time\n \n\tfor i in arange(1,len(tt)):\n\t\tnS = np.random.normal(0., 1.)\n\t\ttau = T-tt[i]\n\t\tSS.append(SS[-1]*expDrift*np.exp(diff*nS))\n\t\tBSValue = BlackScholes(CallPutFlag,SS[-1],X,tau,r,d,v)\n\t\tBSDelta.append(BlackScholesDelta(CallPutFlag,SS[-1],X,tau,r,d,v))\n\t\tstrategyS.append(BSDelta[-1]*SS[-1])\n\t\tvalue.append(BSDelta[-2]*SS[-1] + np.exp(r*dt)*bank[-1])\n\t\tbank.append(value[-1] - strategyS[-1])\n\t\tprofit.append(value[-1] - BSValue) \n\treturn tt, bank, strategyS, profit", "language": "python", "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [], "prompt_number": 28 }, { "cell_type": "heading", "level": 2, "metadata": { "zanadu": {} }, "source": "Delta-hedging strategy" }, { "cell_type": "heading", "level": 3, "metadata": { "zanadu": {} }, "source": "One path" }, { "cell_type": "code", "collapsed": false, "input": "CallPutFlag, S, X, T, r, d, v, nbSteps = True, 100., 95., 1., 0.03, 0., 0.2, 100", "language": "python", "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "prompt_number": 29 }, { "cell_type": "code", "collapsed": false, "input": "tt, bank, strategyS, profit = hedgingStrategy(CallPutFlag,S,X,T,r,d,v,nbSteps)\nfig = plt.figure(figsize=(8,4))\nplt.plot(tt, profit, 'b')\nplt.title(\"PnL in Black-Scholes with delta hedging\", fontsize=12, fontweight='bold')\nplt.xlabel('time', fontsize=12)\nplt.show()", "language": "python", "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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GjZPN3cYk7eyCvcptGCtuIqLMRUUBrVsDlSpZOxLTYMVtw1hxExFlLC5ODvc6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\n3ERERDaEiZuIiMiGMHETERHZkP8DfzYVM7N5bBsAAAAASUVORK5CYII=\n", "text": "" } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 3, "metadata": { "zanadu": {} }, "source": "Multiple paths" }, { "cell_type": "code", "collapsed": false, "input": "CallPutFlag, S, X, T, r, d, v, nbSteps, nbPaths = True, 100., 95., 1., 0.03, 0., 0.2, 20, 100", "language": "python", "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "prompt_number": 34 }, { "cell_type": "code", "collapsed": false, "input": "ii = arange(nbPaths)\nprofits, deltas, banks = [], [], []\nfor i in ii:\n tt, bank, strategyS, prof = hedgingStrategy(CallPutFlag,S,X,T,r,d,v,nbSteps)\n profits.append(prof)\n #deltas.append(strategyS)\n #banks.append(bank)\n\nfig = plt.figure(figsize=(8,4))\nfor i in ii:\n\tplt.plot(tt, profits[i], color = get_cmap('gist_heat')(float(i)/len(ii)))\nplt.title(\"PnL in Black-Scholes with delta hedging\", fontsize=12, fontweight='bold')\nplt.xlabel('time', fontsize=12)\nplt.show()", "language": "python", "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ijqMboHQ9NByFybfD9SuQE7Op37OHf99zD9GZmeQ+9QSBznIM3UdwGtPo0aTg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\nrTbtNHrq8TfffAONRoNx48YhLi4OxcXFMlR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"text": "" } ], "prompt_number": 37 }, { "cell_type": "heading", "level": 4, "metadata": { "zanadu": {} }, "source": "Distribution of the final PnL" }, { "cell_type": "code", "collapsed": false, "input": "pp = [profits[i][-1] for i in arange(nbPaths)]\nbins = numpy.linspace(-6., 6., 50)\npyplot.hist(pp, bins, alpha=0.5)\npyplot.title(\"Distribution of the final profit\")\npyplot.show()", "language": "python", "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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