{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "# Expected Exposure simulation with QuantLib and Python" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Copyright (c) 2015 Matthias Groncki*\n", "\n", "\n", "Redistribution and use in source and binary forms, with or without\n", "modification, are permitted provided that the following conditions are met:\n", "\n", " - Redistributions of source code must retain the above copyright notice,\n", " this list of conditions and the following disclaimer.\n", "\n", "THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\"\n", "AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE\n", "IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n", "DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR CONTRIBUTORS BE LIABLE\n", "FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\n", "DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\n", "SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER\n", "CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,\n", "OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\n", "OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n", "\n", "This disclaimer is taken from the QuantLib license" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# import the used libraries\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import QuantLib as ql\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Setting evaluation date\n", "today = ql.Date(7,4,2015)\n", "ql.Settings.instance().setEvaluationDate(today)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Setup Marketdata\n", "rate = ql.SimpleQuote(0.03)\n", "rate_handle = ql.QuoteHandle(rate)\n", "dc = ql.Actual365Fixed()\n", "yts = ql.FlatForward(today, rate_handle, dc)\n", "yts.enableExtrapolation()\n", "hyts = ql.RelinkableYieldTermStructureHandle(yts)\n", "t0_curve = ql.YieldTermStructureHandle(yts)\n", "euribor6m = ql.Euribor6M(hyts)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Setup a dummy portfolio with two Swaps\n", "def makeSwap(start, maturity, nominal, fixedRate, index, typ=ql.VanillaSwap.Payer):\n", " \"\"\"\n", " creates a plain vanilla swap with fixedLegTenor 1Y\n", " \n", " parameter:\n", " \n", " start (ql.Date) : Start Date\n", " \n", " maturity (ql.Period) : SwapTenor\n", " \n", " nominal (float) : Nominal\n", " \n", " fixedRate (float) : rate paid on fixed leg\n", " \n", " index (ql.IborIndex) : Index\n", " \n", " return: tuple(ql.Swap, list) Swap and all fixing dates\n", " \n", " \n", " \"\"\"\n", " end = ql.TARGET().advance(start, maturity)\n", " fixedLegTenor = ql.Period(\"1y\")\n", " fixedLegBDC = ql.ModifiedFollowing\n", " fixedLegDC = ql.Thirty360(ql.Thirty360.BondBasis)\n", " spread = 0.0\n", " fixedSchedule = ql.Schedule(start,\n", " end, \n", " fixedLegTenor, \n", " index.fixingCalendar(), \n", " fixedLegBDC,\n", " fixedLegBDC, \n", " ql.DateGeneration.Backward,\n", " False)\n", " floatSchedule = ql.Schedule(start,\n", " end,\n", " index.tenor(),\n", " index.fixingCalendar(),\n", " index.businessDayConvention(),\n", " index.businessDayConvention(),\n", " ql.DateGeneration.Backward,\n", " False)\n", " swap = ql.VanillaSwap(typ, \n", " nominal,\n", " fixedSchedule,\n", " fixedRate,\n", " fixedLegDC,\n", " floatSchedule,\n", " index,\n", " spread,\n", " index.dayCounter())\n", " return swap, [index.fixingDate(x) for x in floatSchedule][:-1]\n", "\n", "portfolio = [makeSwap(today + ql.Period(\"2d\"),\n", " ql.Period(\"5Y\"),\n", " 1e6,\n", " 0.03,\n", " euribor6m),\n", " makeSwap(today + ql.Period(\"2d\"),\n", " ql.Period(\"4Y\"),\n", " 5e5,\n", " 0.03,\n", " euribor6m,\n", " ql.VanillaSwap.Receiver),\n", " ]" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#%%timeit\n", "# Setup pricing engine and calculate the npv\n", "engine = ql.DiscountingSwapEngine(hyts)\n", "for deal, fixingDates in portfolio:\n", " deal.setPricingEngine(engine)\n", " deal.NPV()\n", " #print(deal.NPV())" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Stochastic Process " ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Assume the model is already calibrated either historical or market implied\n", "volas = [ql.QuoteHandle(ql.SimpleQuote(0.0075)),\n", " ql.QuoteHandle(ql.SimpleQuote(0.0075))]\n", "meanRev = [ql.QuoteHandle(ql.SimpleQuote(0.02))]\n", "model = ql.Gsr(t0_curve, [today+100], volas, meanRev, 16.)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "process = model.stateProcess()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "27.927\n" ] } ], "source": [ "# Define evaluation grid\n", "date_grid = [today + ql.Period(i,ql.Weeks) for i in range(0,52*6)]\n", "for deal in portfolio:\n", " date_grid += deal[1]\n", "\n", "date_grid = np.unique(np.sort(date_grid))\n", "time_grid = np.vectorize(lambda x: ql.ActualActual().yearFraction(today, x))(date_grid)\n", "dt = time_grid[1:] - time_grid[:-1]\n", "\n", "print(len(time_grid)*1500*2*29e-6)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Random number generator\n", "seed = 1\n", "urng = ql.MersenneTwisterUniformRng(seed)\n", "usrg = ql.MersenneTwisterUniformRsg(len(time_grid)-1,urng)\n", "generator = ql.InvCumulativeMersenneTwisterGaussianRsg(usrg)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#%%timeit\n", "# Generate N paths\n", "N = 1500\n", "x = np.zeros((N, len(time_grid)))\n", "y = np.zeros((N, len(time_grid)))\n", "pillars = np.array([0.0, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])\n", "zero_bonds = np.zeros((N, len(time_grid), 12))\n", "for j in range(12):\n", " zero_bonds[:, 0, j] = model.zerobond(pillars[j],\n", " 0,\n", " 0)\n", "for n in range(0,N):\n", " dWs = generator.nextSequence().value()\n", " for i in range(1, len(time_grid)):\n", " t0 = time_grid[i-1]\n", " t1 = time_grid[i]\n", " x[n,i] = process.expectation(t0, \n", " x[n,i-1], \n", " dt[i-1]) + dWs[i-1] * process.stdDeviation(t0,\n", " x[n,i-1],\n", " dt[i-1])\n", " y[n,i] = (x[n,i] - process.expectation(0,0,t1)) / process.stdDeviation(0,0,t1)\n", " for j in range(12):\n", " zero_bonds[n, i, j] = model.zerobond(t1+pillars[j],\n", " t1,\n", " y[n, i])\n", " " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYAAAAEACAYAAAC6d6FnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXd4FdXWuN85Nb0X0umh994H6SK9dwREUBAQQVDxICBI\n", "B6VJ7x1BivSh915DL4EkJCE9OckpM78/Jt7LtVz5Pq8/P73zPs95kpnZM3ufk5O19l5r7bVAQ0ND\n", "Q0NDQ0NDQ0NDQ0NDQ0NDQ0NDQ0NDQ0NDQ0NDQ0NDQ0NDQ0NDQ+O/lGZADHAPGP0rbebmX78KVHzl\n", "vA+wBbgN3AJq/HHD1NDQ0ND4T6IH7gMFASNwBSj5kzYtgD35v1cHzrxybSXwdv7vBsD7jxqohoaG\n", "hsZ/lprA3leOP85/vcpCoPMrxzFAMKqwf/iHjk5DQ0ND41fR/c77w4DYV46f5Z/7rTbhQCEgCVgO\n", "XAIWA26/czwaGhoaGq/J71UAymu2E37hPgNQCZif/zObn68eNDQ0NDT+IAy/8/7nQMQrxxGoM/x/\n", 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"GBgYGBgYGBgYGBgYGBgYGBgYGBgYGBgYGBgYGBgYGBgYGBgYGBj8x/k/xX2JRqpIrDcAAAAASUVO\n", "RK5CYII=\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot the paths\n", "for i in range(0,N):\n", " plt.plot(time_grid, x[i,:])" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#%%timeit\n", "#Swap pricing under each scenario\n", "npv_cube = np.zeros((N,len(date_grid), len(portfolio)))\n", "for p in range(0,N):\n", " for t in range(0, len(date_grid)):\n", " date = date_grid[t]\n", " ql.Settings.instance().setEvaluationDate(date)\n", " ycDates = [date, \n", " date + ql.Period(6, ql.Months)] \n", " ycDates += [date + ql.Period(i,ql.Years) for i in range(1,11)]\n", " yc = ql.DiscountCurve(ycDates, \n", " zero_bonds[p, t, :], \n", " ql.Actual365Fixed())\n", " yc.enableExtrapolation()\n", " hyts.linkTo(yc)\n", " if euribor6m.isValidFixingDate(date):\n", " fixing = euribor6m.fixing(date)\n", " euribor6m.addFixing(date, fixing)\n", " for i in range(len(portfolio)):\n", " npv_cube[p, t, i] = portfolio[i][0].NPV()\n", " ql.IndexManager.instance().clearHistories()\n", "ql.Settings.instance().setEvaluationDate(today)\n", "hyts.linkTo(yts)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Calculate the portfolio npv by netting all NPV\n", "portfolio_npv = np.sum(npv_cube,axis=2)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAdAAAAFRCAYAAADEsfx9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXd4VNXWh9+T3kNCJ0BC70WKCihwABFBLNgQRbAr+onl\n", "2r16LNivBdtVr72g2DuCslFsIE16J5TQe3omM+f7Y51hJslMGiFF9/s8eTJz6j5nZs5vr7XXWhs0\n", 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"E[E<0]=0\n", "EE = np.sum(E, axis=0)/N" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAcoAAAFRCAYAAAD0Pe1cAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XmcHGWdx/FPJRNCQiAQAgk5JFkgSJAznAIycgbkWuUU\n", "OVYQAVFcWI7AKvFYRVARVMAFRGA5BUTuQyWiIIkc4UoCSUiABHIAIVxyJHn2j9/TdE1Pd0319PFU\n", "TX/fr9e8prv6qKdreupbz1FPgYiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIhIyzsa+FvoQmTInsAf\n", "mri+CcBlTVxfd5wEnBu6ECKSH3OB94F3Yj8XBSzPJOCYGl5/NJWDchSwgo6f9R3goBrWl3WPAdvU\n", "6b1WAP8Wu98OvFKn926UdjqXsa9ftlbTSyM1aQtdAGlZDtgH+EvogniuCesYiO3086YX1ZV7a2A1\n", "YEodyxDV8b1C+RC4BzgS+FngskgVeoUugEgZlwA3x+7/BPiTv90OzMOa2hYDc4Avx57bF/gp8BKw\n", "wL/XyrHH9wemAkuBWVgT4f8AOwG/omPN9tPAA8AbwAw61gDXBG737zMZWK97H5WVgCexZjmA3sDD\n", 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false }, "outputs": [ { "data": { "text/plain": [ "39532.307814450956" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# alternative pfe 95% quantile of the maxima of each exposure paths\n", "PFE = np.sort(np.max(E,axis=1))[0.95*N]\n", "PFE" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }