private void pathGenerator(UnderlyingInfo under) { ulong seed = 1; int timeSteps = 365; // int dimensions = this.processArr_.factors(); double t = processArr_.time(maturity); TimeGrid grid = new TimeGrid(t, timeSteps); IRNG rndGenerator = (IRNG) new PseudoRandom().make_sequence_generator(dimensions * (grid.size() - 1), seed); this.pathGenerator_ = new MultiPathGenerator <IRNG>(this.processArr_, grid, rndGenerator, false); }
private void pathGenerator(UnderlyingInfo under) { ulong seed = 1; int timeSteps = 365; // int dimensions = this.processArr_.factors(); double t = processArr_.time(maturity); TimeGrid grid = new TimeGrid(t, timeSteps); IRNG rndGenerator = (IRNG)new PseudoRandom().make_sequence_generator(dimensions * (grid.size() - 1), seed); this.pathGenerator_ = new MultiPathGenerator<IRNG>(this.processArr_, grid, rndGenerator, false); }
public ScenarioCube(double r, double[] spots, double[] q, double[] vols, double[,] correlations, int nSteps, double dt) { nAssets = spots.Length; this.nSteps = nSteps; this.dt = dt; Processes = new List <StochasticProcess1D>(nAssets); Correlations = new Matrix(nAssets, nAssets); Date now = new Date(DateTime.Now.Date); DayCounter dc = new SimpleDayCounter(); yc = new Handle <YieldTermStructure>(new FlatForward(now, r, dc)); for (int i = 0; i < nAssets; ++i) { Handle <Quote> x0 = new Handle <Quote>(new SimpleQuote(spots[i])); Handle <YieldTermStructure> dyc = new Handle <YieldTermStructure>(new FlatForward(now, q[i], dc)); Handle <BlackVolTermStructure> bv = new Handle <BlackVolTermStructure>(new BlackConstantVol(now, new Calendar(), vols[i], dc)); Processes.Add(new GeneralizedBlackScholesProcess(x0, dyc, yc, bv)); for (int j = 0; j < nAssets; ++j) { if (i == j) { Correlations[i, j] = 1; } else { Correlations[i, j] = Correlations[j, i] = correlations[i, j]; } } } spa = new StochasticProcessArray(Processes, Correlations); rsg = new RandomSequenceGenerator <MersenneTwisterUniformRng>(nSteps * Processes.Count, new MersenneTwisterUniformRng()); tg = new TimeGrid(nSteps * dt, nSteps); var rsg2 = new InverseCumulativeRsg <RandomSequenceGenerator <MersenneTwisterUniformRng>, InverseCumulativeNormal>(rsg, new InverseCumulativeNormal()); mpg = new MultiPathGenerator <InverseCumulativeRsg <RandomSequenceGenerator <MersenneTwisterUniformRng>, InverseCumulativeNormal> >(spa, tg, rsg2, false); }
public void testMultiple(StochasticProcess process, string tag, double[] expected, double[] antithetic) { ulong seed = 42; double length = 10; int timeSteps = 12; int assets = process.size(); var rsg = (InverseCumulativeRsg <RandomSequenceGenerator <MersenneTwisterUniformRng> , InverseCumulativeNormal>) new PseudoRandom().make_sequence_generator(timeSteps * assets, seed); MultiPathGenerator <IRNG> generator = new MultiPathGenerator <IRNG>(process, new TimeGrid(length, timeSteps), rsg, false); int i; for (i = 0; i < 100; i++) { generator.next(); } Sample <MultiPath> sample = generator.next(); Vector calculated = new Vector(assets); double error, tolerance = 2.0e-7; for (int j = 0; j < assets; j++) { calculated[j] = sample.value[j].back(); } for (int j = 0; j < assets; j++) { error = Math.Abs(calculated[j] - expected[j]); if (error > tolerance) { Assert.Fail("using " + tag + " process " + "(" + j + 1 + " asset:)\n" //+ std::setprecision(13) + " calculated: " + calculated[j] + "\n" + " expected: " + expected[j] + "\n" + " error: " + error + "\n" + " tolerance: " + tolerance); } } sample = generator.antithetic(); for (int j = 0; j < assets; j++) { calculated[j] = sample.value[j].back(); } for (int j = 0; j < assets; j++) { error = Math.Abs(calculated[j] - antithetic[j]); if (error > tolerance) { Assert.Fail("using " + tag + " process " + "(" + j + 1 + " asset:)\n" + "antithetic sample:\n" //+ std::setprecision(13) + " calculated: " + calculated[j] + "\n" + " expected: " + antithetic[j] + "\n" + " error: " + error + "\n" + " tolerance: " + tolerance); } } }
public void testSwaptionPricing() { // Testing forward swap and swaption pricing const int size = 10; const int steps = 8 * size; #if QL_USE_INDEXED_COUPON const double tolerance = 1e-6; #else const double tolerance = 1e-12; #endif List <Date> dates = new List <Date>(); List <double> rates = new List <double>(); dates.Add(new Date(4, 9, 2005)); dates.Add(new Date(4, 9, 2011)); rates.Add(0.04); rates.Add(0.08); IborIndex index = makeIndex(dates, rates); LiborForwardModelProcess process = new LiborForwardModelProcess(size, index); LmCorrelationModel corrModel = new LmExponentialCorrelationModel(size, 0.5); LmVolatilityModel volaModel = new LmLinearExponentialVolatilityModel(process.fixingTimes(), 0.291, 1.483, 0.116, 0.00001); // set-up pricing engine process.setCovarParam((LfmCovarianceParameterization) new LfmCovarianceProxy(volaModel, corrModel)); // set-up a small Monte-Carlo simulation to price swations List <double> tmp = process.fixingTimes(); TimeGrid grid = new TimeGrid(tmp, tmp.Count, steps); List <int> location = new List <int>(); for (int i = 0; i < tmp.Count; ++i) { location.Add(grid.index(tmp[i])); } ulong seed = 42; const int nrTrails = 5000; LowDiscrepancy.icInstance = new InverseCumulativeNormal(); IRNG rsg = (InverseCumulativeRsg <RandomSequenceGenerator <MersenneTwisterUniformRng> , InverseCumulativeNormal>) new PseudoRandom().make_sequence_generator(process.factors() * (grid.size() - 1), seed); MultiPathGenerator <IRNG> generator = new MultiPathGenerator <IRNG>(process, grid, rsg, false); LiborForwardModel liborModel = new LiborForwardModel(process, volaModel, corrModel); Calendar calendar = index.fixingCalendar(); DayCounter dayCounter = index.forwardingTermStructure().link.dayCounter(); BusinessDayConvention convention = index.businessDayConvention(); Date settlement = index.forwardingTermStructure().link.referenceDate(); SwaptionVolatilityMatrix m = liborModel.getSwaptionVolatilityMatrix(); for (int i = 1; i < size; ++i) { for (int j = 1; j <= size - i; ++j) { Date fwdStart = settlement + new Period(6 * i, TimeUnit.Months); Date fwdMaturity = fwdStart + new Period(6 * j, TimeUnit.Months); Schedule schedule = new Schedule(fwdStart, fwdMaturity, index.tenor(), calendar, convention, convention, DateGeneration.Rule.Forward, false); double swapRate = 0.0404; VanillaSwap forwardSwap = new VanillaSwap(VanillaSwap.Type.Receiver, 1.0, schedule, swapRate, dayCounter, schedule, index, 0.0, index.dayCounter()); forwardSwap.setPricingEngine(new DiscountingSwapEngine(index.forwardingTermStructure())); // check forward pricing first double expected = forwardSwap.fairRate(); double calculated = liborModel.S_0(i - 1, i + j - 1); if (Math.Abs(expected - calculated) > tolerance) { QAssert.Fail("Failed to reproduce fair forward swap rate" + "\n calculated: " + calculated + "\n expected: " + expected); } swapRate = forwardSwap.fairRate(); forwardSwap = new VanillaSwap(VanillaSwap.Type.Receiver, 1.0, schedule, swapRate, dayCounter, schedule, index, 0.0, index.dayCounter()); forwardSwap.setPricingEngine(new DiscountingSwapEngine(index.forwardingTermStructure())); if (i == j && i <= size / 2) { IPricingEngine engine = new LfmSwaptionEngine(liborModel, index.forwardingTermStructure()); Exercise exercise = new EuropeanExercise(process.fixingDates()[i]); Swaption swaption = new Swaption(forwardSwap, exercise); swaption.setPricingEngine(engine); GeneralStatistics stat = new GeneralStatistics(); for (int n = 0; n < nrTrails; ++n) { Sample <IPath> path = (n % 2 != 0) ? generator.antithetic() : generator.next(); MultiPath value = path.value as MultiPath; Utils.QL_REQUIRE(value != null, () => "Invalid Path"); //Sample<MultiPath> path = generator.next(); List <double> rates_ = new InitializedList <double>(size); for (int k = 0; k < process.size(); ++k) { rates_[k] = value[k][location[i]]; } List <double> dis = process.discountBond(rates_); double npv = 0.0; for (int k = i; k < i + j; ++k) { npv += (swapRate - rates_[k]) * (process.accrualEndTimes()[k] - process.accrualStartTimes()[k]) * dis[k]; } stat.add(Math.Max(npv, 0.0)); } if (Math.Abs(swaption.NPV() - stat.mean()) > stat.errorEstimate() * 2.35) { QAssert.Fail("Failed to reproduce swaption npv" + "\n calculated: " + stat.mean() + "\n expected: " + swaption.NPV()); } } } } }
public void testMultiple(StochasticProcess process, string tag, double[] expected, double[] antithetic ) { ulong seed = 42; double length = 10; int timeSteps = 12; int assets = process.size(); var rsg = (InverseCumulativeRsg<RandomSequenceGenerator<MersenneTwisterUniformRng> ,InverseCumulativeNormal>) new PseudoRandom().make_sequence_generator(timeSteps*assets, seed); MultiPathGenerator<IRNG> generator=new MultiPathGenerator<IRNG>(process, new TimeGrid(length, timeSteps), rsg, false); int i; for (i=0; i<100; i++) generator.next(); Sample<MultiPath> sample = generator.next(); Vector calculated = new Vector(assets); double error, tolerance = 2.0e-7; for (int j=0; j<assets; j++) calculated[j] = sample.value[j].back() ; for (int j=0; j<assets; j++) { error = Math.Abs(calculated[j]-expected[j]); if (error > tolerance) { Assert.Fail("using " + tag + " process " + "(" + j+1 + " asset:)\n" //+ std::setprecision(13) + " calculated: " + calculated[j] + "\n" + " expected: " + expected[j] + "\n" + " error: " + error + "\n" + " tolerance: " + tolerance); } } sample = generator.antithetic(); for (int j=0; j<assets; j++) calculated[j] = sample.value[j].back(); for (int j=0; j<assets; j++) { error = Math.Abs(calculated[j]-antithetic[j]); if (error > tolerance) { Assert.Fail("using " + tag + " process " + "(" + j+1 + " asset:)\n" + "antithetic sample:\n" //+ std::setprecision(13) + " calculated: " + calculated[j] + "\n" + " expected: " + antithetic[j] + "\n" + " error: " + error + "\n" + " tolerance: " + tolerance); } } }
public void testMonteCarloCapletPricing() { //"Testing caplet LMM Monte-Carlo caplet pricing..." //SavedSettings backup; /* factor loadings are taken from Hull & White article plus extra normalisation to get orthogonal eigenvectors http://www.rotman.utoronto.ca/~amackay/fin/libormktmodel2.pdf */ double[] compValues = {0.85549771, 0.46707264, 0.22353259, 0.91915359, 0.37716089, 0.11360610, 0.96438280, 0.26413316,-0.01412414, 0.97939148, 0.13492952,-0.15028753, 0.95970595,-0.00000000,-0.28100621, 0.97939148,-0.13492952,-0.15028753, 0.96438280,-0.26413316,-0.01412414, 0.91915359,-0.37716089, 0.11360610, 0.85549771,-0.46707264, 0.22353259}; Matrix volaComp=new Matrix(9,3); List<double> lcompValues=new InitializedList<double>(27,0); List<double> ltemp = new InitializedList<double>(3, 0); lcompValues=compValues.ToList(); //std::copy(compValues, compValues+9*3, volaComp.begin()); for (int i = 0; i < 9; i++) { ltemp = lcompValues.GetRange(3*i, 3); for (int j = 0; j < 3; j++) volaComp[i, j] = ltemp[j]; } LiborForwardModelProcess process1 = makeProcess(); LiborForwardModelProcess process2 = makeProcess(volaComp); List<double> tmp = process1.fixingTimes(); TimeGrid grid=new TimeGrid(tmp ,12); List<int> location=new List<int>(); for (int i=0; i < tmp.Count; ++i) { location.Add(grid.index(tmp[i])) ; } // set-up a small Monte-Carlo simulation to price caplets // and ratchet caps using a one- and a three factor libor market model ulong seed = 42; LowDiscrepancy.icInstance = new InverseCumulativeNormal(); IRNG rsg1 = (IRNG)new LowDiscrepancy().make_sequence_generator( process1.factors()*(grid.size()-1), seed); IRNG rsg2 = (IRNG)new LowDiscrepancy().make_sequence_generator( process2.factors()*(grid.size()-1), seed); MultiPathGenerator<IRNG> generator1=new MultiPathGenerator<IRNG> (process1, grid, rsg1, false); MultiPathGenerator<IRNG> generator2=new MultiPathGenerator<IRNG> (process2, grid, rsg2, false); const int nrTrails = 250000; List<GeneralStatistics> stat1 = new InitializedList<GeneralStatistics>(process1.size()); List<GeneralStatistics> stat2 = new InitializedList<GeneralStatistics>(process2.size()); List<GeneralStatistics> stat3 = new InitializedList<GeneralStatistics>(process2.size() - 1); for (int i=0; i<nrTrails; ++i) { Sample<MultiPath> path1 = generator1.next(); Sample<MultiPath> path2 = generator2.next(); List<double> rates1=new InitializedList<double>(len); List<double> rates2 = new InitializedList<double>(len); for (int j=0; j<process1.size(); ++j) { rates1[j] = path1.value[j][location[j]]; rates2[j] = path2.value[j][location[j]]; } List<double> dis1 = process1.discountBond(rates1); List<double> dis2 = process2.discountBond(rates2); for (int k=0; k<process1.size(); ++k) { double accrualPeriod = process1.accrualEndTimes()[k] - process1.accrualStartTimes()[k]; // caplet payoff function, cap rate at 4% double payoff1 = Math.Max(rates1[k] - 0.04, 0.0) * accrualPeriod; double payoff2 = Math.Max(rates2[k] - 0.04, 0.0) * accrualPeriod; stat1[k].add(dis1[k] * payoff1); stat2[k].add(dis2[k] * payoff2); if (k != 0) { // ratchet cap payoff function double payoff3 = Math.Max(rates2[k] - (rates2[k-1]+0.0025), 0.0) * accrualPeriod; stat3[k-1].add(dis2[k] * payoff3); } } } double[] capletNpv = {0.000000000000, 0.000002841629, 0.002533279333, 0.009577143571, 0.017746502618, 0.025216116835, 0.031608230268, 0.036645683881, 0.039792254012, 0.041829864365}; double[] ratchetNpv = {0.0082644895, 0.0082754754, 0.0082159966, 0.0082982822, 0.0083803357, 0.0084366961, 0.0084173270, 0.0081803406, 0.0079533814}; for (int k=0; k < process1.size(); ++k) { double calculated1 = stat1[k].mean(); double tolerance1 = stat1[k].errorEstimate(); double expected = capletNpv[k]; if (Math.Abs(calculated1 - expected) > tolerance1) { Assert.Fail("Failed to reproduce expected caplet NPV" + "\n calculated: " + calculated1 + "\n error int: " + tolerance1 + "\n expected: " + expected); } double calculated2 = stat2[k].mean(); double tolerance2 = stat2[k].errorEstimate(); if (Math.Abs(calculated2 - expected) > tolerance2) { Assert.Fail("Failed to reproduce expected caplet NPV" + "\n calculated: " + calculated2 + "\n error int: " + tolerance2 + "\n expected: " + expected); } if (k != 0) { double calculated3 = stat3[k-1].mean(); double tolerance3 = stat3[k-1].errorEstimate(); expected = ratchetNpv[k-1]; double refError = 1e-5; // 1e-5. error bars of the reference values if (Math.Abs(calculated3 - expected) > tolerance3 + refError) { Assert.Fail("Failed to reproduce expected caplet NPV" + "\n calculated: " + calculated3 + "\n error int: " + tolerance3 + refError + "\n expected: " + expected); } } } }
public void testMonteCarloCapletPricing() { //"Testing caplet LMM Monte-Carlo caplet pricing..." //SavedSettings backup; /* factor loadings are taken from Hull & White article * plus extra normalisation to get orthogonal eigenvectors * http://www.rotman.utoronto.ca/~amackay/fin/libormktmodel2.pdf */ double[] compValues = { 0.85549771, 0.46707264, 0.22353259, 0.91915359, 0.37716089, 0.11360610, 0.96438280, 0.26413316, -0.01412414, 0.97939148, 0.13492952, -0.15028753, 0.95970595, -0.00000000, -0.28100621, 0.97939148, -0.13492952, -0.15028753, 0.96438280, -0.26413316, -0.01412414, 0.91915359, -0.37716089, 0.11360610, 0.85549771, -0.46707264, 0.22353259 }; Matrix volaComp = new Matrix(9, 3); List <double> lcompValues = new InitializedList <double>(27, 0); List <double> ltemp = new InitializedList <double>(3, 0); lcompValues = compValues.ToList(); //std::copy(compValues, compValues+9*3, volaComp.begin()); for (int i = 0; i < 9; i++) { ltemp = lcompValues.GetRange(3 * i, 3); for (int j = 0; j < 3; j++) { volaComp[i, j] = ltemp[j]; } } LiborForwardModelProcess process1 = makeProcess(); LiborForwardModelProcess process2 = makeProcess(volaComp); List <double> tmp = process1.fixingTimes(); TimeGrid grid = new TimeGrid(tmp, 12); List <int> location = new List <int>(); for (int i = 0; i < tmp.Count; ++i) { location.Add(grid.index(tmp[i])); } // set-up a small Monte-Carlo simulation to price caplets // and ratchet caps using a one- and a three factor libor market model ulong seed = 42; LowDiscrepancy.icInstance = new InverseCumulativeNormal(); IRNG rsg1 = (IRNG) new LowDiscrepancy().make_sequence_generator( process1.factors() * (grid.size() - 1), seed); IRNG rsg2 = (IRNG) new LowDiscrepancy().make_sequence_generator( process2.factors() * (grid.size() - 1), seed); MultiPathGenerator <IRNG> generator1 = new MultiPathGenerator <IRNG> (process1, grid, rsg1, false); MultiPathGenerator <IRNG> generator2 = new MultiPathGenerator <IRNG> (process2, grid, rsg2, false); const int nrTrails = 250000; List <GeneralStatistics> stat1 = new InitializedList <GeneralStatistics>(process1.size()); List <GeneralStatistics> stat2 = new InitializedList <GeneralStatistics>(process2.size()); List <GeneralStatistics> stat3 = new InitializedList <GeneralStatistics>(process2.size() - 1); for (int i = 0; i < nrTrails; ++i) { Sample <MultiPath> path1 = generator1.next(); Sample <MultiPath> path2 = generator2.next(); List <double> rates1 = new InitializedList <double>(len); List <double> rates2 = new InitializedList <double>(len); for (int j = 0; j < process1.size(); ++j) { rates1[j] = path1.value[j][location[j]]; rates2[j] = path2.value[j][location[j]]; } List <double> dis1 = process1.discountBond(rates1); List <double> dis2 = process2.discountBond(rates2); for (int k = 0; k < process1.size(); ++k) { double accrualPeriod = process1.accrualEndTimes()[k] - process1.accrualStartTimes()[k]; // caplet payoff function, cap rate at 4% double payoff1 = Math.Max(rates1[k] - 0.04, 0.0) * accrualPeriod; double payoff2 = Math.Max(rates2[k] - 0.04, 0.0) * accrualPeriod; stat1[k].add(dis1[k] * payoff1); stat2[k].add(dis2[k] * payoff2); if (k != 0) { // ratchet cap payoff function double payoff3 = Math.Max(rates2[k] - (rates2[k - 1] + 0.0025), 0.0) * accrualPeriod; stat3[k - 1].add(dis2[k] * payoff3); } } } double[] capletNpv = { 0.000000000000, 0.000002841629, 0.002533279333, 0.009577143571, 0.017746502618, 0.025216116835, 0.031608230268, 0.036645683881, 0.039792254012, 0.041829864365 }; double[] ratchetNpv = { 0.0082644895, 0.0082754754, 0.0082159966, 0.0082982822, 0.0083803357, 0.0084366961, 0.0084173270, 0.0081803406, 0.0079533814 }; for (int k = 0; k < process1.size(); ++k) { double calculated1 = stat1[k].mean(); double tolerance1 = stat1[k].errorEstimate(); double expected = capletNpv[k]; if (Math.Abs(calculated1 - expected) > tolerance1) { Assert.Fail("Failed to reproduce expected caplet NPV" + "\n calculated: " + calculated1 + "\n error int: " + tolerance1 + "\n expected: " + expected); } double calculated2 = stat2[k].mean(); double tolerance2 = stat2[k].errorEstimate(); if (Math.Abs(calculated2 - expected) > tolerance2) { Assert.Fail("Failed to reproduce expected caplet NPV" + "\n calculated: " + calculated2 + "\n error int: " + tolerance2 + "\n expected: " + expected); } if (k != 0) { double calculated3 = stat3[k - 1].mean(); double tolerance3 = stat3[k - 1].errorEstimate(); expected = ratchetNpv[k - 1]; double refError = 1e-5; // 1e-5. error bars of the reference values if (Math.Abs(calculated3 - expected) > tolerance3 + refError) { Assert.Fail("Failed to reproduce expected caplet NPV" + "\n calculated: " + calculated3 + "\n error int: " + tolerance3 + refError + "\n expected: " + expected); } } } }
public void testSwaptionPricing() { //"Testing forward swap and swaption pricing..."); //SavedSettings backup; const int size = 10; const int steps = 8*size; #if QL_USE_INDEXED_COUPON const double tolerance = 1e-6; #else const double tolerance = 1e-12; #endif List<Date> dates = new List<Date>(); List<double> rates = new List<double>(); dates.Add(new Date(4,9,2005)); dates.Add(new Date(4,9,2011)); rates.Add(0.04); rates.Add(0.08); IborIndex index = makeIndex(dates, rates); LiborForwardModelProcess process = new LiborForwardModelProcess(size, index); LmCorrelationModel corrModel = new LmExponentialCorrelationModel(size, 0.5); LmVolatilityModel volaModel = new LmLinearExponentialVolatilityModel(process.fixingTimes(), 0.291, 1.483, 0.116, 0.00001); // set-up pricing engine process.setCovarParam((LfmCovarianceParameterization) new LfmCovarianceProxy(volaModel, corrModel)); // set-up a small Monte-Carlo simulation to price swations List<double> tmp = process.fixingTimes(); TimeGrid grid=new TimeGrid(tmp ,steps); List<int> location=new List<int>(); for (int i=0; i < tmp.Count; ++i) { location.Add(grid.index(tmp[i])) ; } ulong seed=42; const int nrTrails = 5000; LowDiscrepancy.icInstance = new InverseCumulativeNormal(); IRNG rsg = (InverseCumulativeRsg<RandomSequenceGenerator<MersenneTwisterUniformRng> ,InverseCumulativeNormal>) new PseudoRandom().make_sequence_generator(process.factors()*(grid.size()-1),seed); MultiPathGenerator<IRNG> generator=new MultiPathGenerator<IRNG>(process, grid, rsg, false); LiborForwardModel liborModel = new LiborForwardModel(process, volaModel, corrModel); Calendar calendar = index.fixingCalendar(); DayCounter dayCounter = index.forwardingTermStructure().link.dayCounter(); BusinessDayConvention convention = index.businessDayConvention(); Date settlement = index.forwardingTermStructure().link.referenceDate(); SwaptionVolatilityMatrix m = liborModel.getSwaptionVolatilityMatrix(); for (int i=1; i < size; ++i) { for (int j=1; j <= size-i; ++j) { Date fwdStart = settlement + new Period(6*i, TimeUnit.Months); Date fwdMaturity = fwdStart + new Period(6*j, TimeUnit.Months); Schedule schedule =new Schedule(fwdStart, fwdMaturity, index.tenor(), calendar, convention, convention, DateGeneration.Rule.Forward, false); double swapRate = 0.0404; VanillaSwap forwardSwap = new VanillaSwap(VanillaSwap.Type.Receiver, 1.0, schedule, swapRate, dayCounter, schedule, index, 0.0, index.dayCounter()); forwardSwap.setPricingEngine(new DiscountingSwapEngine(index.forwardingTermStructure())); // check forward pricing first double expected = forwardSwap.fairRate(); double calculated = liborModel.S_0(i-1,i+j-1); if (Math.Abs(expected - calculated) > tolerance) Assert.Fail("Failed to reproduce fair forward swap rate" + "\n calculated: " + calculated + "\n expected: " + expected); swapRate = forwardSwap.fairRate(); forwardSwap = new VanillaSwap(VanillaSwap.Type.Receiver, 1.0, schedule, swapRate, dayCounter, schedule, index, 0.0, index.dayCounter()); forwardSwap.setPricingEngine(new DiscountingSwapEngine(index.forwardingTermStructure())); if (i == j && i<=size/2) { IPricingEngine engine = new LfmSwaptionEngine(liborModel, index.forwardingTermStructure()); Exercise exercise = new EuropeanExercise(process.fixingDates()[i]); Swaption swaption = new Swaption(forwardSwap, exercise); swaption.setPricingEngine(engine); GeneralStatistics stat = new GeneralStatistics(); for (int n=0; n<nrTrails; ++n) { Sample<MultiPath> path = (n%2!=0) ? generator.antithetic() : generator.next(); //Sample<MultiPath> path = generator.next(); List<double> rates_ = new InitializedList<double>(size); for (int k=0; k<process.size(); ++k) { rates_[k] = path.value[k][location[i]]; } List<double> dis = process.discountBond(rates_); double npv=0.0; for (int k=i; k < i+j; ++k) { npv += (swapRate - rates_[k]) * ( process.accrualEndTimes()[k] - process.accrualStartTimes()[k])*dis[k]; } stat.add(Math.Max(npv, 0.0)); } if (Math.Abs(swaption.NPV() - stat.mean()) > stat.errorEstimate()*2.35) Assert.Fail("Failed to reproduce swaption npv" + "\n calculated: " + stat.mean() + "\n expected: " + swaption.NPV()); } } } }
public void testCallableEquityPricing() { // Testing the pricing of a callable equity product /* * For the definition of the example product see * Alexander Giese, On the Pricing of Auto-Callable Equity * Structures in the Presence of Stochastic Volatility and * Stochastic Interest Rates . * http://workshop.mathfinance.de/2006/papers/giese/slides.pdf */ int maturity = 7; DayCounter dc = new Actual365Fixed(); Date today = Date.Today; Settings.Instance.setEvaluationDate(today); Handle <Quote> spot = new Handle <Quote>(new SimpleQuote(100.0)); SimpleQuote qRate = new SimpleQuote(0.04); Handle <YieldTermStructure> qTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, qRate, dc)); SimpleQuote rRate = new SimpleQuote(0.04); Handle <YieldTermStructure> rTS = new Handle <YieldTermStructure>(Utilities.flatRate(today, rRate, dc)); HestonProcess hestonProcess = new HestonProcess(rTS, qTS, spot, 0.0625, 1.0, 0.24 * 0.24, 1e-4, 0.0); // FLOATING_POINT_EXCEPTION HullWhiteForwardProcess hwProcess = new HullWhiteForwardProcess(rTS, 0.00883, 0.00526); hwProcess.setForwardMeasureTime(dc.yearFraction(today, today + new Period(maturity + 1, TimeUnit.Years))); HybridHestonHullWhiteProcess jointProcess = new HybridHestonHullWhiteProcess(hestonProcess, hwProcess, -0.4); Schedule schedule = new Schedule(today, today + new Period(maturity, TimeUnit.Years), new Period(1, TimeUnit.Years), new TARGET(), BusinessDayConvention.Following, BusinessDayConvention.Following, DateGeneration.Rule.Forward, false); List <double> times = new InitializedList <double>(maturity + 1); for (int i = 0; i <= maturity; ++i) { times[i] = i; } TimeGrid grid = new TimeGrid(times, times.Count); List <double> redemption = new InitializedList <double>(maturity); for (int i = 0; i < maturity; ++i) { redemption[i] = 1.07 + 0.03 * i; } ulong seed = 42; IRNG rsg = (InverseCumulativeRsg <RandomSequenceGenerator <MersenneTwisterUniformRng> , InverseCumulativeNormal>) new PseudoRandom().make_sequence_generator(jointProcess.factors() * (grid.size() - 1), seed); MultiPathGenerator <IRNG> generator = new MultiPathGenerator <IRNG>(jointProcess, grid, rsg, false); GeneralStatistics stat = new GeneralStatistics(); double antitheticPayoff = 0; int nrTrails = 40000; for (int i = 0; i < nrTrails; ++i) { bool antithetic = (i % 2) != 0; Sample <IPath> path = antithetic ? generator.antithetic() : generator.next(); MultiPath value = path.value as MultiPath; Utils.QL_REQUIRE(value != null, () => "Invalid Path"); double payoff = 0; for (int j = 1; j <= maturity; ++j) { if (value[0][j] > spot.link.value()) { Vector states = new Vector(3); for (int k = 0; k < 3; ++k) { states[k] = value[k][j]; } payoff = redemption[j - 1] / jointProcess.numeraire(grid[j], states); break; } else if (j == maturity) { Vector states = new Vector(3); for (int k = 0; k < 3; ++k) { states[k] = value[k][j]; } payoff = 1.0 / jointProcess.numeraire(grid[j], states); } } if (antithetic) { stat.add(0.5 * (antitheticPayoff + payoff)); } else { antitheticPayoff = payoff; } } double expected = 0.938; double calculated = stat.mean(); double error = stat.errorEstimate(); if (Math.Abs(expected - calculated) > 3 * error) { QAssert.Fail("Failed to reproduce auto-callable equity structure price" + "\n calculated: " + calculated + "\n error: " + error + "\n expected: " + expected); } }
public void testZeroBondPricing() { // Testing Monte-Carlo zero bond pricing DayCounter dc = new Actual360(); Date today = Date.Today; Settings.Instance.setEvaluationDate(today); // construct a strange yield curve to check drifts and discounting // of the joint stochastic process List <Date> dates = new List <Date>(); List <double> times = new List <double>(); List <double> rates = new List <double>(); dates.Add(today); rates.Add(0.02); times.Add(0.0); for (int i = 120; i < 240; ++i) { dates.Add(today + new Period(i, TimeUnit.Months)); rates.Add(0.02 + 0.0002 * Math.Exp(Math.Sin(i / 8.0))); times.Add(dc.yearFraction(today, dates.Last())); } Date maturity = dates.Last() + new Period(10, TimeUnit.Years); dates.Add(maturity); rates.Add(0.04); //times.Add(dc.yearFraction(today, dates.Last())); Handle <Quote> s0 = new Handle <Quote>(new SimpleQuote(100)); Handle <YieldTermStructure> ts = new Handle <YieldTermStructure>(new InterpolatedZeroCurve <Linear>(dates, rates, dc)); Handle <YieldTermStructure> ds = new Handle <YieldTermStructure>(Utilities.flatRate(today, 0.0, dc)); HestonProcess hestonProcess = new HestonProcess(ts, ds, s0, 0.02, 1.0, 0.2, 0.5, -0.8); HullWhiteForwardProcess hwProcess = new HullWhiteForwardProcess(ts, 0.05, 0.05); hwProcess.setForwardMeasureTime(dc.yearFraction(today, maturity)); HullWhite hwModel = new HullWhite(ts, 0.05, 0.05); HybridHestonHullWhiteProcess jointProcess = new HybridHestonHullWhiteProcess(hestonProcess, hwProcess, -0.4); TimeGrid grid = new TimeGrid(times); int factors = jointProcess.factors(); int steps = grid.size() - 1; SobolBrownianBridgeRsg rsg = new SobolBrownianBridgeRsg(factors, steps); MultiPathGenerator <SobolBrownianBridgeRsg> generator = new MultiPathGenerator <SobolBrownianBridgeRsg>( jointProcess, grid, rsg, false); int m = 90; List <GeneralStatistics> zeroStat = new InitializedList <GeneralStatistics>(m); List <GeneralStatistics> optionStat = new InitializedList <GeneralStatistics>(m); int nrTrails = 8191; int optionTenor = 24; double strike = 0.5; for (int i = 0; i < nrTrails; ++i) { Sample <IPath> path = generator.next(); MultiPath value = path.value as MultiPath; Utils.QL_REQUIRE(value != null, () => "Invalid Path"); for (int j = 1; j < m; ++j) { double t = grid[j]; // zero end and option maturity double T = grid[j + optionTenor]; // maturity of zero bond // of option Vector states = new Vector(3); Vector optionStates = new Vector(3); for (int k = 0; k < jointProcess.size(); ++k) { states[k] = value[k][j]; optionStates[k] = value[k][j + optionTenor]; } double zeroBond = 1.0 / jointProcess.numeraire(t, states); double zeroOption = zeroBond * Math.Max(0.0, hwModel.discountBond(t, T, states[2]) - strike); zeroStat[j].add(zeroBond); optionStat[j].add(zeroOption); } } for (int j = 1; j < m; ++j) { double t = grid[j]; double calculated = zeroStat[j].mean(); double expected = ts.link.discount(t); if (Math.Abs(calculated - expected) > 0.03) { QAssert.Fail("Failed to reproduce expected zero bond prices" + "\n t: " + t + "\n calculated: " + calculated + "\n expected: " + expected); } double T = grid[j + optionTenor]; calculated = optionStat[j].mean(); expected = hwModel.discountBondOption(Option.Type.Call, strike, t, T); if (Math.Abs(calculated - expected) > 0.0035) { QAssert.Fail("Failed to reproduce expected zero bond option prices" + "\n t: " + t + "\n T: " + T + "\n calculated: " + calculated + "\n expected: " + expected); } } }
public override void Reset() { PseudoRandom rsg = new PseudoRandom(); _pg = rsg.make_sequence_generator(_process.size() * (_grid.size() - 1), _seed) as MultiPathGenerator <InverseCumulativeRsg <RandomSequenceGenerator <MersenneTwisterUniformRng>, InverseCumulativeNormal> >; }