Example #1
0
        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());
                        }
                    }
                }
            }
        }
Example #2
0
        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);
                    }
                }
            }
        }