public void testLambdaBootstrapping()
{
//"Testing caplet LMM lambda bootstrapping..."
//SavedSettings backup;
double tolerance = 1e-10;
double[] lambdaExpected = { 14.3010297550, 19.3821411939, 15.9816590141,
15.9953118303, 14.0570815635, 13.5687599894,
12.7477197786, 13.7056638165, 11.6191989567 };
LiborForwardModelProcess process = makeProcess();
Matrix covar = process.covariance(0.0, null, 1.0);
for (int i = 0; i < 9; ++i)
{
double calculated = Math.Sqrt(covar[i + 1, i + 1]);
double expected = lambdaExpected[i] / 100;
if (Math.Abs(calculated - expected) > tolerance)
{
Assert.Fail("Failed to reproduce expected lambda values"
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}
}
LfmCovarianceParameterization param = process.covarParam();
List <double> tmp = process.fixingTimes();
TimeGrid grid = new TimeGrid(tmp.Last(), 14);
for (int t = 0; t < grid.size(); ++t)
{
//verifier la presence du null
Matrix diff = param.integratedCovariance(grid[t], null)
- param.integratedCovariance(grid[t], null);
for (int i = 0; i < diff.rows(); ++i)
{
for (int j = 0; j < diff.columns(); ++j)
{
if (Math.Abs(diff[i, j]) > tolerance)
{
Assert.Fail("Failed to reproduce integrated covariance"
+ "\n calculated: " + diff[i, j]
+ "\n expected: " + 0);
}
}
}
}
}
LiborForwardModelProcess makeProcess(Matrix volaComp)
{
int factors = (volaComp.empty() ? 1 : volaComp.columns());
IborIndex index = makeIndex();
LiborForwardModelProcess process = new LiborForwardModelProcess(len, index, null);
LfmCovarianceParameterization fct = new LfmHullWhiteParameterization(
process,
makeCapVolCurve(Settings.evaluationDate()),
volaComp * Matrix.transpose(volaComp), factors);
process.setCovarParam(fct);
return(process);
}
public void testInitialisation()
{
//"Testing caplet LMM process initialisation..."
//SavedSettings backup;
DayCounter dayCounter = new Actual360();
RelinkableHandle <YieldTermStructure> termStructure = new RelinkableHandle <YieldTermStructure>();;
termStructure.linkTo(Utilities.flatRate(Date.Today, 0.04, dayCounter));
IborIndex index = new Euribor6M(termStructure);
OptionletVolatilityStructure capletVol = new ConstantOptionletVolatility(
termStructure.currentLink().referenceDate(),
termStructure.currentLink().calendar(),
BusinessDayConvention.Following,
0.2,
termStructure.currentLink().dayCounter());
Calendar calendar = index.fixingCalendar();
for (int daysOffset = 0; daysOffset < 1825 /* 5 year*/; daysOffset += 8)
{
Date todaysDate = calendar.adjust(Date.Today + daysOffset);
Settings.setEvaluationDate(todaysDate);
Date settlementDate =
calendar.advance(todaysDate, index.fixingDays(), TimeUnit.Days);
termStructure.linkTo(Utilities.flatRate(settlementDate, 0.04, dayCounter));
LiborForwardModelProcess process = new LiborForwardModelProcess(60, index);
List <double> fixings = process.fixingTimes();
for (int i = 1; i < fixings.Count - 1; ++i)
{
int ileft = process.nextIndexReset(fixings[i] - 0.000001);
int iright = process.nextIndexReset(fixings[i] + 0.000001);
int ii = process.nextIndexReset(fixings[i]);
if ((ileft != i) || (iright != i + 1) || (ii != i + 1))
{
Assert.Fail("Failed to next index resets");
}
}
}
}
public void testCapletPricing()
{
//"Testing caplet pricing...";
//SavedSettings backup;
const int size = 10;
#if QL_USE_INDEXED_COUPON
const double tolerance = 1e-5;
#else
const double tolerance = 1e-12;
#endif
IborIndex index = makeIndex();
LiborForwardModelProcess process = new LiborForwardModelProcess(size, index);
// set-up pricing engine
OptionletVolatilityStructure capVolCurve = makeCapVolCurve(Settings.evaluationDate());
Vector variances = new LfmHullWhiteParameterization(process, capVolCurve).covariance(0.0, null).diagonal();
LmVolatilityModel volaModel = new LmFixedVolatilityModel(Vector.Sqrt(variances), process.fixingTimes());
LmCorrelationModel corrModel = new LmExponentialCorrelationModel(size, 0.3);
IAffineModel model = (IAffineModel)(new LiborForwardModel(process, volaModel, corrModel));
Handle <YieldTermStructure> termStructure = process.index().forwardingTermStructure();
AnalyticCapFloorEngine engine1 = new AnalyticCapFloorEngine(model, termStructure);
Cap cap1 = new Cap(process.cashFlows(),
new InitializedList <double>(size, 0.04));
cap1.setPricingEngine(engine1);
const double expected = 0.015853935178;
double calculated = cap1.NPV();
if (Math.Abs(expected - calculated) > tolerance)
{
Assert.Fail("Failed to reproduce npv"
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}
}
CapletVarianceCurve makeCapVolCurve(Date todaysDate)
{
double[] vols = { 14.40, 17.15, 16.81, 16.64, 16.17,
15.78, 15.40, 15.21, 14.86, 14.54 };
List <Date> dates = new List <Date>();
List <double> capletVols = new List <double>();
LiborForwardModelProcess process = new LiborForwardModelProcess(len + 1, makeIndex(), null);
for (int i = 0; i < len; ++i)
{
capletVols.Add(vols[i] / 100);
dates.Add(process.fixingDates()[i + 1]);
}
return(new CapletVarianceCurve(todaysDate, dates,
capletVols, new ActualActual()));
}
OptionletVolatilityStructure makeCapVolCurve(Date todaysDate)
{
double[] vols = { 14.40, 17.15, 16.81, 16.64, 16.17,
15.78, 15.40, 15.21, 14.86 };
List <Date> dates = new List <Date>();
List <double> capletVols = new List <double>();
LiborForwardModelProcess process =
new LiborForwardModelProcess(10, makeIndex());
for (int i = 0; i < 9; ++i)
{
capletVols.Add(vols[i] / 100);
dates.Add(process.fixingDates()[i + 1]);
}
return(new CapletVarianceCurve(todaysDate, dates,
capletVols, new Actual360()));
}
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 testCalibration()
{
// Testing calibration of a Libor forward model
const int size = 14;
const double tolerance = 8e-3;
double[] capVols = { 0.145708, 0.158465, 0.166248, 0.168672,
0.169007, 0.167956, 0.166261, 0.164239,
0.162082, 0.159923, 0.157781, 0.155745,
0.153776, 0.151950, 0.150189, 0.148582,
0.147034, 0.145598, 0.144248 };
double[] swaptionVols = { 0.170595, 0.166844, 0.158306, 0.147444,
0.136930, 0.126833, 0.118135, 0.175963,
0.166359, 0.155203, 0.143712, 0.132769,
0.122947, 0.114310, 0.174455, 0.162265,
0.150539, 0.138734, 0.128215, 0.118470,
0.110540, 0.169780, 0.156860, 0.144821,
0.133537, 0.123167, 0.114363, 0.106500,
0.164521, 0.151223, 0.139670, 0.128632,
0.119123, 0.110330, 0.103114, 0.158956,
0.146036, 0.134555, 0.124393, 0.115038,
0.106996, 0.100064 };
IborIndex index = makeIndex();
LiborForwardModelProcess process = new LiborForwardModelProcess(size, index);
Handle <YieldTermStructure> termStructure = index.forwardingTermStructure();
// set-up the model
LmVolatilityModel volaModel = new LmExtLinearExponentialVolModel(process.fixingTimes(),
0.5, 0.6, 0.1, 0.1);
LmCorrelationModel corrModel = new LmLinearExponentialCorrelationModel(size, 0.5, 0.8);
LiborForwardModel model = new LiborForwardModel(process, volaModel, corrModel);
int swapVolIndex = 0;
DayCounter dayCounter = index.forwardingTermStructure().link.dayCounter();
// set-up calibration helper
List <CalibrationHelper> calibrationHelper = new List <CalibrationHelper>();
int i;
for (i = 2; i < size; ++i)
{
Period maturity = i * index.tenor();
Handle <Quote> capVol = new Handle <Quote>(new SimpleQuote(capVols[i - 2]));
CalibrationHelper caphelper = new CapHelper(maturity, capVol, index, Frequency.Annual,
index.dayCounter(), true, termStructure, CalibrationHelper.CalibrationErrorType.ImpliedVolError);
caphelper.setPricingEngine(new AnalyticCapFloorEngine(model, termStructure));
calibrationHelper.Add(caphelper);
if (i <= size / 2)
{
// add a few swaptions to test swaption calibration as well
for (int j = 1; j <= size / 2; ++j)
{
Period len = j * index.tenor();
Handle <Quote> swaptionVol = new Handle <Quote>(
new SimpleQuote(swaptionVols[swapVolIndex++]));
CalibrationHelper swaptionHelper =
new SwaptionHelper(maturity, len, swaptionVol, index,
index.tenor(), dayCounter,
index.dayCounter(),
termStructure, CalibrationHelper.CalibrationErrorType.ImpliedVolError);
swaptionHelper.setPricingEngine(new LfmSwaptionEngine(model, termStructure));
calibrationHelper.Add(swaptionHelper);
}
}
}
LevenbergMarquardt om = new LevenbergMarquardt(1e-6, 1e-6, 1e-6);
//ConjugateGradient gc = new ConjugateGradient();
model.calibrate(calibrationHelper,
om,
new EndCriteria(2000, 100, 1e-6, 1e-6, 1e-6),
new Constraint(),
new List <double>());
// measure the calibration error
double calculated = 0.0;
for (i = 0; i < calibrationHelper.Count; ++i)
{
double diff = calibrationHelper[i].calibrationError();
calculated += diff * diff;
}
if (Math.Sqrt(calculated) > tolerance)
{
QAssert.Fail("Failed to calibrate libor forward model"
+ "\n calculated diff: " + Math.Sqrt(calculated)
+ "\n expected : smaller than " + tolerance);
}
}
public void testSimpleCovarianceModels()
{
// Testing simple covariance models
const int size = 10;
const double tolerance = 1e-14;
int i;
LmCorrelationModel corrModel = new LmExponentialCorrelationModel(size, 0.1);
Matrix recon = corrModel.correlation(0.0, null)
- corrModel.pseudoSqrt(0.0, null) * Matrix.transpose(corrModel.pseudoSqrt(0.0, null));
for (i = 0; i < size; ++i)
{
for (int j = 0; j < size; ++j)
{
if (Math.Abs(recon[i, j]) > tolerance)
{
QAssert.Fail("Failed to reproduce correlation matrix"
+ "\n calculated: " + recon[i, j]
+ "\n expected: " + 0);
}
}
}
List <double> fixingTimes = new InitializedList <double>(size);
for (i = 0; i < size; ++i)
{
fixingTimes[i] = 0.5 * i;
}
const double a = 0.2;
const double b = 0.1;
const double c = 2.1;
const double d = 0.3;
LmVolatilityModel volaModel = new LmLinearExponentialVolatilityModel(fixingTimes, a, b, c, d);
LfmCovarianceProxy covarProxy = new LfmCovarianceProxy(volaModel, corrModel);
LiborForwardModelProcess process = new LiborForwardModelProcess(size, makeIndex());
LiborForwardModel liborModel = new LiborForwardModel(process, volaModel, corrModel);
for (double t = 0; t < 4.6; t += 0.31)
{
recon = covarProxy.covariance(t, null)
- covarProxy.diffusion(t, null) * Matrix.transpose(covarProxy.diffusion(t, null));
for (int k = 0; k < size; ++k)
{
for (int j = 0; j < size; ++j)
{
if (Math.Abs(recon[k, j]) > tolerance)
{
QAssert.Fail("Failed to reproduce correlation matrix"
+ "\n calculated: " + recon[k, j]
+ "\n expected: " + 0);
}
}
}
Vector volatility = volaModel.volatility(t, null);
for (int k = 0; k < size; ++k)
{
double expected = 0;
if (k > 2 * t)
{
double T = fixingTimes[k];
expected = (a * (T - t) + d) * Math.Exp(-b * (T - t)) + c;
}
if (Math.Abs(expected - volatility[k]) > tolerance)
{
QAssert.Fail("Failed to reproduce volatities"
+ "\n calculated: " + volatility[k]
+ "\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);
}
}
}
}
