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 testCalibration()
{
//("Testing calibration of a Libor forward model...");
//SavedSettings backup;
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)
Assert.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...";
//SavedSettings backup;
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)
Assert.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)
Assert.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)
Assert.Fail("Failed to reproduce volatities"
+ "\n calculated: " + volatility[k]
+ "\n expected: " + expected);
}
}
}
