public void testCachedHullWhite()
{
//("Testing Hull-White calibration against cached values...");
Date today=new Date(15, Month.February, 2002);
Date settlement=new Date(19, Month.February, 2002);
Settings.setEvaluationDate(today);
Handle<YieldTermStructure> termStructure=
new Handle<YieldTermStructure>(Utilities.flatRate(settlement, 0.04875825, new Actual365Fixed()));
//termStructure.link
HullWhite model=new HullWhite(termStructure);
CalibrationData[] data = { new CalibrationData( 1, 5, 0.1148 ),
new CalibrationData( 2, 4, 0.1108 ),
new CalibrationData( 3, 3, 0.1070 ),
new CalibrationData( 4, 2, 0.1021 ),
new CalibrationData( 5, 1, 0.1000 )};
IborIndex index = new Euribor6M(termStructure);
IPricingEngine engine = new JamshidianSwaptionEngine(model);
List<CalibrationHelper> swaptions = new List<CalibrationHelper>();
for (int i=0; i<data.Length; i++) {
Quote vol = new SimpleQuote(data[i].volatility);
CalibrationHelper helper =
new SwaptionHelper(new Period(data[i].start,TimeUnit.Years),
new Period(data[i].length, TimeUnit.Years),
new Handle<Quote>(vol),
index,
new Period(1, TimeUnit.Years),
new Thirty360(),
new Actual360(),
termStructure);
helper.setPricingEngine(engine);
swaptions.Add(helper);
}
// Set up the optimization problem
// Real simplexLambda = 0.1;
// Simplex optimizationMethod(simplexLambda);
LevenbergMarquardt optimizationMethod = new LevenbergMarquardt(1.0e-8,1.0e-8,1.0e-8);
EndCriteria endCriteria = new EndCriteria(10000, 100, 1e-6, 1e-8, 1e-8);
//Optimize
model.calibrate(swaptions, optimizationMethod, endCriteria, new Constraint(),new List<double>());
EndCriteria.Type ecType = model.endCriteria();
// Check and print out results
#if QL_USE_INDEXED_COUPON
double cachedA = 0.0488199, cachedSigma = 0.00593579;
#else
double cachedA = 0.0488565, cachedSigma = 0.00593662;
#endif
double tolerance = 1.120e-5;
//double tolerance = 1.0e-6;
Vector xMinCalculated = model.parameters();
double yMinCalculated = model.value(xMinCalculated, swaptions);
Vector xMinExpected = new Vector(2);
xMinExpected[0]= cachedA;
xMinExpected[1]= cachedSigma;
double yMinExpected = model.value(xMinExpected, swaptions);
if (Math.Abs(xMinCalculated[0]-cachedA) > tolerance
|| Math.Abs(xMinCalculated[1]-cachedSigma) > tolerance) {
Assert.Fail ("Failed to reproduce cached calibration results:\n"
+ "calculated: a = " + xMinCalculated[0] + ", "
+ "sigma = " + xMinCalculated[1] + ", "
+ "f(a) = " + yMinCalculated + ",\n"
+ "expected: a = " + xMinExpected[0] + ", "
+ "sigma = " + xMinExpected[1] + ", "
+ "f(a) = " + yMinExpected + ",\n"
+ "difference: a = " + (xMinCalculated[0]-xMinExpected[0]) + ", "
+ "sigma = " + (xMinCalculated[1]-xMinExpected[1]) + ", "
+ "f(a) = " + (yMinCalculated - yMinExpected) + ",\n"
+ "end criteria = " + ecType );
}
}
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);
}
