double caplet_lmm(const Date& todaysDate_,
const Date& settlementDate_,
const Date& maturity_,
Rate spot_,
Rate strike,
Rate Numeraire, //zero-coupon bond
//Volatility volatility
double correl,
double a,
double b,
double c,
double d
)
{
//SavedSettings backup;
const Size size = 10;
#if defined(QL_USE_INDEXED_COUPON)
const Real tolerance = 1e-5;
#else
const Real tolerance = 1e-12;
#endif
boost::shared_ptr<IborIndex> index = makeIndex();
boost::shared_ptr<LiborForwardModelProcess> process(new LiborForwardModelProcess(size, index));
// set-up pricing engine
const boost::shared_ptr<OptionletVolatilityStructure> capVolCurve = makeCapVolCurve(Settings::instance().evaluationDate());
Array variances = LfmHullWhiteParameterization(process, capVolCurve).covariance(0.0).diagonal();
boost::shared_ptr<LmVolatilityModel> volaModel(new LmFixedVolatilityModel(Sqrt(variances),process->fixingTimes()));
boost::shared_ptr<LmCorrelationModel> corrModel(new LmExponentialCorrelationModel(size, correl));
boost::shared_ptr<AffineModel> model(new LiborForwardModel(process, volaModel, corrModel));
const Handle<YieldTermStructure> termStructure = process->index()->forwardingTermStructure();
boost::shared_ptr<AnalyticCapFloorEngine> engine1(new AnalyticCapFloorEngine(model, termStructure));
boost::shared_ptr<Cap> cap1(new Cap(process->cashFlows(),std::vector<Rate>(size, strike)));
cap1->setPricingEngine(engine1);
return cap1->NPV();
}
boost::shared_ptr<AnalyticCapFloorEngine> MustCapFloor::setEngineQuantLibLMM(){
CurveData cData;
// Fill out with some sample market data
cData.sampleMktData(cData);
//Date today(10, October, 2014);
//Settings::instance().evaluationDate() = today;
// Build a curve linked to this market data
boost::shared_ptr<YieldTermStructure> ocurve = (cData.buildCurve(cData));
// Link the curve to the term structure
boost::shared_ptr<IborIndex> index = boost::shared_ptr<IborIndex>(new Euribor6M(forwardingTermStructure));
Date todaysDate =
myIndex->fixingCalendar().adjust(today);
Settings::instance().evaluationDate() = todaysDate;
this->forwardingTermStructure.linkTo(ocurve);
const Size size = floatingLeg.size();
boost::shared_ptr<LiborForwardModelProcess> process(
new LiborForwardModelProcess(size, myIndex));
//// set-up the model
///* const Real a = 0.02;
//const Real b = 0.12;
//const Real c = 0.1;
//const Real d = 0.01;*/
const Real a = 0.025;
const Real b = 0.12;
const Real c = 0.1;
const Real d = 0.01;
boost::shared_ptr<LmVolatilityModel> volaModel(
new LmLinearExponentialVolatilityModel(process->fixingTimes(), a, b, c, d));
boost::shared_ptr<LmCorrelationModel> corrModel(
new LmLinearExponentialCorrelationModel(size, 0.1, 0.1));
boost::shared_ptr<LiborForwardModel> liborModel(
new LiborForwardModel(process, volaModel, corrModel));
return boost::shared_ptr<AnalyticCapFloorEngine> (
new AnalyticCapFloorEngine(liborModel, forwardingTermStructure));
}
void test1Y10(boost::shared_ptr<IborIndex> libor,
utilities::csvBuilder & file) {
std::cout << "Testing calibration of a Libor forward model with 1Y10 settings..."
<< std::endl;
/* basic settings */
SavedSettings backup;
const Size size_ = 44; // 44 trimesters
const Real tolerance_ = 8e-3; // tolerance
boost::shared_ptr<IborIndex> libor = curveCreation();
std::vector<swaptionData> swaptions // swaption data
= std::vector<swaptionData> {
//{ 50.200, Period(1, Months), Period(1, Years) },
{ 54.475, Period(3, Months), Period(1, Years) },
{ 63.350, Period(6, Months), Period(1, Years) },
//{ 68.650, Period(1, Years), Period(1, Years) },
//{ 49.850, Period(2, Years), Period(1, Years) },
//{ 38.500, Period(3, Years), Period(1, Years) },
//{ 31.900, Period(4, Years), Period(1, Years) },
//{ 28.500, Period(5, Years), Period(1, Years) },
{ 26.500, Period(6, Years), Period(1, Years) },
{ 24.625, Period(7, Years), Period(1, Years) },
{ 23.500, Period(8, Years), Period(1, Years) },
{ 22.550, Period(9, Years), Period(1, Years) },
{ 21.150, Period(10, Years), Period(1, Years) },
//{ 60.950, Period(1, Months), Period(2, Years) },
{ 55.700, Period(3, Months), Period(2, Years) },
{ 58.100, Period(6, Months), Period(2, Years) },
{ 56.550, Period(1, Years), Period(2, Years) },
//{ 42.600, Period(2, Years), Period(2, Years) },
//{ 34.300, Period(3, Years), Period(2, Years) },
//{ 29.400, Period(4, Years), Period(2, Years) },
{ 26.900, Period(5, Years), Period(2, Years) },
{ 25.050, Period(6, Years), Period(2, Years) },
{ 23.800, Period(7, Years), Period(2, Years) },
{ 22.700, Period(8, Years), Period(2, Years) },
{ 21.600, Period(9, Years), Period(2, Years) },
{ 51.050, Period(1, Months), Period(3, Years) },
{ 48.300, Period(3, Months), Period(3, Years) },
{ 48.900, Period(6, Months), Period(3, Years) },
{ 47.000, Period(1, Years), Period(3, Years) },
//{ 37.000, Period(2, Years), Period(3, Years) },
//{ 31.275, Period(3, Years), Period(3, Years) },
{ 27.650, Period(4, Years), Period(3, Years) },
{ 25.650, Period(5, Years), Period(3, Years) },
{ 24.200, Period(6, Years), Period(3, Years) },
{ 23.050, Period(7, Years), Period(3, Years) },
{ 22.050, Period(8, Years), Period(3, Years) },
{ 40.800, Period(1, Months), Period(4, Years) },
{ 40.225, Period(3, Months), Period(4, Years) },
{ 40.200, Period(6, Months), Period(4, Years) },
{ 39.300, Period(1, Years), Period(4, Years) },
//{ 32.800, Period(2, Years), Period(4, Years) },
{ 28.925, Period(3, Years), Period(4, Years) },
{ 26.150, Period(4, Years), Period(4, Years) },
{ 24.650, Period(5, Years), Period(4, Years) },
{ 23.500, Period(6, Years), Period(4, Years) },
{ 22.350, Period(7, Years), Period(4, Years) },
{ 36.025, Period(1, Months), Period(5, Years) },
{ 35.600, Period(3, Months), Period(5, Years) },
{ 35.425, Period(6, Months), Period(5, Years) },
{ 34.250, Period(1, Years), Period(5, Years) },
{ 29.850, Period(2, Years), Period(5, Years) },
{ 26.900, Period(3, Years), Period(5, Years) },
{ 24.925, Period(4, Years), Period(5, Years) },
{ 23.700, Period(5, Years), Period(5, Years) },
{ 22.750, Period(6, Years), Period(5, Years) },
{ 30.800, Period(1, Months), Period(6, Years) },
{ 30.700, Period(3, Months), Period(6, Years) },
//{ 31.200, Period(6, Months), Period(6, Years) },
{ 30.750, Period(1, Years), Period(6, Years) },
{ 27.850, Period(2, Years), Period(6, Years) },
{ 25.775, Period(3, Years), Period(6, Years) },
{ 24.125, Period(4, Years), Period(6, Years) },
{ 23.100, Period(5, Years), Period(6, Years) },
{ 27.600, Period(1, Months), Period(7, Years) },
{ 27.750, Period(3, Months), Period(7, Years) },
{ 28.350, Period(6, Months), Period(7, Years) },
{ 28.200, Period(1, Years), Period(7, Years) },
{ 26.400, Period(2, Years), Period(7, Years) },
{ 24.750, Period(3, Years), Period(7, Years) },
{ 23.400, Period(4, Years), Period(7, Years) },
{ 25.250, Period(1, Months), Period(8, Years) },
{ 25.450, Period(3, Months), Period(8, Years) },
{ 26.000, Period(6, Months), Period(8, Years) },
{ 26.250, Period(1, Years), Period(8, Years) },
{ 25.225, Period(2, Years), Period(8, Years) },
{ 23.875, Period(3, Years), Period(8, Years) },
{ 23.575, Period(1, Months), Period(9, Years) },
{ 23.575, Period(3, Months), Period(9, Years) },
{ 24.600, Period(6, Months), Period(9, Years) },
{ 24.800, Period(1, Years), Period(9, Years) },
{ 24.150, Period(2, Years), Period(9, Years) },
{ 22.275, Period(1, Months), Period(10, Years) },
{ 22.125, Period(3, Months), Period(10, Years) },
{ 23.300, Period(6, Months), Period(10, Years) },
{ 23.600, Period(1, Years), Period(10, Years) }
};
Handle<YieldTermStructure> termStructure = libor->forwardingTermStructure();
// set up the process
boost::shared_ptr<LiborForwardModelProcess> process(
new LiborForwardModelProcess(size_, libor));
std::vector<Time> fixingT = process->fixingTimes();
// set-up the model
boost::shared_ptr<LmVolatilityModel> volaModel(
new LmExtLinearExponentialVolModel(process->fixingTimes(),
0.5, 0.6, 0.1, 0.1));
boost::shared_ptr<LmCorrelationModel> corrModel(
new LmLinearExponentialCorrelationModel(size_, 0.5, 0.8));
boost::shared_ptr<LiborForwardModel> model(
new LiborForwardModel(process, volaModel, corrModel));
Size swapVolIndex = 0;
DayCounter dayCounter = libor->forwardingTermStructure()->dayCounter();
// set-up calibration helper
std::vector<boost::shared_ptr<CalibrationHelper> > calibrationHelper;
Size i;
for (i = 0; i < swaptions.size(); i++) {
Handle<Quote> swaptionVol(
boost::shared_ptr<Quote>(
new SimpleQuote(swaptions[i].volatility_ / 100)));
boost::shared_ptr<CalibrationHelper> swaptionHelper(
new SwaptionHelper(swaptions[i].lenght_,
swaptions[i].maturity_, swaptionVol, libor,
libor->tenor(), dayCounter,
libor->dayCounter(),
termStructure,
CalibrationHelper::ImpliedVolError));
swaptionHelper->setPricingEngine(
boost::shared_ptr<PricingEngine>(
new LfmSwaptionEngine(model, termStructure)));
calibrationHelper.push_back(swaptionHelper);
}
#ifdef _DEBUG
LevenbergMarquardt om(1e-5, 1e-5, 1e-5);
model->calibrate(calibrationHelper, om, EndCriteria(100, 20, 1e-5, 1e-5, 1e-6));
#else
boost::shared_ptr<OptimizationMethod> om(
new LevenbergMarquardt(1e-6, 1e-6, 1e-6));
//boost::shared_ptr<OptimizationMethod> om(new SteepestDescent);
model->calibrate(calibrationHelper, *om, EndCriteria(2000, 100, 1e-6, 1e-6, 1e-6));
#endif
// measure the calibration error
Real calculated = 0.0;
for (i = 0; i<calibrationHelper.size(); ++i) {
Real diff = calibrationHelper[i]->calibrationError();
calculated += diff * diff;
}
// create diagnostic file
{
std::string fileStr("C:/Temp/liborModel_1Y10_"); // build file path
fileStr.append(boost::posix_time::to_iso_string(
boost::posix_time::second_clock::local_time()));
fileStr.append(".csv");
utilities::csvBuilder file(fileStr); // csv builder
Array times(size_, 0.0); Array rates(size_, 0.0); // saves yield curve data
for (int i = 0; i < size_; i++) {
times[i] = fixingT[i]; // the fixing times from model
rates[i] = libor->forwardingTermStructure()->zeroRate(
times[i], Continuous);
}
file.add("times", 1, 1); file.add("rates", 1, 2); // adds the yield curve data
file.add(times, 2, 1); file.add(rates, 2, 2);
file.add(std::string("calibration result:"), 1, 4); // calibration result
file.add(model->endCriteria(), 2, 4);
file.add(std::string("calculated diff:"), 4, 4); // calibration result
file.add(std::sqrt(calculated), 5, 4);
file.add("correlation matrix at time zero", 1, 6); // correlation
file.add(corrModel->correlation(0), 2, 6);
}
}
