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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 Ferdinando Ametrano
Copyright (C) 2007 Marco Bianchetti
Copyright (C) 2007 Cristina Duminuco
Copyright (C) 2007 Mark Joshi
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<https://www.quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
#include "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/models/marketmodels/models/capletcoterminalalphacalibration.hpp>
#include <ql/models/marketmodels/correlations/cotswapfromfwdcorrelation.hpp>
#include <ql/models/marketmodels/correlations/timehomogeneousforwardcorrelation.hpp>
#include <ql/models/marketmodels/models/piecewiseconstantabcdvariance.hpp>
#include <ql/models/marketmodels/models/capletcoterminalswaptioncalibration.hpp>
#include <ql/models/marketmodels/models/cotswaptofwdadapter.hpp>
#include <ql/models/marketmodels/models/pseudorootfacade.hpp>
#include <ql/models/marketmodels/products/multistep/multistepcoterminalswaps.hpp>
#include <ql/models/marketmodels/products/multistep/multistepcoterminalswaptions.hpp>
#include <ql/models/marketmodels/products/multistep/multistepswap.hpp>
#include <ql/models/marketmodels/products/multiproductcomposite.hpp>
#include <ql/models/marketmodels/accountingengine.hpp>
#include <ql/models/marketmodels/utilities.hpp>
#include <ql/models/marketmodels/evolvers/lognormalcotswapratepc.hpp>
#include <ql/models/marketmodels/evolvers/lognormalfwdratepc.hpp>
#include <ql/models/marketmodels/correlations/expcorrelations.hpp>
#include <ql/models/marketmodels/models/flatvol.hpp>
#include <ql/models/marketmodels/models/abcdvol.hpp>
#include <ql/models/marketmodels/browniangenerators/mtbrowniangenerator.hpp>
#include <ql/models/marketmodels/browniangenerators/sobolbrowniangenerator.hpp>
#include <ql/models/marketmodels/swapforwardmappings.hpp>
#include <ql/models/marketmodels/curvestates/coterminalswapcurvestate.hpp>
#include <ql/methods/montecarlo/genericlsregression.hpp>
#include <ql/legacy/libormarketmodels/lmlinexpcorrmodel.hpp>
#include <ql/legacy/libormarketmodels/lmextlinexpvolmodel.hpp>
#include <ql/time/schedule.hpp>
#include <ql/time/calendars/nullcalendar.hpp>
#include <ql/time/daycounters/simpledaycounter.hpp>
#include <ql/pricingengines/blackformula.hpp>
#include <ql/pricingengines/blackcalculator.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <ql/math/integrals/segmentintegral.hpp>
#include <ql/math/statistics/convergencestatistics.hpp>
#include <ql/math/optimization/simplex.hpp>
#include <ql/math/statistics/sequencestatistics.hpp>
#include <sstream>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(MarketModelSmmCapletAlphaCalibrationTests)
Date todaysDate_, startDate_, endDate_;
std::vector<Time> rateTimes_;
std::vector<Real> accruals_;
Calendar calendar_;
DayCounter dayCounter_;
std::vector<Rate> todaysForwards_, todaysSwaps_;
std::vector<Real> coterminalAnnuity_;
Size numberOfFactors_;
Real alpha_, alphaMax_, alphaMin_;
Spread displacement_;
std::vector<DiscountFactor> todaysDiscounts_;
std::vector<Volatility> swaptionDisplacedVols_, swaptionVols_;
std::vector<Volatility> capletDisplacedVols_, capletVols_;
Real a_, b_, c_, d_;
Real longTermCorrelation_, beta_;
Size measureOffset_;
unsigned long seed_;
Size paths_, trainingPaths_;
bool printReport_ = false;
void setup() {
// Times
calendar_ = NullCalendar();
todaysDate_ = Settings::instance().evaluationDate();
//startDate = todaysDate + 5*Years;
endDate_ = todaysDate_ + 66*Months;
Schedule dates(todaysDate_, endDate_, Period(Semiannual),
calendar_, Following, Following, DateGeneration::Backward, false);
rateTimes_ = std::vector<Time>(dates.size()-1);
accruals_ = std::vector<Real>(rateTimes_.size()-1);
dayCounter_ = SimpleDayCounter();
for (Size i=1; i<dates.size(); ++i)
rateTimes_[i-1] = dayCounter_.yearFraction(todaysDate_, dates[i]);
for (Size i=1; i<rateTimes_.size(); ++i)
accruals_[i-1] = rateTimes_[i] - rateTimes_[i-1];
// Rates & displacement
todaysForwards_ = std::vector<Rate>(accruals_.size());
numberOfFactors_ = 3;
alpha_ = 0.0;
alphaMax_ = 1.0;
alphaMin_ = -1.0;
displacement_ = 0.0;
for (Size i=0; i<todaysForwards_.size(); ++i) {
todaysForwards_[i] = 0.03 + 0.0025*i;
// todaysForwards_[i] = 0.03;
}
LMMCurveState curveState_lmm(rateTimes_);
curveState_lmm.setOnForwardRates(todaysForwards_);
todaysSwaps_ = curveState_lmm.coterminalSwapRates();
// Discounts
todaysDiscounts_ = std::vector<DiscountFactor>(rateTimes_.size());
todaysDiscounts_[0] = 0.95;
for (Size i=1; i<rateTimes_.size(); ++i)
todaysDiscounts_[i] = todaysDiscounts_[i-1] /
(1.0+todaysForwards_[i-1]*accruals_[i-1]);
//// Swaption Volatilities
//Volatility mktSwaptionVols[] = {
// 0.15541283,
// 0.18719678,
// 0.20890740,
// 0.22318179,
// 0.23212717,
// 0.23731450,
// 0.23988649,
// 0.24066384,
// 0.24023111,
// 0.23900189,
// 0.23726699,
// 0.23522952,
// 0.23303022,
// 0.23076564,
// 0.22850101,
// 0.22627951,
// 0.22412881,
// 0.22206569,
// 0.22009939
//};
//a = -0.0597;
//b = 0.1677;
//c = 0.5403;
//d = 0.1710;
a_ = 0.0;
b_ = 0.17;
c_ = 1.0;
d_ = 0.10;
Volatility mktCapletVols[] = {
0.1640,
0.1740,
0.1840,
0.1940,
0.1840,
0.1740,
0.1640,
0.1540,
0.1440,
0.1340376439125532
};
//swaptionDisplacedVols = std::vector<Volatility>(todaysSwaps.size());
//swaptionVols = std::vector<Volatility>(todaysSwaps.size());
//capletDisplacedVols = std::vector<Volatility>(todaysSwaps.size());
capletVols_.resize(todaysSwaps_.size());
for (Size i=0; i<todaysSwaps_.size(); i++) {
// swaptionDisplacedVols[i] = todaysSwaps[i]*mktSwaptionVols[i]/
// (todaysSwaps[i]+displacement);
// swaptionVols[i]= mktSwaptionVols[i];
// capletDisplacedVols[i] = todaysForwards[i]*mktCapletVols[i]/
// (todaysForwards[i]+displacement);
capletVols_[i]= mktCapletVols[i];
}
// Cap/Floor Correlation
longTermCorrelation_ = 0.5;
beta_ = 0.2;
measureOffset_ = 5;
// Monte Carlo
seed_ = 42;
#ifdef _DEBUG
paths_ = 127;
trainingPaths_ = 31;
#else
paths_ = 32767; //262144-1; //; // 2^15-1
trainingPaths_ = 8191; // 2^13-1
#endif
}
enum MarketModelType { ExponentialCorrelationFlatVolatility,
ExponentialCorrelationAbcdVolatility/*,
CalibratedMM*/
};
enum MeasureType { ProductSuggested, Terminal,
MoneyMarket, MoneyMarketPlus };
enum EvolverType { Ipc, Pc , NormalPc};
BOOST_AUTO_TEST_CASE(testFunction) {
BOOST_TEST_MESSAGE("Testing alpha caplet calibration "
"in a lognormal coterminal swap market model...");
setup();
Size numberOfRates = todaysForwards_.size();
EvolutionDescription evolution(rateTimes_);
// Size numberOfSteps = evolution.numberOfSteps();
ext::shared_ptr<PiecewiseConstantCorrelation> fwdCorr(new
ExponentialForwardCorrelation(rateTimes_,
longTermCorrelation_,
beta_));
ext::shared_ptr<LMMCurveState> cs(new LMMCurveState(rateTimes_));
cs->setOnForwardRates(todaysForwards_);
ext::shared_ptr<PiecewiseConstantCorrelation> corr(new
CotSwapFromFwdCorrelation(fwdCorr, *cs, displacement_));
std::vector<ext::shared_ptr<PiecewiseConstantVariance> >
swapVariances(numberOfRates);
for (Size i=0; i<numberOfRates; ++i) {
swapVariances[i] = ext::shared_ptr<PiecewiseConstantVariance>(new
PiecewiseConstantAbcdVariance(a_, b_, c_, d_,
i, rateTimes_));
}
// create calibrator
std::vector<Real> alphaInitial(numberOfRates, alpha_);
std::vector<Real> alphaMax(numberOfRates, 1.0);
std::vector<Real> alphaMin(numberOfRates, -1.0);
bool maximizeHomogeneity = false; //?
if (printReport_) {
BOOST_TEST_MESSAGE("caplet market vols: " << std::fixed <<
std::setprecision(4) << io::sequence(capletVols_));
BOOST_TEST_MESSAGE("alphaMin: " << alphaMin_);
BOOST_TEST_MESSAGE("alphaInitial: " << alpha_);
BOOST_TEST_MESSAGE("alphaMax: " << alphaMax_);
BOOST_TEST_MESSAGE("maximizeHomogeneity:" << maximizeHomogeneity);
}
CTSMMCapletAlphaFormCalibration calibrator(evolution,
corr,
swapVariances,
capletVols_,
cs,
displacement_,
alphaInitial,
alphaMax,
alphaMin,
maximizeHomogeneity);
// calibrate
Natural maxIterations = 10;
Real capletTolerance = 1e-4; // i.e. 1 bp
Natural innerMaxIterations = 100;
Real innerTolerance = 1e-8;
if (printReport_) {
BOOST_TEST_MESSAGE("numberOfFactors: " << numberOfFactors_);
BOOST_TEST_MESSAGE("maxIterations: " << maxIterations);
BOOST_TEST_MESSAGE("capletTolerance: " << io::rate(capletTolerance));
BOOST_TEST_MESSAGE("innerMaxIterations: " << innerMaxIterations);
BOOST_TEST_MESSAGE("innerTolerance: " << io::rate(innerTolerance));
}
bool result = calibrator.calibrate(numberOfFactors_,
maxIterations,
capletTolerance,
innerMaxIterations,
innerTolerance);
if (!result)
BOOST_ERROR("calibration failed");
const std::vector<Matrix>& swapPseudoRoots = calibrator.swapPseudoRoots();
ext::shared_ptr<MarketModel> smm(new
PseudoRootFacade(swapPseudoRoots,
rateTimes_,
cs->coterminalSwapRates(),
std::vector<Spread>(numberOfRates, displacement_)));
CotSwapToFwdAdapter flmm(smm);
Matrix capletTotCovariance = flmm.totalCovariance(numberOfRates-1);
std::vector<Volatility> capletVols(numberOfRates);
for (Size i=0; i<numberOfRates; ++i) {
capletVols[i] = std::sqrt(capletTotCovariance[i][i]/rateTimes_[i]);
}
if (printReport_) {
BOOST_TEST_MESSAGE("caplet smm implied vols: " << std::fixed <<
std::setprecision(4) << io::sequence(capletVols));
BOOST_TEST_MESSAGE("failures: " << calibrator.failures());
BOOST_TEST_MESSAGE("deformationSize: " << calibrator.deformationSize());
BOOST_TEST_MESSAGE("capletRmsError: " << calibrator.capletRmsError());
BOOST_TEST_MESSAGE("capletMaxError: " << calibrator.capletMaxError());
BOOST_TEST_MESSAGE("swaptionRmsError: " << calibrator.swaptionRmsError());
BOOST_TEST_MESSAGE("swaptionMaxError: " << calibrator.swaptionMaxError());
}
// check perfect swaption fit
Real error, swapTolerance = 1e-14;
Matrix swapTerminalCovariance(numberOfRates, numberOfRates, 0.0);
for (Size i=0; i<numberOfRates; ++i) {
Volatility expSwaptionVol = swapVariances[i]->totalVolatility(i);
swapTerminalCovariance += swapPseudoRoots[i] * transpose(swapPseudoRoots[i]);
Volatility swaptionVol = std::sqrt(swapTerminalCovariance[i][i]/rateTimes_[i]);
error = std::fabs(swaptionVol-expSwaptionVol);
if (error>swapTolerance)
BOOST_ERROR("failed to reproduce " << io::ordinal(i+1) << " swaption vol:"
"\n expected: " << io::rate(expSwaptionVol) <<
"\n realized: " << io::rate(swaptionVol) <<
"\n error: " << error <<
"\n tolerance: " << swapTolerance);
}
// check caplet fit
for (Size i=0; i<numberOfRates; ++i) {
error = std::fabs(capletVols[i]-capletVols_[i]);
if (error>capletTolerance)
BOOST_ERROR("failed to reproduce " << io::ordinal(i+1) << " caplet vol:"
"\n expected: " << io::rate(capletVols_[i]) <<
"\n realized: " << io::rate(capletVols[i]) <<
"\n percentage error: " << error/capletVols_[i] <<
"\n error: " << error <<
"\n tolerance: " << capletTolerance);
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
|
