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|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 Ferdinando Ametrano
Copyright (C) 2006 François du Vignaud
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
<http://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/swapforwardmappings.hpp>
#include <ql/models/marketmodels/correlations/timehomogeneousforwardcorrelation.hpp>
#include <ql/models/marketmodels/curvestates/lmmcurvestate.hpp>
#include <ql/models/marketmodels/evolutiondescription.hpp>
#include <ql/models/marketmodels/evolvers/lognormalfwdratepc.hpp>
#include <ql/models/marketmodels/models/flatvol.hpp>
#include <ql/models/marketmodels/correlations/expcorrelations.hpp>
#include <ql/models/marketmodels/browniangenerators/sobolbrowniangenerator.hpp>
#include <ql/models/marketmodels/products/multistep/multistepcoterminalswaptions.hpp>
#include <ql/models/marketmodels/accountingengine.hpp>
#include <ql/models/marketmodels/models/cotswaptofwdadapter.hpp>
#include <ql/models/marketmodels/curvestates/coterminalswapcurvestate.hpp>
#include <ql/time/schedule.hpp>
#include <ql/time/daycounters/simpledaycounter.hpp>
#include <ql/math/statistics/sequencestatistics.hpp>
#include <ql/pricingengines/blackcalculator.hpp>
#include <ql/models/marketmodels/products/multistep/multistepswaption.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
using std::fabs;
using std::sqrt;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(SwapForwardMappingsTests)
class MarketModelData{
public:
MarketModelData();
const std::vector<Time>& rateTimes(){return rateTimes_;}
const std::vector<Rate>& forwards(){return forwards_;}
const std::vector<Volatility>& volatilities(){return volatilities_;}
const std::vector<Rate>& displacements(){return displacements_;}
const std::vector<DiscountFactor>& discountFactors(){return discountFactors_;}
Size nbRates() const { return nbRates_; }
private:
std::vector<Time> rateTimes_, accruals_;
std::vector<Rate> forwards_;
std::vector<Spread> displacements_;
std::vector<Volatility> volatilities_;
std::vector<DiscountFactor> discountFactors_;
Size nbRates_;
};
MarketModelData::MarketModelData(){
// Times
Calendar calendar = NullCalendar();
Date todaysDate = Settings::instance().evaluationDate();
Date endDate = todaysDate + 9*Years; // change back
Schedule dates(todaysDate, endDate, Period(Semiannual),
calendar, Following, Following, DateGeneration::Backward, false);
nbRates_ = dates.size()-2;
rateTimes_ = std::vector<Time>(nbRates_+1);
//paymentTimes_ = std::vector<Time>(rateTimes_.size()-1);
accruals_ = std::vector<Time>(nbRates_);
DayCounter dayCounter = SimpleDayCounter();
for (Size i=1; i<nbRates_+2; ++i)
rateTimes_[i-1] = dayCounter.yearFraction(todaysDate, dates[i]);
displacements_ = std::vector<Rate>(nbRates_, .0);
forwards_ = std::vector<Rate>(nbRates_);
discountFactors_ = std::vector<Rate>(nbRates_+1);
discountFactors_[0] = 1.0; // .95; fdv1-> WHY ???????
for (Size i=0; i<nbRates_; ++i){
forwards_[i] = 0.03 + 0.0010*i;
accruals_[i] = rateTimes_[i+1] - rateTimes_[i];
discountFactors_[i+1] = discountFactors_[i]
/(1+forwards_[i]*accruals_[i]);
}
Volatility mktVols[] = {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
/*
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2,
0.2
*/
};
volatilities_ = std::vector<Volatility>(nbRates_);
for (Size i = 0; i < volatilities_.size(); ++i)
volatilities_[i] = mktVols[i];//.0;
}
ext::shared_ptr<SequenceStatisticsInc>
simulate(const std::vector<Real>& todaysDiscounts,
const ext::shared_ptr<MarketModelEvolver>& evolver,
const MarketModelMultiProduct& product) {
Size paths_;
#ifdef _DEBUG
paths_ = 127;// //
#else
paths_ = 32767; //262144-1; // //; // 2^15-1
#endif
Size initialNumeraire = evolver->numeraires().front();
Real initialNumeraireValue = todaysDiscounts[initialNumeraire];
AccountingEngine engine(evolver, product, initialNumeraireValue);
ext::shared_ptr<SequenceStatisticsInc> stats(new
SequenceStatisticsInc(product.numberOfProducts()));
engine.multiplePathValues(*stats, paths_);
return stats;
}
// MultiStepCoterminalSwaptions makeMultiStepCoterminalSwaptions(
// const std::vector<Time>& rateTimes, Real strike ){
// std::vector<Time> paymentTimes(rateTimes.begin(), rateTimes.end()-1);
// std::vector<ext::shared_ptr<StrikedTypePayoff> > payoffs(paymentTimes.size());
// for (auto& payoff : payoffs) {
// payoff = ext::shared_ptr<StrikedTypePayoff>(
// new PlainVanillaPayoff(Option::Call, strike));
// }
// return MultiStepCoterminalSwaptions (rateTimes,
// paymentTimes, payoffs);
//
// }
BOOST_AUTO_TEST_CASE(testForwardSwapJacobians)
{
{
BOOST_TEST_MESSAGE("Testing forward-rate coinitial-swap Jacobian...");
MarketModelData marketData;
const std::vector<Time>& rateTimes = marketData.rateTimes();
const std::vector<Rate>& forwards = marketData.forwards();
const Size nbRates = marketData.nbRates();
LMMCurveState lmmCurveState(rateTimes);
lmmCurveState.setOnForwardRates(forwards);
Real bumpSize = 1e-8;
std::vector<Rate> bumpedForwards(forwards);
Matrix coinitialJacobian(nbRates,nbRates);
for (Size i=0; i < nbRates; ++i)
for (Size j=0; j < nbRates; ++j)
{
bumpedForwards = forwards;
bumpedForwards[j]+= bumpSize;
lmmCurveState.setOnForwardRates(bumpedForwards);
Real upRate = lmmCurveState.cmSwapRate(0,i+1);
bumpedForwards[j]-= 2.0*bumpSize;
lmmCurveState.setOnForwardRates(bumpedForwards);
Real downRate = lmmCurveState.cmSwapRate(0,i+1);
Real deriv = (upRate-downRate)/(2.0*bumpSize);
coinitialJacobian[i][j] = deriv;
}
Matrix modelJacobian(SwapForwardMappings::coinitialSwapForwardJacobian(lmmCurveState));
Real errorTolerance = 1e-5;
for (Size i=0; i < nbRates; ++i)
for (Size j=0; j < nbRates; ++j)
if( fabs(modelJacobian[i][j]-coinitialJacobian[i][j]) > errorTolerance)
{
BOOST_TEST_MESSAGE("rate " << i
<< ", sensitivity " << j
<< ", formula value " << modelJacobian[i][j]
<< " bumping value " << coinitialJacobian[i][j]
<< "\n");
BOOST_ERROR("test failed");
}
}
{
BOOST_TEST_MESSAGE("Testing forward-rate constant-maturity swap Jacobian...");
MarketModelData marketData;
const std::vector<Time>& rateTimes = marketData.rateTimes();
const std::vector<Rate>& forwards = marketData.forwards();
const Size nbRates = marketData.nbRates();
LMMCurveState lmmCurveState(rateTimes);
lmmCurveState.setOnForwardRates(forwards);
Real bumpSize = 1e-8;
for( Size spanningForwards = 1; spanningForwards < nbRates; ++spanningForwards)
{
std::vector<Rate> bumpedForwards(forwards);
Matrix cmsJacobian(nbRates,nbRates);
for (Size i=0; i < nbRates; ++i)
for (Size j=0; j < nbRates; ++j)
{
bumpedForwards = forwards;
bumpedForwards[j]+= bumpSize;
lmmCurveState.setOnForwardRates(bumpedForwards);
Real upRate = lmmCurveState.cmSwapRate(i,spanningForwards);
bumpedForwards[j]-= 2.0*bumpSize;
lmmCurveState.setOnForwardRates(bumpedForwards);
Real downRate = lmmCurveState.cmSwapRate(i,spanningForwards);
Real deriv = (upRate-downRate)/(2.0*bumpSize);
cmsJacobian[i][j] = deriv;
}
Matrix modelJacobian(SwapForwardMappings::cmSwapForwardJacobian(lmmCurveState, spanningForwards));
Real errorTolerance = 1e-5;
for (Size i=0; i < nbRates; ++i)
for (Size j=0; j < nbRates; ++j)
if( fabs(modelJacobian[i][j]-cmsJacobian[i][j]) > errorTolerance)
{
BOOST_TEST_MESSAGE(
"rate " << i
<< ", sensitivity " << j
<< ", formula value " << modelJacobian[i][j]
<< " bumping value " << cmsJacobian[i][j]
<< "\n");
BOOST_ERROR("test failed");
}
}
}
}
//BOOST_AUTO_TEST_CASE(testForwardCoterminalMappings) {
//
// BOOST_TEST_MESSAGE("Testing forward-rate coterminal-swap mappings...");
// MarketModelData marketData;
// const std::vector<Time>& rateTimes = marketData.rateTimes();
// const std::vector<Rate>& forwards = marketData.forwards();
// const Size nbRates = marketData.nbRates();
// LMMCurveState lmmCurveState(rateTimes);
// lmmCurveState.setOnForwardRates(forwards);
//
// const Real longTermCorr=0.5;
// const Real beta = .2;
// Real strike = .03;
// MultiStepCoterminalSwaptions product
// = makeMultiStepCoterminalSwaptions(rateTimes, strike);
//
// const EvolutionDescription& evolution = product.evolution();
// const Size numberOfFactors = nbRates;
// Spread displacement = marketData.displacements().front();
// Matrix jacobian =
// SwapForwardMappings::coterminalSwapZedMatrix(
// lmmCurveState, displacement);
//
// Matrix correlations = exponentialCorrelations(evolution.rateTimes(),
// longTermCorr,
// beta);
// ext::shared_ptr<PiecewiseConstantCorrelation> corr(new
// TimeHomogeneousForwardCorrelation(correlations,
// rateTimes));
// ext::shared_ptr<MarketModel> smmMarketModel(new
// FlatVol(marketData.volatilities(),
// corr,
// evolution,
// numberOfFactors,
// lmmCurveState.coterminalSwapRates(),
// marketData.displacements()));
//
// ext::shared_ptr<MarketModel>
// lmmMarketModel(new CotSwapToFwdAdapter(smmMarketModel));
//
// SobolBrownianGeneratorFactory generatorFactory(SobolBrownianGenerator::Diagonal);
// std::vector<Size> numeraires(nbRates,
// nbRates);
// ext::shared_ptr<MarketModelEvolver> evolver(new LogNormalFwdRatePc
// (lmmMarketModel, generatorFactory, numeraires));
//
// ext::shared_ptr<SequenceStatisticsInc> stats =
// simulate(marketData.discountFactors(), evolver, product);
// std::vector<Real> results = stats->mean();
// std::vector<Real> errors = stats->errorEstimate();
//
// const std::vector<DiscountFactor>& todaysDiscounts = marketData.discountFactors();
// const std::vector<Rate>& todaysCoterminalSwapRates = lmmCurveState.coterminalSwapRates();
// for (Size i=0; i<nbRates; ++i) {
// const Matrix& cotSwapsCovariance = smmMarketModel->totalCovariance(i);
// //Matrix cotSwapsCovariance= jacobian * forwardsCovariance * transpose(jacobian);
// //Time expiry = rateTimes[i];
// ext::shared_ptr<PlainVanillaPayoff> payoff(
// new PlainVanillaPayoff(Option::Call, strike+displacement));
// //const std::vector<Time>& taus = lmmCurveState.rateTaus();
// Real expectedSwaption = BlackCalculator(payoff,
// todaysCoterminalSwapRates[i]+displacement,
// std::sqrt(cotSwapsCovariance[i][i]),
// lmmCurveState.coterminalSwapAnnuity(i,i) *
// todaysDiscounts[i]).value();
// if (fabs(expectedSwaption-results[i]) > 0.0001)
// BOOST_ERROR(
// "expected\t" << expectedSwaption <<
// "\tLMM\t" << results[i]
// << "\tstdev:\t" << errors[i] <<
// "\t" <<std::fabs(results[i]- expectedSwaption)/errors[i]);
// }
//}
BOOST_AUTO_TEST_CASE(testSwaptionImpliedVolatility)
{
BOOST_TEST_MESSAGE("Testing implied swaption vol in LMM using HW approximation...");
MarketModelData marketData;
const std::vector<Time>& rateTimes = marketData.rateTimes();
const std::vector<Rate>& forwards = marketData.forwards();
const Size nbRates = marketData.nbRates();
LMMCurveState lmmCurveState(rateTimes);
lmmCurveState.setOnForwardRates(forwards);
const Real longTermCorr=0.5;
const Real beta = .2;
Real strike = .03;
for (Size startIndex = 1; startIndex+2 < nbRates; startIndex = startIndex+5)
{
Size endIndex = nbRates-2;
ext::shared_ptr<StrikedTypePayoff> payoff(new
PlainVanillaPayoff(Option::Call, strike));
MultiStepSwaption product(rateTimes, startIndex, endIndex,payoff );
const EvolutionDescription& evolution = product.evolution();
const Size numberOfFactors = nbRates;
Spread displacement = marketData.displacements().front();
Matrix jacobian =
SwapForwardMappings::coterminalSwapZedMatrix(
lmmCurveState, displacement);
Matrix correlations = exponentialCorrelations(evolution.rateTimes(),
longTermCorr,
beta);
ext::shared_ptr<PiecewiseConstantCorrelation> corr(new
TimeHomogeneousForwardCorrelation(correlations,
rateTimes));
ext::shared_ptr<MarketModel> lmmMarketModel(new
FlatVol(marketData.volatilities(),
corr,
evolution,
numberOfFactors,
lmmCurveState.forwardRates(),
marketData.displacements()));
SobolBrownianGeneratorFactory generatorFactory(SobolBrownianGenerator::Diagonal);
std::vector<Size> numeraires(nbRates,
nbRates);
ext::shared_ptr<MarketModelEvolver> evolver(new LogNormalFwdRatePc
(lmmMarketModel, generatorFactory, numeraires));
ext::shared_ptr<SequenceStatisticsInc> stats =
simulate(marketData.discountFactors(), evolver, product);
std::vector<Real> results = stats->mean();
std::vector<Real> errors = stats->errorEstimate();
Real estimatedImpliedVol = SwapForwardMappings::swaptionImpliedVolatility(*lmmMarketModel,startIndex,endIndex);
Real swapRate = lmmCurveState.cmSwapRate(startIndex,endIndex-startIndex);
Real swapAnnuity = lmmCurveState.cmSwapAnnuity(startIndex,startIndex,endIndex-startIndex)*marketData.discountFactors()[startIndex];
ext::shared_ptr<PlainVanillaPayoff> payoffDis( new PlainVanillaPayoff(Option::Call, strike+displacement));
Real expectedSwaption = BlackCalculator(payoffDis,
swapRate+displacement, estimatedImpliedVol *sqrt(rateTimes[startIndex]),
swapAnnuity).value();
Real error = expectedSwaption - results[0];
Real errorInSds = error/errors[0];
if (fabs(errorInSds) > 3.5 )
BOOST_ERROR(
"expected\t" << expectedSwaption <<
"\tLMM\t" << results[0]
<< "\tstdev:\t" << errors[0] <<
"\t" <<errorInSds);
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
|
