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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Roland Lichters
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 "preconditions.hpp"
#include "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/currencies/europe.hpp>
#include <ql/experimental/credit/cdo.hpp>
#include <ql/experimental/credit/gaussianlhplossmodel.hpp>
#include <ql/experimental/credit/homogeneouspooldef.hpp>
#include <ql/experimental/credit/inhomogeneouspooldef.hpp>
#include <ql/experimental/credit/integralcdoengine.hpp>
#include <ql/experimental/credit/midpointcdoengine.hpp>
#include <ql/experimental/credit/pool.hpp>
#include <ql/experimental/credit/randomdefaultlatentmodel.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/termstructures/credit/flathazardrate.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <boost/mpl/vector.hpp>
#include <iomanip>
#include <iostream>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(CdoTests, *precondition(if_speed(Slow)))
#ifndef QL_PATCH_SOLARIS
Real hwAttachment[] = { 0.00, 0.03, 0.06, 0.10 };
Real hwDetachment[] = { 0.03, 0.06, 0.10, 1.00 };
struct hwDatum {
Real correlation;
Integer nm;
Integer nz;
Real trancheSpread[4];
};
// HW Table 7
// corr, Nm, Nz, 0-3, 3-6, 6-10, 10-100
hwDatum hwData7[] = {
{ 0.1, -1, -1, { 2279, 450, 89, 1 } },
{ 0.3, -1, -1, { 1487, 472, 203, 7 } },
// Opening the T, T&G tests too. The convolution is analytical
// now so it runs it a time comparable to the gaussian tests and
// has enough precission to pass the tests.
// Below the T models are integrated with a quadrature, even if this
// is incorrect the test pass good enough, the quadrature gets to
// be worst as the kernel deviates from a normal, this is low
// orders of the T; here 5 is enough, 3 would not be.
{ 0.3, -1, 5, { 1766, 420, 161, 6 } },
{ 0.3, 5, -1, { 1444, 408, 171, 10 } },
{ 0.3, 5, 5, { 1713, 359, 136, 9 } }
};
void check(int i, int j, const std::string& desc, Real found, Real expected,
Real bpTolerance, Real relativeTolerance)
{
/* Uncomment to display the full show if your debugging:
std::cout<< "Case: "<< i << " " << j << " " << found << " :: "
<< expected << " ("<< desc << ") " << std::endl;
*/
Real absDiff = found - expected;
Real relDiff = absDiff / expected;
BOOST_CHECK_MESSAGE (fabs(relDiff) < relativeTolerance ||
fabs(absDiff) < bpTolerance,
"case " << i << " " << j << " ("<< desc << "): "
<< found << " vs. " << expected);
}
struct dataSetOne { static const int dataset{0}; };
struct dataSetTwo { static const int dataset{1}; };
struct dataSetThree { static const int dataset{2}; };
struct dataSetFour { static const int dataset{3}; };
struct dataSetFive { static const int dataset{4}; };
using dataSets = boost::mpl::vector<dataSetOne, dataSetTwo, dataSetThree, dataSetFour, dataSetFive>;
BOOST_AUTO_TEST_CASE_TEMPLATE(testHW, T, dataSets) {
const int dataSet = T::dataset;
BOOST_TEST_MESSAGE("Testing CDO premiums against Hull-White values"
" for data set "
<< dataSet << "...");
Size poolSize = 100;
Real lambda = 0.01;
// nBuckets and period determine the computation time
Size nBuckets = 200;
// Period period = 1*Months;
// for MC engines
Size numSims = 5000;
Real rate = 0.05;
DayCounter daycount = Actual360();
Compounding cmp = Continuous; // Simple;
Real recovery = 0.4;
std::vector<Real> nominals(poolSize, 100.0);
Real premium = 0.02;
Period maxTerm(5, Years);
Schedule schedule = MakeSchedule()
.from(Date(1, September, 2006))
.to(Date(1, September, 2011))
.withTenor(Period(3, Months))
.withCalendar(TARGET());
Date asofDate = Date(31, August, 2006);
Settings::instance().evaluationDate() = asofDate;
ext::shared_ptr<YieldTermStructure> yieldPtr(
new FlatForward(asofDate, rate, daycount, cmp));
Handle<YieldTermStructure> yieldHandle(yieldPtr);
Handle<Quote> hazardRate(ext::shared_ptr<Quote>(new SimpleQuote(lambda)));
std::vector<Handle<DefaultProbabilityTermStructure>> basket;
ext::shared_ptr<DefaultProbabilityTermStructure> ptr(
new FlatHazardRate(asofDate, hazardRate, ActualActual(ActualActual::ISDA)));
ext::shared_ptr<Pool> pool(new Pool());
std::vector<std::string> names;
// probability key items
std::vector<Issuer> issuers;
std::vector<std::pair<DefaultProbKey, Handle<DefaultProbabilityTermStructure>>>
probabilities;
probabilities.emplace_back(
NorthAmericaCorpDefaultKey(EURCurrency(), SeniorSec, Period(0, Weeks), 10.),
Handle<DefaultProbabilityTermStructure>(ptr));
for (Size i = 0; i < poolSize; ++i) {
std::ostringstream o;
o << "issuer-" << i;
names.push_back(o.str());
basket.emplace_back(ptr);
issuers.emplace_back(probabilities);
pool->add(names.back(), issuers.back(),
NorthAmericaCorpDefaultKey(EURCurrency(), QuantLib::SeniorSec, Period(), 1.));
}
ext::shared_ptr<SimpleQuote> correlation(new SimpleQuote(0.0));
Handle<Quote> hCorrelation(correlation);
QL_REQUIRE(std::size(hwAttachment) == std::size(hwDetachment), "data length does not match");
ext::shared_ptr<PricingEngine> midPCDOEngine(new MidPointCDOEngine(yieldHandle));
ext::shared_ptr<PricingEngine> integralCDOEngine(new IntegralCDOEngine(yieldHandle));
const Size i = dataSet;
correlation->setValue(hwData7[i].correlation);
QL_REQUIRE(std::size(hwAttachment) == std::size(hwData7[i].trancheSpread),
"data length does not match");
std::vector<ext::shared_ptr<DefaultLossModel>> basketModels;
std::vector<std::string> modelNames;
std::vector<Real> relativeToleranceMidp, relativeTolerancePeriod, absoluteTolerance;
if (hwData7[i].nm == -1 && hwData7[i].nz == -1) {
ext::shared_ptr<GaussianConstantLossLM> gaussKtLossLM(
new GaussianConstantLossLM(hCorrelation, std::vector<Real>(poolSize, recovery),
LatentModelIntegrationType::GaussianQuadrature, poolSize,
GaussianCopulaPolicy::initTraits()));
// 1.-Inhomogeneous gaussian
modelNames.emplace_back("Inhomogeneous gaussian");
basketModels.push_back(ext::shared_ptr<DefaultLossModel>(
new IHGaussPoolLossModel(gaussKtLossLM, nBuckets, 5., -5, 15)));
absoluteTolerance.push_back(1.);
relativeToleranceMidp.push_back(0.04);
relativeTolerancePeriod.push_back(0.04);
// 2.-homogeneous gaussian
modelNames.emplace_back("Homogeneous gaussian");
basketModels.push_back(ext::shared_ptr<DefaultLossModel>(
new HomogGaussPoolLossModel(gaussKtLossLM, nBuckets, 5., -5, 15)));
absoluteTolerance.push_back(1.);
relativeToleranceMidp.push_back(0.04);
relativeTolerancePeriod.push_back(0.04);
// 3.-random default gaussian
modelNames.emplace_back("Random default gaussian");
basketModels.push_back(ext::shared_ptr<DefaultLossModel>(
new RandomDefaultLM<GaussianCopulaPolicy>(gaussKtLossLM, numSims)));
absoluteTolerance.push_back(1.);
relativeToleranceMidp.push_back(0.07);
relativeTolerancePeriod.push_back(0.07);
// SECOND MC
// gaussian LHP
modelNames.emplace_back("Gaussian LHP");
basketModels.push_back(ext::shared_ptr<DefaultLossModel>(
new GaussianLHPLossModel(hCorrelation, std::vector<Real>(poolSize, recovery))));
absoluteTolerance.push_back(10.);
relativeToleranceMidp.push_back(0.5);
relativeTolerancePeriod.push_back(0.5);
// Binomial...
// Saddle point...
// Recursive ...
} else if (hwData7[i].nm > 0 && hwData7[i].nz > 0) {
TCopulaPolicy::initTraits initTG;
initTG.tOrders.push_back(hwData7[i].nm);
initTG.tOrders.push_back(hwData7[i].nz);
ext::shared_ptr<TConstantLossLM> TKtLossLM(new TConstantLossLM(
hCorrelation, std::vector<Real>(poolSize, recovery),
LatentModelIntegrationType::GaussianQuadrature, poolSize, initTG));
// 1.-inhomogeneous studentT
modelNames.emplace_back("Inhomogeneous student");
basketModels.push_back(ext::shared_ptr<DefaultLossModel>(
new IHStudentPoolLossModel(TKtLossLM, nBuckets, 5., -5., 15)));
absoluteTolerance.push_back(1.);
relativeToleranceMidp.push_back(0.04);
relativeTolerancePeriod.push_back(0.04);
// 2.-homogeneous student T
modelNames.emplace_back("Homogeneous student");
basketModels.push_back(ext::shared_ptr<DefaultLossModel>(
new HomogTPoolLossModel(TKtLossLM, nBuckets, 5., -5., 15)));
absoluteTolerance.push_back(1.);
relativeToleranceMidp.push_back(0.04);
relativeTolerancePeriod.push_back(0.04);
// 3.-random default student T
modelNames.emplace_back("Random default studentT");
basketModels.push_back(ext::shared_ptr<DefaultLossModel>(
new RandomDefaultLM<TCopulaPolicy>(TKtLossLM, numSims)));
absoluteTolerance.push_back(1.);
relativeToleranceMidp.push_back(0.07);
relativeTolerancePeriod.push_back(0.07);
// SECOND MC
// Binomial...
// Saddle point...
// Recursive ...
} else if (hwData7[i].nm > 0 && hwData7[i].nz == -1) {
TCopulaPolicy::initTraits initTG;
initTG.tOrders.push_back(hwData7[i].nm);
initTG.tOrders.push_back(45);
/* T_{55} is pretty close to a gaussian. Probably theres no need to
be this conservative as the polynomial convolution gets shorter and
faster as the order decreases.
*/
ext::shared_ptr<TConstantLossLM> TKtLossLM(new TConstantLossLM(
hCorrelation, std::vector<Real>(poolSize, recovery),
LatentModelIntegrationType::GaussianQuadrature, poolSize, initTG));
// 1.-inhomogeneous
modelNames.emplace_back("Inhomogeneous student-gaussian");
basketModels.push_back(ext::shared_ptr<DefaultLossModel>(
new IHStudentPoolLossModel(TKtLossLM, nBuckets, 5., -5., 15)));
absoluteTolerance.push_back(1.);
relativeToleranceMidp.push_back(0.04);
relativeTolerancePeriod.push_back(0.04);
// 2.-homogeneous
modelNames.emplace_back("Homogeneous student-gaussian");
basketModels.push_back(ext::shared_ptr<DefaultLossModel>(
new HomogTPoolLossModel(TKtLossLM, nBuckets, 5., -5., 15)));
absoluteTolerance.push_back(1.);
relativeToleranceMidp.push_back(0.04);
relativeTolerancePeriod.push_back(0.04);
// 3.-random default
modelNames.emplace_back("Random default student-gaussian");
basketModels.push_back(ext::shared_ptr<DefaultLossModel>(
new RandomDefaultLM<TCopulaPolicy>(TKtLossLM, numSims)));
absoluteTolerance.push_back(1.);
relativeToleranceMidp.push_back(0.07);
relativeTolerancePeriod.push_back(0.07);
// SECOND MC
// Binomial...
// Saddle point...
// Recursive ...
} else if (hwData7[i].nm == -1 && hwData7[i].nz > 0) {
TCopulaPolicy::initTraits initTG;
initTG.tOrders.push_back(45); // pretty close to gaussian
initTG.tOrders.push_back(hwData7[i].nz);
ext::shared_ptr<TConstantLossLM> TKtLossLM(new TConstantLossLM(
hCorrelation, std::vector<Real>(poolSize, recovery),
LatentModelIntegrationType::GaussianQuadrature, poolSize, initTG));
// 1.-inhomogeneous gaussian
modelNames.emplace_back("Inhomogeneous gaussian-student");
basketModels.push_back(ext::shared_ptr<DefaultLossModel>(
new IHStudentPoolLossModel(TKtLossLM, nBuckets, 5., -5., 15)));
absoluteTolerance.push_back(1.);
relativeToleranceMidp.push_back(0.04);
relativeTolerancePeriod.push_back(0.04);
// 2.-homogeneous gaussian
modelNames.emplace_back("Homogeneous gaussian-student");
basketModels.push_back(ext::shared_ptr<DefaultLossModel>(
new HomogTPoolLossModel(TKtLossLM, nBuckets, 5., -5., 15)));
absoluteTolerance.push_back(1.);
relativeToleranceMidp.push_back(0.04);
relativeTolerancePeriod.push_back(0.04);
// 3.-random default gaussian
modelNames.emplace_back("Random default gaussian-student");
basketModels.push_back(ext::shared_ptr<DefaultLossModel>(
new RandomDefaultLM<TCopulaPolicy>(TKtLossLM, numSims)));
absoluteTolerance.push_back(1.);
relativeToleranceMidp.push_back(0.07);
relativeTolerancePeriod.push_back(0.07);
// SECOND MC
// Binomial...
// Saddle point...
// Recursive ...
} else {
return;
}
for (Size j = 0; j < std::size(hwAttachment); j++) {
ext::shared_ptr<Basket> basketPtr(
new Basket(asofDate, names, nominals, pool, hwAttachment[j], hwDetachment[j]));
std::ostringstream trancheId;
trancheId << "[" << hwAttachment[j] << " , " << hwDetachment[j] << "]";
SyntheticCDO cdoe(basketPtr, Protection::Seller, schedule, 0.0, premium, daycount,
Following);
for (Size im = 0; im < basketModels.size(); im++) {
basketPtr->setLossModel(basketModels[im]);
cdoe.setPricingEngine(midPCDOEngine);
check(i, j,
modelNames[im] + std::string(" with midp integration on ") + trancheId.str(),
cdoe.fairPremium() * 1e4, hwData7[i].trancheSpread[j], absoluteTolerance[im],
relativeToleranceMidp[im]);
cdoe.setPricingEngine(integralCDOEngine);
check(i, j,
modelNames[im] + std::string(" with step integration on ") + trancheId.str(),
cdoe.fairPremium() * 1e4, hwData7[i].trancheSpread[j], absoluteTolerance[im],
relativeTolerancePeriod[im]);
}
}
}
#endif
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
|
