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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/constantlosslatentmodel.hpp>
#include <ql/experimental/credit/integralntdengine.hpp>
#include <ql/experimental/credit/nthtodefault.hpp>
#include <ql/experimental/credit/pool.hpp>
#include <ql/experimental/credit/randomdefaultlatentmodel.hpp>
#include <ql/instruments/creditdefaultswap.hpp>
#include <ql/pricingengines/credit/integralcdsengine.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 <iostream>
#include <string>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(NthToDefaultTests)
#ifndef QL_PATCH_SOLARIS
struct hwDatum {
Size rank;
Real spread[3];
};
/* Spread (bp p.a.) to buy protection for the nth to default from
a basket of 10 names. All pairs have same correlation, 0 in
column 2, 0.3 in column 3, 0.6 in column 4. Default intensity
for all names is constant at 0.01, maturity 5 years, equal
notional amounts.
*/
hwDatum hwData[] = {
{ 1, { 603, 440, 293 } },
{ 2, { 98, 139, 137 } },
{ 3, { 12, 53, 79 } },
{ 4, { 1, 21, 49 } },
{ 5, { 0, 8, 31 } },
{ 6, { 0, 3, 19 } },
{ 7, { 0, 1, 12 } },
{ 8, { 0, 0, 7 } },
{ 9, { 0, 0, 3 } },
{10, { 0, 0, 1 } }
};
Real hwCorrelation[] = { 0.0, 0.3, 0.6 };
struct hwDatumDist {
Size rank;
Real spread[4];
};
// HW Table 3, Nth to Default Basket
// corr = 0.3
// NM/NZ
// rank inf/inf 5/inf inf/5 5/5
hwDatumDist hwDataDist[] = {
{ 1, { 440, 419, 474, 455 } },
{ 2, { 139, 127, 127, 116 } },
{ 3, { 53, 51, 44, 44 } },
{ 4, { 21, 24, 18, 22 } },
{ 5, { 8, 13, 7, 13 } },
{ 6, { 3, 8, 3, 8 } },
{ 7, { 1, 5, 1, 5 } },
{ 8, { 0, 3, 0, 4 } },
{ 9, { 0, 2, 0, 2 } },
{10, { 0, 1, 0, 1 } }
};
BOOST_AUTO_TEST_CASE(testGauss, *precondition(if_speed(Slow))) {
BOOST_TEST_MESSAGE("Testing nth-to-default against Hull-White values "
"with Gaussian copula...");
/*************************
* Tolerances
*/
Real relTolerance = 0.015; // relative difference
Real absTolerance = 1; // absolute difference in bp
Period timeUnit = 1*Weeks; // required to reach accuracy
Size names = 10;
QL_REQUIRE (std::size(hwData) == names, "hwData length does not match");
Real rate = 0.05;
DayCounter dc = Actual365Fixed();
Compounding cmp = Continuous; // Simple;
Real recovery = 0.4;
std::vector<Real> lambda (names, 0.01);
Real namesNotional = 100.0;
Schedule schedule = MakeSchedule().from(Date (1, September, 2006))
.to(Date (1, September, 2011))
.withTenor(3*Months)
.withCalendar(TARGET());
Date asofDate(31, August, 2006);
Settings::instance().evaluationDate() = asofDate;
std::vector<Date> gridDates = {
asofDate,
TARGET().advance (asofDate, Period (1, Years)),
TARGET().advance (asofDate, Period (5, Years)),
TARGET().advance (asofDate, Period (7, Years))
};
ext::shared_ptr<YieldTermStructure> yieldPtr (
new FlatForward (asofDate, rate, dc, cmp));
Handle<YieldTermStructure> yieldHandle (yieldPtr);
std::vector<Handle<DefaultProbabilityTermStructure> > probabilities;
Period maxTerm (10, Years);
for (Real i : lambda) {
Handle<Quote> h(ext::shared_ptr<Quote>(new SimpleQuote(i)));
ext::shared_ptr<DefaultProbabilityTermStructure> ptr (
new FlatHazardRate(asofDate, h, dc));
probabilities.emplace_back(ptr);
}
ext::shared_ptr<SimpleQuote> simpleQuote (new SimpleQuote(0.0));
Handle<Quote> correlationHandle (simpleQuote);
ext::shared_ptr<DefaultLossModel> copula( new
ConstantLossModel<GaussianCopulaPolicy>( correlationHandle,
std::vector<Real>(names, recovery),
LatentModelIntegrationType::GaussianQuadrature, names,
GaussianCopulaPolicy::initTraits()));
/* If you like the action you can price with the simulation engine below
instead below. But you need at least 1e6 simulations to pass the pricing
error tests
*/
//ext::shared_ptr<GaussianDefProbLM> gLM(
// ext::make_shared<GaussianDefProbLM>(correlationHandle, names,
// LatentModelIntegrationType::GaussianQuadrature,
// // g++ requires this when using make_shared
// GaussianCopulaPolicy::initTraits()));
//Size numSimulations = 1000000;
//// Size numCoresUsed = 4; use your are in the multithread branch
//// Sobol, many cores
//ext::shared_ptr<RandomDefaultLM<GaussianCopulaPolicy> > copula(
// new RandomDefaultLM<GaussianCopulaPolicy>(gLM,
// std::vector<Real>(names, recovery), numSimulations, 1.e-6,
// 2863311530));
// Set up pool and basket
std::vector<std::string> namesIds;
namesIds.reserve(names);
for(Size i=0; i<names; i++)
namesIds.push_back(std::string("Name") + std::to_string(i));
std::vector<Issuer> issuers;
for(Size i=0; i<names; i++) {
std::vector<QuantLib::Issuer::key_curve_pair> curves(1,
std::make_pair(NorthAmericaCorpDefaultKey(
EURCurrency(), QuantLib::SeniorSec,
Period(), 1. // amount threshold
), probabilities[i]));
issuers.emplace_back(curves);
}
ext::shared_ptr<Pool> thePool = ext::make_shared<Pool>();
for(Size i=0; i<names; i++)
thePool->add(namesIds[i], issuers[i], NorthAmericaCorpDefaultKey(
EURCurrency(), QuantLib::SeniorSec, Period(), 1.));
std::vector<DefaultProbKey> defaultKeys(probabilities.size(),
NorthAmericaCorpDefaultKey(EURCurrency(), SeniorSec, Period(), 1.));
ext::shared_ptr<Basket> basket(new Basket(asofDate, namesIds,
std::vector<Real>(names, namesNotional/names), thePool, 0., 1.));
ext::shared_ptr<PricingEngine> engine(
new IntegralNtdEngine(timeUnit, yieldHandle));
std::vector<NthToDefault> ntd;
for (Size i = 1; i <= probabilities.size(); i++) {
ntd.emplace_back(basket, i, Protection::Seller, schedule, 0.0, 0.02, Actual360(),
namesNotional * names, true);
ntd.back().setPricingEngine(engine);
}
static_assert(std::size(hwCorrelation) == 3,
"correlation length does not match");
Real diff, maxDiff = 0;
basket->setLossModel(copula);
for (Size j = 0; j < std::size(hwCorrelation); j++) {
simpleQuote->setValue (hwCorrelation[j]);
for (Size i = 0; i < ntd.size(); i++) {
QL_REQUIRE(ntd[i].rank() == hwData[i].rank, "rank does not match");
diff = 1e4 * ntd[i].fairPremium() - hwData[i].spread[j];
maxDiff = std::max(maxDiff, fabs (diff));
BOOST_CHECK_MESSAGE (fabs(diff/hwData[i].spread[j]) < relTolerance
|| fabs(diff) < absTolerance,
"tolerance " << relTolerance << "|"
<< absTolerance << " exceeded");
}
}
}
BOOST_AUTO_TEST_CASE(testStudent, *precondition(if_speed(Slow))) {
BOOST_TEST_MESSAGE("Testing nth-to-default against Hull-White values "
"with Student copula...");
/*************************
* Tolerances
*/
Real relTolerance = 0.017; // relative difference
Real absTolerance = 1; // absolute difference in bp
Period timeUnit = 1*Weeks; // required to reach accuracy
Size names = 10;
QL_REQUIRE (std::size(hwDataDist) == names, "hwDataDist length does not match");
Real rate = 0.05;
DayCounter dc = Actual365Fixed();
Compounding cmp = Continuous; // Simple;
Real recovery = 0.4;
std::vector<Real> lambda (names, 0.01);
Real namesNotional = 100.0;
Schedule schedule = MakeSchedule().from(Date (1, September, 2006))
.to(Date (1, September, 2011))
.withTenor(3*Months)
.withCalendar(TARGET());
Date asofDate(31, August, 2006);
Settings::instance().evaluationDate() = asofDate;
std::vector<Date> gridDates {
asofDate,
TARGET().advance (asofDate, Period (1, Years)),
TARGET().advance (asofDate, Period (5, Years)),
TARGET().advance (asofDate, Period (7, Years))
};
ext::shared_ptr<YieldTermStructure> yieldPtr (
new FlatForward (asofDate, rate, dc, cmp));
Handle<YieldTermStructure> yieldHandle (yieldPtr);
std::vector<Handle<DefaultProbabilityTermStructure> > probabilities;
Period maxTerm (10, Years);
for (Real i : lambda) {
Handle<Quote> h(ext::shared_ptr<Quote>(new SimpleQuote(i)));
ext::shared_ptr<DefaultProbabilityTermStructure> ptr (
new FlatHazardRate(asofDate, h, dc));
probabilities.emplace_back(ptr);
}
ext::shared_ptr<SimpleQuote> simpleQuote (new SimpleQuote(0.0));
Handle<Quote> correlationHandle (simpleQuote);
TCopulaPolicy::initTraits iniT;
iniT.tOrders = std::vector<QuantLib::Integer>(2,5);
ext::shared_ptr<DefaultLossModel> copula( new
ConstantLossModel<TCopulaPolicy>( correlationHandle,
std::vector<Real>(names, recovery),
LatentModelIntegrationType::GaussianQuadrature, names, iniT));
// Set up pool and basket
std::vector<std::string> namesIds;
namesIds.reserve(names);
for(Size i=0; i<names; i++)
namesIds.push_back(std::string("Name") + std::to_string(i));
std::vector<Issuer> issuers;
for(Size i=0; i<names; i++) {
std::vector<QuantLib::Issuer::key_curve_pair> curves(1,
std::make_pair(NorthAmericaCorpDefaultKey(
EURCurrency(), QuantLib::SeniorSec,
Period(), 1. // amount threshold
), probabilities[i]));
issuers.emplace_back(curves);
}
ext::shared_ptr<Pool> thePool = ext::make_shared<Pool>();
for(Size i=0; i<names; i++)
thePool->add(namesIds[i], issuers[i], NorthAmericaCorpDefaultKey(
EURCurrency(), QuantLib::SeniorSec, Period(), 1.));
std::vector<DefaultProbKey> defaultKeys(probabilities.size(),
NorthAmericaCorpDefaultKey(EURCurrency(), SeniorSec, Period(), 1.));
ext::shared_ptr<Basket> basket(new Basket(asofDate, namesIds,
std::vector<Real>(names, namesNotional/names), thePool, 0., 1.));
ext::shared_ptr<PricingEngine> engine(
new IntegralNtdEngine(timeUnit, yieldHandle));
std::vector<NthToDefault> ntd;
for (Size i = 1; i <= probabilities.size(); i++) {
ntd.emplace_back(basket, i, Protection::Seller, schedule, 0.0, 0.02, Actual360(),
namesNotional * names, true);
ntd.back().setPricingEngine(engine);
}
static_assert(std::size(hwCorrelation) == 3,
"correlation length does not match");
Real maxDiff = 0;
basket->setLossModel(copula);
// This is the necessary code, but a proper hwData for the t copula is needed.
// Real diff;
// for (Size j = 0; j < std::size(hwCorrelation); j++) {
// simpleQuote->setValue (hwCorrelation[j]);
// for (Size i = 0; i < ntd.size(); i++) {
// QL_REQUIRE (ntd[i].rank() == hwData[i].rank, "rank does not match");
// static_assert(std::size(hwCorrelation) == std::size(hwData[i].spread),
// "vector length does not match");
// diff = 1e4 * ntd[i].fairPremium() - hwData[i].spread[j];
// maxDiff = std::max(maxDiff, fabs (diff));
// BOOST_CHECK_MESSAGE (fabs(diff/hwData[i].spread[j]) < relTolerance
// || fabs(diff) < absTolerance,
// "tolerance2 " << relTolerance << "|"
// << absTolerance << " exceeded";
// }
// }
//instead of this BEGIN
simpleQuote->setValue (0.3);
for (Size i = 0; i < ntd.size(); i++) {
QL_REQUIRE (ntd[i].rank() == hwDataDist[i].rank, "rank does not match");
Real diff = 1e4 * ntd[i].fairPremium() - hwDataDist[i].spread[3];
maxDiff = std::max(maxDiff, fabs (diff));
BOOST_CHECK_MESSAGE (fabs(diff / hwDataDist[i].spread[3]) < relTolerance ||
fabs(diff) < absTolerance,
"tolerance " << relTolerance << "|"
<< absTolerance << " exceeded" << i << "|"
<< abs(diff) << "|" << hwDataDist[i].spread[3]);
}
//END
}
#endif
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
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