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catbonds.cpp
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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2012, 2013 Grzegorz Andruszkiewicz
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
<[email protected]>. 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 "catbonds.hpp"
#include "utilities.hpp"
#include <ql/types.hpp>
#include <ql/experimental/catbonds/all.hpp>
#include <ql/instruments/bonds/floatingratebond.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/calendars/unitedstates.hpp>
#include <ql/time/calendars/brazil.hpp>
#include <ql/time/calendars/nullcalendar.hpp>
#include <ql/time/daycounters/thirty360.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <ql/time/daycounters/business252.hpp>
#include <ql/indexes/ibor/usdlibor.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <ql/time/schedule.hpp>
#include <ql/cashflows/fixedratecoupon.hpp>
#include <ql/cashflows/simplecashflow.hpp>
#include <ql/cashflows/couponpricer.hpp>
#include <ql/cashflows/cashflows.hpp>
#include <ql/pricingengines/bond/discountingbondengine.hpp>
#include <ql/pricingengines/bond/bondfunctions.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
using boost::shared_ptr;
namespace {
std::pair<Date, Real> data[] = {std::pair<Date, Real>(Date(1, February, 2012), 100), std::pair<Date, Real>(Date(1, July, 2013), 150), std::pair<Date, Real>(Date(5, January, 2014), 50)};
boost::shared_ptr<std::vector<std::pair<Date, Real> > > sampleEvents(new std::vector<std::pair<Date, Real> >(data, data+3));
Date eventsStart(1, January, 2011);
Date eventsEnd(31, December, 2014);
}
void CatBondTest::testEventSetForWholeYears() {
BOOST_TEST_MESSAGE("Testing that catastrophe events are split correctly for periods of whole years...");
EventSet catRisk(sampleEvents, eventsStart, eventsEnd);
boost::shared_ptr<CatSimulation> simulation = catRisk.newSimulation(Date(1, January, 2015), Date(31, December, 2015));
BOOST_REQUIRE(simulation);
std::vector<std::pair<Date, Real> > path;
BOOST_REQUIRE(simulation->nextPath(path));
BOOST_CHECK_EQUAL(Size(0), path.size());
BOOST_REQUIRE(simulation->nextPath(path));
BOOST_CHECK_EQUAL(Size(1), path.size());
BOOST_CHECK_EQUAL(Date(1, February, 2015), path.at(0).first);
BOOST_CHECK_EQUAL(100, path.at(0).second);
BOOST_REQUIRE(simulation->nextPath(path));
BOOST_CHECK_EQUAL(Size(1), path.size());
BOOST_CHECK_EQUAL(Date(1, July, 2015), path.at(0).first);
BOOST_CHECK_EQUAL(150, path.at(0).second);
BOOST_REQUIRE(simulation->nextPath(path));
BOOST_CHECK_EQUAL(Size(1), path.size());
BOOST_CHECK_EQUAL(Date(5, January, 2015), path.at(0).first);
BOOST_CHECK_EQUAL(50, path.at(0).second);
BOOST_REQUIRE(!simulation->nextPath(path));
}
void CatBondTest::testEventSetForIrregularPeriods() {
BOOST_TEST_MESSAGE("Testing that catastrophe events are split correctly for irregular periods...");
EventSet catRisk(sampleEvents, eventsStart, eventsEnd);
boost::shared_ptr<CatSimulation> simulation = catRisk.newSimulation(Date(2, January, 2015), Date(5, January, 2016));
BOOST_REQUIRE(simulation);
std::vector<std::pair<Date, Real> > path;
BOOST_REQUIRE(simulation->nextPath(path));
BOOST_CHECK_EQUAL(Size(0), path.size());
BOOST_REQUIRE(simulation->nextPath(path));
BOOST_CHECK_EQUAL(Size(2), path.size());
BOOST_CHECK_EQUAL(Date(1, July, 2015), path.at(0).first);
BOOST_CHECK_EQUAL(150, path.at(0).second);
BOOST_CHECK_EQUAL(Date(5, January, 2016), path.at(1).first);
BOOST_CHECK_EQUAL(50, path.at(1).second);
BOOST_REQUIRE(!simulation->nextPath(path));
}
void CatBondTest::testEventSetForNoEvents () {
BOOST_TEST_MESSAGE("Testing that catastrophe events are split correctly when there are no simulated events...");
boost::shared_ptr<std::vector<std::pair<Date, Real> > > emptyEvents(new std::vector<std::pair<Date, Real> >());
EventSet catRisk(emptyEvents, eventsStart, eventsEnd);
boost::shared_ptr<CatSimulation> simulation = catRisk.newSimulation(Date(2, January, 2015), Date(5, January, 2016));
BOOST_REQUIRE(simulation);
std::vector<std::pair<Date, Real> > path;
BOOST_REQUIRE(simulation->nextPath(path));
BOOST_CHECK_EQUAL(Size(0), path.size());
BOOST_REQUIRE(simulation->nextPath(path));
BOOST_CHECK_EQUAL(Size(0), path.size());
BOOST_REQUIRE(!simulation->nextPath(path));
}
void CatBondTest::testBetaRisk() {
BOOST_TEST_MESSAGE("Testing that beta risk gives correct terminal distribution...");
const size_t PATHS = 1000000;
BetaRisk catRisk(100.0, 100.0, 10.0, 15.0);
boost::shared_ptr<CatSimulation> simulation = catRisk.newSimulation(Date(2, January, 2015), Date(2, January, 2018));
BOOST_REQUIRE(simulation);
std::vector<std::pair<Date, Real> > path;
Real sum = 0.0;
Real sumSquares = 0.0;
Real poissonSum = 0.0;
Real poissonSumSquares = 0.0;
for(size_t i=0; i<PATHS; ++i)
{
BOOST_REQUIRE(simulation->nextPath(path));
Real processValue = 0.0;
for(size_t j=0; j<path.size(); ++j) processValue+=path[j].second;
sum+=processValue;
sumSquares+=processValue*processValue;
poissonSum+=path.size();
poissonSumSquares+=path.size()*path.size();
}
Real poissonMean = poissonSum/PATHS;
BOOST_CHECK_CLOSE(Real(3.0/100.0), poissonMean, 2);
Real poissonVar = poissonSumSquares/PATHS - poissonMean*poissonMean;
BOOST_CHECK_CLOSE(Real(3.0/100.0), poissonVar, 5);
Real expectedMean = 3.0*10.0/100.0;
Real actualMean = sum/PATHS;
BOOST_CHECK_CLOSE(expectedMean, actualMean, 1);
Real expectedVar = 3.0*(15.0*15.0+10*10)/100.0;
Real actualVar = sumSquares/PATHS - actualMean*actualMean;
#if BOOST_VERSION > 106300
// changes in Boost.Random after 1.64 increased numerical error
BOOST_CHECK_CLOSE(expectedVar, actualVar, 1.5);
#else
BOOST_CHECK_CLOSE(expectedVar, actualVar, 1);
#endif
}
namespace {
struct CommonVars {
// common data
Calendar calendar;
Date today;
Real faceAmount;
// cleanup
SavedSettings backup;
// setup
CommonVars() {
calendar = TARGET();
today = calendar.adjust(Date::todaysDate());
Settings::instance().evaluationDate() = today;
faceAmount = 1000000.0;
}
};
}
void CatBondTest::testRiskFreeAgainstFloatingRateBond() {
BOOST_TEST_MESSAGE("Testing floating-rate cat bond against risk-free floating-rate bond...");
CommonVars vars;
Date today(22,November,2004);
Settings::instance().evaluationDate() = today;
Natural settlementDays = 1;
Handle<YieldTermStructure> riskFreeRate(flatRate(today,0.025,Actual360()));
Handle<YieldTermStructure> discountCurve(flatRate(today,0.03,Actual360()));
shared_ptr<IborIndex> index(new USDLibor(6*Months, riskFreeRate));
Natural fixingDays = 1;
Real tolerance = 1.0e-6;
shared_ptr<IborCouponPricer> pricer(new
BlackIborCouponPricer(Handle<OptionletVolatilityStructure>()));
// plain
Schedule sch(Date(30,November,2004),
Date(30,November,2008),
Period(Semiannual),
UnitedStates(UnitedStates::GovernmentBond),
ModifiedFollowing, ModifiedFollowing,
DateGeneration::Backward, false);
boost::shared_ptr<CatRisk> noCatRisk(new EventSet(
boost::shared_ptr<std::vector<std::pair<Date, Real> > >(new std::vector<std::pair<Date, Real> >()),
Date(1, Jan, 2000), Date(31, Dec, 2010)));
boost::shared_ptr<EventPaymentOffset> paymentOffset(new NoOffset());
boost::shared_ptr<NotionalRisk> notionalRisk(new DigitalNotionalRisk(paymentOffset, 100));
FloatingRateBond bond1(settlementDays, vars.faceAmount, sch,
index, ActualActual(ActualActual::ISMA),
ModifiedFollowing, fixingDays,
std::vector<Real>(), std::vector<Spread>(),
std::vector<Rate>(), std::vector<Rate>(),
false,
100.0, Date(30,November,2004));
FloatingCatBond catBond1(settlementDays, vars.faceAmount, sch,
index, ActualActual(ActualActual::ISMA),
notionalRisk,
ModifiedFollowing, fixingDays,
std::vector<Real>(), std::vector<Spread>(),
std::vector<Rate>(), std::vector<Rate>(),
false,
100.0, Date(30,November,2004));
shared_ptr<PricingEngine> bondEngine(
new DiscountingBondEngine(riskFreeRate));
bond1.setPricingEngine(bondEngine);
setCouponPricer(bond1.cashflows(),pricer);
shared_ptr<PricingEngine> catBondEngine(new MonteCarloCatBondEngine(noCatRisk, riskFreeRate));
catBond1.setPricingEngine(catBondEngine);
setCouponPricer(catBond1.cashflows(),pricer);
#if defined(QL_USE_INDEXED_COUPON)
Real cachedPrice1 = 99.874645;
#else
Real cachedPrice1 = 99.874646;
#endif
Real price = bond1.cleanPrice();
Real catPrice = catBond1.cleanPrice();
if (std::fabs(price-cachedPrice1) > tolerance || std::fabs(catPrice-price) > tolerance) {
BOOST_FAIL("failed to reproduce floating rate bond price:\n"
<< std::fixed
<< " floating bond: " << price << "\n"
<< " catBond bond: " << catPrice << "\n"
<< " expected: " << cachedPrice1 << "\n"
<< " error: " << catPrice-price);
}
// different risk-free and discount curve
FloatingRateBond bond2(settlementDays, vars.faceAmount, sch,
index, ActualActual(ActualActual::ISMA),
ModifiedFollowing, fixingDays,
std::vector<Rate>(), std::vector<Spread>(),
std::vector<Rate>(), std::vector<Rate>(),
false,
100.0, Date(30,November,2004));
FloatingCatBond catBond2(settlementDays, vars.faceAmount, sch,
index, ActualActual(ActualActual::ISMA),
notionalRisk,
ModifiedFollowing, fixingDays,
std::vector<Rate>(), std::vector<Spread>(),
std::vector<Rate>(), std::vector<Rate>(),
false,
100.0, Date(30,November,2004));
shared_ptr<PricingEngine> bondEngine2(
new DiscountingBondEngine(discountCurve));
bond2.setPricingEngine(bondEngine2);
setCouponPricer(bond2.cashflows(),pricer);
shared_ptr<PricingEngine> catBondEngine2(new MonteCarloCatBondEngine(noCatRisk, discountCurve));
catBond2.setPricingEngine(catBondEngine2);
setCouponPricer(catBond2.cashflows(),pricer);
#if defined(QL_USE_INDEXED_COUPON)
Real cachedPrice2 = 97.955904;
#else
Real cachedPrice2 = 97.955904;
#endif
price = bond2.cleanPrice();
catPrice = catBond2.cleanPrice();
if (std::fabs(price-cachedPrice2) > tolerance || std::fabs(catPrice-price) > tolerance) {
BOOST_FAIL("failed to reproduce floating rate bond price:\n"
<< std::fixed
<< " floating bond: " << price << "\n"
<< " catBond bond: " << catPrice << "\n"
<< " expected: " << cachedPrice2 << "\n"
<< " error: " << catPrice-price);
}
// varying spread
std::vector<Rate> spreads(4);
spreads[0] = 0.001;
spreads[1] = 0.0012;
spreads[2] = 0.0014;
spreads[3] = 0.0016;
FloatingRateBond bond3(settlementDays, vars.faceAmount, sch,
index, ActualActual(ActualActual::ISMA),
ModifiedFollowing, fixingDays,
std::vector<Real>(), spreads,
std::vector<Rate>(), std::vector<Rate>(),
false,
100.0, Date(30,November,2004));
FloatingCatBond catBond3(settlementDays, vars.faceAmount, sch,
index, ActualActual(ActualActual::ISMA),
notionalRisk,
ModifiedFollowing, fixingDays,
std::vector<Real>(), spreads,
std::vector<Rate>(), std::vector<Rate>(),
false,
100.0, Date(30,November,2004));
bond3.setPricingEngine(bondEngine2);
setCouponPricer(bond3.cashflows(),pricer);
catBond3.setPricingEngine(catBondEngine2);
setCouponPricer(catBond3.cashflows(),pricer);
#if defined(QL_USE_INDEXED_COUPON)
Real cachedPrice3 = 98.495458;
#else
Real cachedPrice3 = 98.495459;
#endif
price = bond3.cleanPrice();
catPrice = catBond3.cleanPrice();
if (std::fabs(price-cachedPrice3) > tolerance || std::fabs(catPrice-price) > tolerance) {
BOOST_FAIL("failed to reproduce floating rate bond price:\n"
<< std::fixed
<< " floating bond: " << price << "\n"
<< " catBond bond: " << catPrice << "\n"
<< " expected: " << cachedPrice2 << "\n"
<< " error: " << catPrice-price);
}
}
void CatBondTest::testCatBondInDoomScenario() {
BOOST_TEST_MESSAGE("Testing floating-rate cat bond in a doom scenario (certain default)...");
CommonVars vars;
Date today(22,November,2004);
Settings::instance().evaluationDate() = today;
Natural settlementDays = 1;
Handle<YieldTermStructure> riskFreeRate(flatRate(today,0.025,Actual360()));
Handle<YieldTermStructure> discountCurve(flatRate(today,0.03,Actual360()));
shared_ptr<IborIndex> index(new USDLibor(6*Months, riskFreeRate));
Natural fixingDays = 1;
Real tolerance = 1.0e-6;
shared_ptr<IborCouponPricer> pricer(new
BlackIborCouponPricer(Handle<OptionletVolatilityStructure>()));
Schedule sch(Date(30,November,2004),
Date(30,November,2008),
Period(Semiannual),
UnitedStates(UnitedStates::GovernmentBond),
ModifiedFollowing, ModifiedFollowing,
DateGeneration::Backward, false);
boost::shared_ptr<std::vector<std::pair<Date, Real> > > events(new std::vector<std::pair<Date, Real> >());
events->push_back(std::pair<Date, Real>(Date(30,November,2004), 1000));
boost::shared_ptr<CatRisk> doomCatRisk(new EventSet(
events,
Date(30,November,2004), Date(30,November,2008)));
boost::shared_ptr<EventPaymentOffset> paymentOffset(new NoOffset());
boost::shared_ptr<NotionalRisk> notionalRisk(new DigitalNotionalRisk(paymentOffset, 100));
FloatingCatBond catBond(settlementDays, vars.faceAmount, sch,
index, ActualActual(ActualActual::ISMA),
notionalRisk,
ModifiedFollowing, fixingDays,
std::vector<Rate>(), std::vector<Spread>(),
std::vector<Rate>(), std::vector<Rate>(),
false,
100.0, Date(30,November,2004));
shared_ptr<PricingEngine> catBondEngine(new MonteCarloCatBondEngine(doomCatRisk, discountCurve));
catBond.setPricingEngine(catBondEngine);
setCouponPricer(catBond.cashflows(),pricer);
Real price = catBond.cleanPrice();
BOOST_CHECK_EQUAL(0, price);
Real lossProbability = catBond.lossProbability();
Real exhaustionProbability = catBond.exhaustionProbability();
Real expectedLoss = catBond.expectedLoss();
BOOST_CHECK_CLOSE(Real(1.0), lossProbability, tolerance);
BOOST_CHECK_CLOSE(Real(1.0), exhaustionProbability, tolerance);
BOOST_CHECK_CLOSE(Real(1.0), expectedLoss, tolerance);
}
void CatBondTest::testCatBondWithDoomOnceInTenYears() {
BOOST_TEST_MESSAGE("Testing floating-rate cat bond in a doom once in 10 years scenario...");
CommonVars vars;
Date today(22,November,2004);
Settings::instance().evaluationDate() = today;
Natural settlementDays = 1;
Handle<YieldTermStructure> riskFreeRate(flatRate(today,0.025,Actual360()));
Handle<YieldTermStructure> discountCurve(flatRate(today,0.03,Actual360()));
shared_ptr<IborIndex> index(new USDLibor(6*Months, riskFreeRate));
Natural fixingDays = 1;
Real tolerance = 1.0e-6;
shared_ptr<IborCouponPricer> pricer(new
BlackIborCouponPricer(Handle<OptionletVolatilityStructure>()));
Schedule sch(Date(30,November,2004),
Date(30,November,2008),
Period(Semiannual),
UnitedStates(UnitedStates::GovernmentBond),
ModifiedFollowing, ModifiedFollowing,
DateGeneration::Backward, false);
boost::shared_ptr<std::vector<std::pair<Date, Real> > > events(new std::vector<std::pair<Date, Real> >());
events->push_back(std::pair<Date, Real>(Date(30,November,2008), 1000));
boost::shared_ptr<CatRisk> doomCatRisk(new EventSet(
events,
Date(30,November,2004), Date(30,November,2044)));
boost::shared_ptr<CatRisk> noCatRisk(new EventSet(
boost::shared_ptr<std::vector<std::pair<Date, Real> > >(new std::vector<std::pair<Date, Real> >()),
Date(1, Jan, 2000), Date(31, Dec, 2010)));
boost::shared_ptr<EventPaymentOffset> paymentOffset(new NoOffset());
boost::shared_ptr<NotionalRisk> notionalRisk(new DigitalNotionalRisk(paymentOffset, 100));
FloatingCatBond catBond(settlementDays, vars.faceAmount, sch,
index, ActualActual(ActualActual::ISMA),
notionalRisk,
ModifiedFollowing, fixingDays,
std::vector<Rate>(), std::vector<Spread>(),
std::vector<Rate>(), std::vector<Rate>(),
false,
100.0, Date(30,November,2004));
shared_ptr<PricingEngine> catBondEngine(new MonteCarloCatBondEngine(doomCatRisk, discountCurve));
catBond.setPricingEngine(catBondEngine);
setCouponPricer(catBond.cashflows(),pricer);
Real price = catBond.cleanPrice();
Real yield = catBond.yield(ActualActual(ActualActual::ISMA), Simple, Annual);
Real lossProbability = catBond.lossProbability();
Real exhaustionProbability = catBond.exhaustionProbability();
Real expectedLoss = catBond.expectedLoss();
BOOST_CHECK_CLOSE(Real(0.1), lossProbability, tolerance);
BOOST_CHECK_CLOSE(Real(0.1), exhaustionProbability, tolerance);
BOOST_CHECK_CLOSE(Real(0.1), expectedLoss, tolerance);
shared_ptr<PricingEngine> catBondEngineRF(new MonteCarloCatBondEngine(noCatRisk, discountCurve));
catBond.setPricingEngine(catBondEngineRF);
Real riskFreePrice = catBond.cleanPrice();
Real riskFreeYield = catBond.yield(ActualActual(ActualActual::ISMA), Simple, Annual);
Real riskFreeLossProbability = catBond.lossProbability();
Real riskFreeExhaustionProbability = catBond.exhaustionProbability();
Real riskFreeExpectedLoss = catBond.expectedLoss();
BOOST_CHECK_CLOSE(Real(0.0), riskFreeLossProbability, tolerance);
BOOST_CHECK_CLOSE(Real(0.0), riskFreeExhaustionProbability, tolerance);
BOOST_CHECK(std::abs(riskFreeExpectedLoss) < tolerance);
BOOST_CHECK_CLOSE(riskFreePrice*0.9, price, tolerance);
BOOST_CHECK_LT(riskFreeYield, yield);
}
void CatBondTest::testCatBondWithDoomOnceInTenYearsProportional() {
BOOST_TEST_MESSAGE("Testing floating-rate cat bond in a doom once in 10 years scenario with proportional notional reduction...");
CommonVars vars;
Date today(22,November,2004);
Settings::instance().evaluationDate() = today;
Natural settlementDays = 1;
Handle<YieldTermStructure> riskFreeRate(flatRate(today,0.025,Actual360()));
Handle<YieldTermStructure> discountCurve(flatRate(today,0.03,Actual360()));
shared_ptr<IborIndex> index(new USDLibor(6*Months, riskFreeRate));
Natural fixingDays = 1;
Real tolerance = 1.0e-6;
shared_ptr<IborCouponPricer> pricer(new
BlackIborCouponPricer(Handle<OptionletVolatilityStructure>()));
Schedule sch(Date(30,November,2004),
Date(30,November,2008),
Period(Semiannual),
UnitedStates(UnitedStates::GovernmentBond),
ModifiedFollowing, ModifiedFollowing,
DateGeneration::Backward, false);
boost::shared_ptr<std::vector<std::pair<Date, Real> > > events(new std::vector<std::pair<Date, Real> >());
events->push_back(std::pair<Date, Real>(Date(30,November,2008), 1000));
boost::shared_ptr<CatRisk> doomCatRisk(new EventSet(
events,
Date(30,November,2004), Date(30,November,2044)));
boost::shared_ptr<CatRisk> noCatRisk(new EventSet(
boost::shared_ptr<std::vector<std::pair<Date, Real> > >(new std::vector<std::pair<Date, Real> >()),
Date(1, Jan, 2000), Date(31, Dec, 2010)));
boost::shared_ptr<EventPaymentOffset> paymentOffset(new NoOffset());
boost::shared_ptr<NotionalRisk> notionalRisk(new ProportionalNotionalRisk(paymentOffset, 500, 1500));
FloatingCatBond catBond(settlementDays, vars.faceAmount, sch,
index, ActualActual(ActualActual::ISMA),
notionalRisk,
ModifiedFollowing, fixingDays,
std::vector<Rate>(), std::vector<Spread>(),
std::vector<Rate>(), std::vector<Rate>(),
false,
100.0, Date(30,November,2004));
shared_ptr<PricingEngine> catBondEngine(new MonteCarloCatBondEngine(doomCatRisk, discountCurve));
catBond.setPricingEngine(catBondEngine);
setCouponPricer(catBond.cashflows(),pricer);
Real price = catBond.cleanPrice();
Real yield = catBond.yield(ActualActual(ActualActual::ISMA), Simple, Annual);
Real lossProbability = catBond.lossProbability();
Real exhaustionProbability = catBond.exhaustionProbability();
Real expectedLoss = catBond.expectedLoss();
BOOST_CHECK_CLOSE(Real(0.1), lossProbability, tolerance);
BOOST_CHECK_CLOSE(Real(0.0), exhaustionProbability, tolerance);
BOOST_CHECK_CLOSE(Real(0.05), expectedLoss, tolerance);
shared_ptr<PricingEngine> catBondEngineRF(new MonteCarloCatBondEngine(noCatRisk, discountCurve));
catBond.setPricingEngine(catBondEngineRF);
Real riskFreePrice = catBond.cleanPrice();
Real riskFreeYield = catBond.yield(ActualActual(ActualActual::ISMA), Simple, Annual);
Real riskFreeLossProbability = catBond.lossProbability();
Real riskFreeExpectedLoss = catBond.expectedLoss();
BOOST_CHECK_CLOSE(Real(0.0), riskFreeLossProbability, tolerance);
BOOST_CHECK(std::abs(riskFreeExpectedLoss) < tolerance);
BOOST_CHECK_CLOSE(riskFreePrice*0.95, price, tolerance);
BOOST_CHECK_LT(riskFreeYield, yield);
}
void CatBondTest::testCatBondWithGeneratedEventsProportional() {
BOOST_TEST_MESSAGE("Testing floating-rate cat bond in a generated scenario with proportional notional reduction...");
CommonVars vars;
Date today(22,November,2004);
Settings::instance().evaluationDate() = today;
Natural settlementDays = 1;
Handle<YieldTermStructure> riskFreeRate(flatRate(today,0.025,Actual360()));
Handle<YieldTermStructure> discountCurve(flatRate(today,0.03,Actual360()));
shared_ptr<IborIndex> index(new USDLibor(6*Months, riskFreeRate));
Natural fixingDays = 1;
Real tolerance = 1.0e-6;
shared_ptr<IborCouponPricer> pricer(new
BlackIborCouponPricer(Handle<OptionletVolatilityStructure>()));
Schedule sch(Date(30,November,2004),
Date(30,November,2008),
Period(Semiannual),
UnitedStates(UnitedStates::GovernmentBond),
ModifiedFollowing, ModifiedFollowing,
DateGeneration::Backward, false);
boost::shared_ptr<CatRisk> betaCatRisk(new BetaRisk(5000, 50, 500, 500));
boost::shared_ptr<CatRisk> noCatRisk(new EventSet(
boost::shared_ptr<std::vector<std::pair<Date, Real> > >(new std::vector<std::pair<Date, Real> >()),
Date(1, Jan, 2000), Date(31, Dec, 2010)));
boost::shared_ptr<EventPaymentOffset> paymentOffset(new NoOffset());
boost::shared_ptr<NotionalRisk> notionalRisk(new ProportionalNotionalRisk(paymentOffset, 500, 1500));
FloatingCatBond catBond(settlementDays, vars.faceAmount, sch,
index, ActualActual(ActualActual::ISMA),
notionalRisk,
ModifiedFollowing, fixingDays,
std::vector<Rate>(), std::vector<Spread>(),
std::vector<Rate>(), std::vector<Rate>(),
false,
100.0, Date(30,November,2004));
shared_ptr<PricingEngine> catBondEngine(new MonteCarloCatBondEngine(betaCatRisk, discountCurve));
catBond.setPricingEngine(catBondEngine);
setCouponPricer(catBond.cashflows(),pricer);
Real price = catBond.cleanPrice();
Real yield = catBond.yield(ActualActual(ActualActual::ISMA), Simple, Annual);
Real lossProbability = catBond.lossProbability();
Real exhaustionProbability = catBond.exhaustionProbability();
Real expectedLoss = catBond.expectedLoss();
BOOST_CHECK(lossProbability<1.0 && lossProbability>0.0);
BOOST_CHECK(exhaustionProbability<1.0 && exhaustionProbability>0.0);
BOOST_CHECK(expectedLoss>0.0);
shared_ptr<PricingEngine> catBondEngineRF(new MonteCarloCatBondEngine(noCatRisk, discountCurve));
catBond.setPricingEngine(catBondEngineRF);
Real riskFreePrice = catBond.cleanPrice();
Real riskFreeYield = catBond.yield(ActualActual(ActualActual::ISMA), Simple, Annual);
Real riskFreeLossProbability = catBond.lossProbability();
Real riskFreeExpectedLoss = catBond.expectedLoss();
BOOST_CHECK_CLOSE(Real(0.0), riskFreeLossProbability, tolerance);
BOOST_CHECK(std::abs(riskFreeExpectedLoss) < tolerance);
BOOST_CHECK_GT(riskFreePrice, price);
BOOST_CHECK_LT(riskFreeYield, yield);
}
test_suite* CatBondTest::suite() {
test_suite* suite = BOOST_TEST_SUITE("CatBond tests");
suite->add(QUANTLIB_TEST_CASE(&CatBondTest::testEventSetForWholeYears));
suite->add(QUANTLIB_TEST_CASE(&CatBondTest::testEventSetForIrregularPeriods));
suite->add(QUANTLIB_TEST_CASE(&CatBondTest::testEventSetForNoEvents));
suite->add(QUANTLIB_TEST_CASE(&CatBondTest::testBetaRisk));
suite->add(QUANTLIB_TEST_CASE(&CatBondTest::testRiskFreeAgainstFloatingRateBond));
suite->add(QUANTLIB_TEST_CASE(&CatBondTest::testCatBondInDoomScenario));
suite->add(QUANTLIB_TEST_CASE(&CatBondTest::testCatBondWithDoomOnceInTenYears));
suite->add(QUANTLIB_TEST_CASE(&CatBondTest::testCatBondWithDoomOnceInTenYearsProportional));
suite->add(QUANTLIB_TEST_CASE(&CatBondTest::testCatBondWithGeneratedEventsProportional));
return suite;
}