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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003 RiskMap srl
Copyright (C) 2004, 2005, 2006, 2007 StatPro Italia srl
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 "capfloor.hpp"
#include "utilities.hpp"
#include <ql/instruments/capfloor.hpp>
#include <ql/instruments/vanillaswap.hpp>
#include <ql/cashflows/cashflowvectors.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/indexes/ibor/euribor.hpp>
#include <ql/pricingengines/capfloor/blackcapfloorengine.hpp>
#include <ql/pricingengines/swap/discountingswapengine.hpp>
#include <ql/models/marketmodels/models/flatvol.hpp>
#include <ql/models/marketmodels/correlations/expcorrelations.hpp>
#include <ql/math/matrix.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/time/schedule.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <ql/cashflows/cashflows.hpp>
#include <ql/cashflows/couponpricer.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
QL_BEGIN_TEST_LOCALS(CapFloorTest)
struct CommonVars {
// common data
Date settlement;
std::vector<Real> nominals;
BusinessDayConvention convention;
Frequency frequency;
boost::shared_ptr<IborIndex> index;
Calendar calendar;
Natural fixingDays;
RelinkableHandle<YieldTermStructure> termStructure;
// cleanup
SavedSettings backup;
// setup
CommonVars() {
nominals = std::vector<Real>(1,100);
frequency = Semiannual;
index = boost::shared_ptr<IborIndex>(new Euribor6M(termStructure));
calendar = index->fixingCalendar();
convention = ModifiedFollowing;
Date today = calendar.adjust(Date::todaysDate());
Settings::instance().evaluationDate() = today;
Natural settlementDays = 2;
fixingDays = 2;
settlement = calendar.advance(today,settlementDays,Days);
termStructure.linkTo(flatRate(settlement,0.05,
ActualActual(ActualActual::ISDA)));
}
// utilities
Leg makeLeg(const Date& startDate, Integer length) {
Date endDate = calendar.advance(startDate,length*Years,convention);
Schedule schedule(startDate, endDate, Period(frequency), calendar,
convention, convention,
DateGeneration::Forward, false);
return IborLeg(schedule, index)
.withNotionals(nominals)
.withPaymentDayCounter(index->dayCounter())
.withPaymentAdjustment(convention)
.withFixingDays(fixingDays);
}
boost::shared_ptr<PricingEngine> makeEngine(Volatility volatility) {
Handle<Quote> vol(boost::shared_ptr<Quote>(
new SimpleQuote(volatility)));
return boost::shared_ptr<PricingEngine>(
new BlackCapFloorEngine(termStructure, vol));
}
boost::shared_ptr<CapFloor> makeCapFloor(CapFloor::Type type,
const Leg& leg,
Rate strike,
Volatility volatility) {
boost::shared_ptr<CapFloor> result;
switch (type) {
case CapFloor::Cap:
result = boost::shared_ptr<CapFloor>(
new Cap(leg, std::vector<Rate>(1, strike)));
break;
case CapFloor::Floor:
result = boost::shared_ptr<CapFloor>(
new Floor(leg, std::vector<Rate>(1, strike)));
break;
default:
QL_FAIL("unknown cap/floor type");
}
result->setPricingEngine(makeEngine(volatility));
return result;
}
};
bool checkAbsError(Real x1, Real x2, Real tolerance){
return std::fabs(x1 - x2) < tolerance;
}
std::string typeToString(CapFloor::Type type) {
switch (type) {
case CapFloor::Cap:
return "cap";
case CapFloor::Floor:
return "floor";
case CapFloor::Collar:
return "collar";
default:
QL_FAIL("unknown cap/floor type");
}
}
QL_END_TEST_LOCALS(CapFloorTest)
void CapFloorTest::testVega() {
BOOST_MESSAGE("Testing cap/floor vega...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 4, 5, 6, 7, 10, 15, 20, 30 };
Volatility vols[] = { 0.01, 0.05, 0.10, 0.15, 0.20 };
Rate strikes[] = { 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09 };
CapFloor::Type types[] = { CapFloor::Cap, CapFloor::Floor};
Date startDate = vars.termStructure->referenceDate();
static const Real shift = 1e-8;
static const Real tolerance = 0.005;
for (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(vols); j++) {
for (Size k=0; k<LENGTH(strikes); k++) {
for (Size h=0; h<LENGTH(types); h++) {
Leg leg = vars.makeLeg(startDate, lengths[i]);
boost::shared_ptr<CapFloor> capFloor =
vars.makeCapFloor(types[h],leg,
strikes[k],vols[j]);
boost::shared_ptr<CapFloor> shiftedCapFloor2 =
vars.makeCapFloor(types[h],leg,
strikes[k],vols[j]+shift);
boost::shared_ptr<CapFloor> shiftedCapFloor1 =
vars.makeCapFloor(types[h],leg,
strikes[k],vols[j]-shift);
Real value1 = shiftedCapFloor1->NPV();
Real value2 = shiftedCapFloor2->NPV();
Real numericalVega = (value2 - value1) / (2*shift);
if (numericalVega>1.0e-4) {
Real analyticalVega = capFloor->result<Real>("vega");
Real discrepancy =
std::fabs(numericalVega - analyticalVega);
discrepancy /= numericalVega;
if (discrepancy > tolerance)
BOOST_FAIL(
"failed to compute cap/floor vega:" <<
"\n lengths: " << lengths[j]*Years <<
"\n strike: " << io::rate(strikes[k]) <<
//"\n types: " << types[h] <<
QL_FIXED << std::setprecision(12) <<
"\n calculated: " << analyticalVega <<
"\n expected: " << numericalVega <<
"\n discrepancy: " << io::rate(discrepancy) <<
"\n tolerance: " << io::rate(tolerance));
}
}
}
}
}
}
void CapFloorTest::testStrikeDependency() {
BOOST_MESSAGE("Testing cap/floor dependency on strike...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
Volatility vols[] = { 0.01, 0.05, 0.10, 0.15, 0.20 };
Rate strikes[] = { 0.03, 0.04, 0.05, 0.06, 0.07 };
Date startDate = vars.termStructure->referenceDate();
for (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(vols); j++) {
// store the results for different strikes...
std::vector<Real> cap_values, floor_values;
for (Size k=0; k<LENGTH(strikes); k++) {
Leg leg = vars.makeLeg(startDate,lengths[i]);
boost::shared_ptr<Instrument> cap =
vars.makeCapFloor(CapFloor::Cap,leg,
strikes[k],vols[j]);
cap_values.push_back(cap->NPV());
boost::shared_ptr<Instrument> floor =
vars.makeCapFloor(CapFloor::Floor,leg,
strikes[k],vols[j]);
floor_values.push_back(floor->NPV());
}
// and check that they go the right way
std::vector<Real>::iterator it =
std::adjacent_find(cap_values.begin(),cap_values.end(),
std::less<Real>());
if (it != cap_values.end()) {
Size n = it - cap_values.begin();
BOOST_FAIL(
"NPV is increasing with the strike in a cap: \n"
<< std::setprecision(2)
<< " length: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[j]) << "\n"
<< " value: " << cap_values[n]
<< " at strike: " << io::rate(strikes[n]) << "\n"
<< " value: " << cap_values[n+1]
<< " at strike: " << io::rate(strikes[n+1]));
}
// same for floors
it = std::adjacent_find(floor_values.begin(),floor_values.end(),
std::greater<Real>());
if (it != floor_values.end()) {
Size n = it - floor_values.begin();
BOOST_FAIL(
"NPV is decreasing with the strike in a floor: \n"
<< std::setprecision(2)
<< " length: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[j]) << "\n"
<< " value: " << floor_values[n]
<< " at strike: " << io::rate(strikes[n]) << "\n"
<< " value: " << floor_values[n+1]
<< " at strike: " << io::rate(strikes[n+1]));
}
}
}
}
void CapFloorTest::testConsistency() {
BOOST_MESSAGE("Testing consistency between cap, floor and collar...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
Rate cap_rates[] = { 0.03, 0.04, 0.05, 0.06, 0.07 };
Rate floor_rates[] = { 0.03, 0.04, 0.05, 0.06, 0.07 };
Volatility vols[] = { 0.01, 0.05, 0.10, 0.15, 0.20 };
Date startDate = vars.termStructure->referenceDate();
for (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(cap_rates); j++) {
for (Size k=0; k<LENGTH(floor_rates); k++) {
for (Size l=0; l<LENGTH(vols); l++) {
Leg leg = vars.makeLeg(startDate,lengths[i]);
boost::shared_ptr<Instrument> cap =
vars.makeCapFloor(CapFloor::Cap,leg,
cap_rates[j],vols[l]);
boost::shared_ptr<Instrument> floor =
vars.makeCapFloor(CapFloor::Floor,leg,
floor_rates[k],vols[l]);
Collar collar(leg,std::vector<Rate>(1,cap_rates[j]),
std::vector<Rate>(1,floor_rates[k]));
collar.setPricingEngine(vars.makeEngine(vols[l]));
if (std::fabs((cap->NPV()-floor->NPV())-collar.NPV()) > 1e-10) {
BOOST_FAIL(
"inconsistency between cap, floor and collar:\n"
<< " length: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[l]) << "\n"
<< " cap value: " << cap->NPV()
<< " at strike: " << io::rate(cap_rates[j]) << "\n"
<< " floor value: " << floor->NPV()
<< " at strike: " << io::rate(floor_rates[k]) << "\n"
<< " collar value: " << collar.NPV());
}
}
}
}
}
}
void CapFloorTest::testParity() {
BOOST_MESSAGE("Testing cap/floor parity...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
Rate strikes[] = { 0., 0.03, 0.04, 0.05, 0.06, 0.07 };
Volatility vols[] = { 0.01, 0.05, 0.10, 0.15, 0.20 };
Date startDate = vars.termStructure->referenceDate();
for (Size i=0; i<LENGTH(lengths); i++) {
for (Size j=0; j<LENGTH(strikes); j++) {
for (Size k=0; k<LENGTH(vols); k++) {
Leg leg = vars.makeLeg(startDate,lengths[i]);
boost::shared_ptr<Instrument> cap =
vars.makeCapFloor(CapFloor::Cap,leg,
strikes[j],vols[k]);
boost::shared_ptr<Instrument> floor =
vars.makeCapFloor(CapFloor::Floor,leg,
strikes[j],vols[k]);
Date maturity = vars.calendar.advance(startDate,lengths[i],Years,
vars.convention);
Schedule schedule(startDate,maturity,
Period(vars.frequency),vars.calendar,
vars.convention,vars.convention,
DateGeneration::Forward,false);
VanillaSwap swap(VanillaSwap::Payer, vars.nominals[0],
schedule, strikes[j], vars.index->dayCounter(),
schedule, vars.index, 0.0,
vars.index->dayCounter());
swap.setPricingEngine(boost::shared_ptr<PricingEngine>(
new DiscountingSwapEngine(vars.termStructure)));
// FLOATING_POINT_EXCEPTION
if (std::fabs((cap->NPV()-floor->NPV()) - swap.NPV()) > 1.0e-10) {
BOOST_FAIL(
"put/call parity violated:\n"
<< " length: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[k]) << "\n"
<< " strike: " << io::rate(strikes[j]) << "\n"
<< " cap value: " << cap->NPV() << "\n"
<< " floor value: " << floor->NPV() << "\n"
<< " swap value: " << swap.NPV());
}
}
}
}
}
void CapFloorTest::testATMRate() {
BOOST_MESSAGE("Testing cap/floor ATM rate...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
Rate strikes[] = { 0., 0.03, 0.04, 0.05, 0.06, 0.07 };
Volatility vols[] = { 0.01, 0.05, 0.10, 0.15, 0.20 };
Date startDate = vars.termStructure->referenceDate();
for (Size i=0; i<LENGTH(lengths); i++) {
Leg leg = vars.makeLeg(startDate,lengths[i]);
Date maturity = vars.calendar.advance(startDate,lengths[i],Years,
vars.convention);
Schedule schedule(startDate,maturity,
Period(vars.frequency),vars.calendar,
vars.convention,vars.convention,
DateGeneration::Forward,false);
for (Size j=0; j<LENGTH(strikes); j++) {
for (Size k=0; k<LENGTH(vols); k++) {
boost::shared_ptr<CapFloor> cap =
vars.makeCapFloor(CapFloor::Cap, leg, strikes[j],vols[k]);
boost::shared_ptr<CapFloor> floor =
vars.makeCapFloor(CapFloor::Floor, leg, strikes[j],vols[k]);
Rate capATMRate = cap->atmRate(**vars.termStructure);
Rate floorATMRate = floor->atmRate(**vars.termStructure);
if (!checkAbsError(floorATMRate, capATMRate, 1.0e-10))
BOOST_FAIL(
"Cap ATM Rate and floor ATM Rate should be equal :\n"
<< " length: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[k]) << "\n"
<< " strike: " << io::rate(strikes[j]) << "\n"
<< " cap ATM rate: " << capATMRate << "\n"
<< " floor ATM rate:" << floorATMRate << "\n"
<< " relative Error:"
<< relativeError(capATMRate, floorATMRate,
capATMRate)*100 << "%" );
VanillaSwap swap(VanillaSwap::Payer, vars.nominals[0],
schedule, floorATMRate,
vars.index->dayCounter(),
schedule, vars.index, 0.0,
vars.index->dayCounter());
swap.setPricingEngine(boost::shared_ptr<PricingEngine>(
new DiscountingSwapEngine(vars.termStructure)));
Real swapNPV = swap.NPV();
if (!checkAbsError(swapNPV, 0, 1.0e-10))
BOOST_FAIL(
"the NPV of a Swap struck at ATM rate "
"should be equal to 0:\n"
<< " length: " << lengths[i] << " years\n"
<< " volatility: " << io::volatility(vols[k]) << "\n"
<< " ATM rate: " << io::rate(floorATMRate) << "\n"
<< " swap NPV: " << swapNPV);
}
}
}
}
void CapFloorTest::testImpliedVolatility() {
BOOST_MESSAGE("Testing implied term volatility for cap and floor...");
CommonVars vars;
Size maxEvaluations = 100;
Real tolerance = 1.0e-6;
CapFloor::Type types[] = { CapFloor::Cap, CapFloor::Floor };
Rate strikes[] = { 0.02, 0.03, 0.04 };
Integer lengths[] = { 1, 5, 10 };
// test data
Rate rRates[] = { 0.02, 0.03, 0.04 };
Volatility vols[] = { 0.01, 0.20, 0.30, 0.70, 0.90 };
for (Size k=0; k<LENGTH(lengths); k++) {
Leg leg = vars.makeLeg(vars.settlement, lengths[k]);
for (Size i=0; i<LENGTH(types); i++) {
for (Size j=0; j<LENGTH(strikes); j++) {
boost::shared_ptr<CapFloor> capfloor =
vars.makeCapFloor(types[i], leg, strikes[j], 0.0);
for (Size n=0; n<LENGTH(rRates); n++) {
for (Size m=0; m<LENGTH(vols); m++) {
Rate r = rRates[n];
Volatility v = vols[m];
vars.termStructure.linkTo(flatRate(vars.settlement,r,
Actual360()));
capfloor->setPricingEngine(vars.makeEngine(v));
Real value = capfloor->NPV();
Volatility implVol = 0.0;
try {
implVol =
capfloor->impliedVolatility(value,
vars.termStructure,
tolerance,
maxEvaluations);
} catch (std::exception& e) {
BOOST_FAIL(typeToString(types[i]) <<
"\n strike: " << io::rate(strikes[j]) <<
"\n risk-free: " << io::rate(r) <<
"\n length: " << lengths[k] << "Y" <<
"\n volatility: " << io::volatility(v) <<
"\n" << e.what());
}
if (std::fabs(implVol-v) > tolerance) {
// the difference might not matter
capfloor->setPricingEngine(
vars.makeEngine(implVol));
Real value2 = capfloor->NPV();
if (std::fabs(value-value2) > tolerance) {
BOOST_FAIL(
typeToString(types[i]) << ":\n"
<< " strike: "
<< strikes[j] << "\n"
<< " risk-free rate: "
<< io::rate(r) << "\n"
<< " length: "
<< lengths[k] << " years\n\n"
<< " original volatility: "
<< io::volatility(v) << "\n"
<< " price: "
<< value << "\n"
<< " implied volatility: "
<< io::volatility(implVol) << "\n"
<< " corresponding price: " << value2);
}
}
}
}
}
}
}
}
void CapFloorTest::testCachedValue() {
BOOST_MESSAGE("Testing Black cap/floor price against cached values...");
CommonVars vars;
Date cachedToday(14,March,2002),
cachedSettlement(18,March,2002);
Settings::instance().evaluationDate() = cachedToday;
vars.termStructure.linkTo(flatRate(cachedSettlement, 0.05, Actual360()));
Date startDate = vars.termStructure->referenceDate();
Leg leg = vars.makeLeg(startDate,20);
boost::shared_ptr<Instrument> cap = vars.makeCapFloor(CapFloor::Cap,leg,
0.07,0.20);
boost::shared_ptr<Instrument> floor = vars.makeCapFloor(CapFloor::Floor,leg,
0.03,0.20);
#ifndef QL_USE_INDEXED_COUPON
// par coupon price
Real cachedCapNPV = 6.87570026732,
cachedFloorNPV = 2.65812927959;
#else
// index fixing price
Real cachedCapNPV = 6.87630307745,
cachedFloorNPV = 2.65796764715;
#endif
// test Black cap price against cached value
if (std::fabs(cap->NPV()-cachedCapNPV) > 1.0e-11)
BOOST_ERROR(
"failed to reproduce cached cap value:\n"
<< std::setprecision(12)
<< " calculated: " << cap->NPV() << "\n"
<< " expected: " << cachedCapNPV);
// test Black floor price against cached value
if (std::fabs(floor->NPV()-cachedFloorNPV) > 1.0e-11)
BOOST_ERROR(
"failed to reproduce cached floor value:\n"
<< std::setprecision(12)
<< " calculated: " << floor->NPV() << "\n"
<< " expected: " << cachedFloorNPV);
}
test_suite* CapFloorTest::suite() {
test_suite* suite = BOOST_TEST_SUITE("Cap/floor tests");
suite->add(BOOST_TEST_CASE(&CapFloorTest::testStrikeDependency));
suite->add(BOOST_TEST_CASE(&CapFloorTest::testConsistency));
// FLOATING_POINT_EXCEPTION
suite->add(BOOST_TEST_CASE(&CapFloorTest::testParity));
suite->add(BOOST_TEST_CASE(&CapFloorTest::testVega));
suite->add(BOOST_TEST_CASE(&CapFloorTest::testATMRate));
suite->add(BOOST_TEST_CASE(&CapFloorTest::testImpliedVolatility));
suite->add(BOOST_TEST_CASE(&CapFloorTest::testCachedValue));
return suite;
}
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