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|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006 Cristina Duminuco
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 "capflooredcoupon.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/math/matrix.hpp>
#include <ql/termstructures/volatility/optionlet/constantoptionletvol.hpp>
#include <ql/time/daycounters/thirty360.hpp>
#include <ql/time/daycounters/actualactual.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(CapFlooredCouponTest)
// global data
Date today_, settlement_, startDate_;
Calendar calendar_;
Real nominal_;
std::vector<Real> nominals_;
BusinessDayConvention convention_;
Frequency frequency_;
boost::shared_ptr<IborIndex> index_;
Natural settlementDays_, fixingDays_;
RelinkableHandle<YieldTermStructure> termStructure_;
std::vector<Rate> caps_;
std::vector<Rate> floors_;
Integer length_;
Volatility volatility_;
void setup() {
length_ = 20; //years
volatility_ = 0.20;
nominal_ = 100.;
nominals_ = std::vector<Real>(length_,nominal_);
frequency_ = Annual;
index_ = boost::shared_ptr<IborIndex>(new Euribor1Y(termStructure_));
calendar_ = index_->fixingCalendar();
convention_ = ModifiedFollowing;
today_ = calendar_.adjust(Date::todaysDate());
Settings::instance().evaluationDate() = today_;
settlementDays_ = 2;
fixingDays_ = 2;
settlement_ = calendar_.advance(today_,settlementDays_,Days);
startDate_ = settlement_;
termStructure_.linkTo(flatRate(settlement_,0.05,
ActualActual(ActualActual::ISDA)));
}
// utilities
Leg makeFixedLeg(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);
std::vector<Rate> coupons(length, 0.0);
return FixedRateLeg(schedule, Thirty360())
.withNotionals(nominals_)
.withCouponRates(coupons);
}
Leg makeFloatingLeg(const Date& startDate,
Integer length,
const Rate gearing = 1.0,
const Rate spread = 0.0) {
Date endDate = calendar_.advance(startDate,length,Years,convention_);
Schedule schedule(startDate,endDate,Period(frequency_),calendar_,
convention_,convention_, DateGeneration::Forward, false);
std::vector<Real> gearingVector(length_, gearing);
std::vector<Spread> spreadVector(length_, spread);
return IborLeg(schedule, index_)
.withNotionals(nominals_)
.withPaymentDayCounter(index_->dayCounter())
.withPaymentAdjustment(convention_)
.withFixingDays(fixingDays_)
.withGearings(gearingVector)
.withSpreads(spreadVector);
}
Leg makeCapFlooredLeg(const Date& startDate,
Integer length,
const std::vector<Rate> caps,
const std::vector<Rate> floors,
Volatility volatility,
const Rate gearing = 1.0,
const Rate spread = 0.0) {
Date endDate = calendar_.advance(startDate,length,Years,convention_);
Schedule schedule(startDate,endDate,Period(frequency_),calendar_,
convention_,convention_, DateGeneration::Forward, false);
Handle<OptionletVolatilityStructure> vol;
vol = Handle<OptionletVolatilityStructure>(
boost::shared_ptr<OptionletVolatilityStructure>(new
ConstantOptionletVol(volatility, calendar_, Actual365Fixed())));
boost::shared_ptr<IborCouponPricer> pricer(new BlackIborCouponPricer(vol));
std::vector<Rate> gearingVector(length_, gearing);
std::vector<Spread> spreadVector(length_, spread);
Leg iborLeg = IborLeg(schedule, index_)
.withNotionals(nominals_)
.withPaymentDayCounter(index_->dayCounter())
.withPaymentAdjustment(convention_)
.withFixingDays(fixingDays_)
.withGearings(gearingVector)
.withSpreads(spreadVector)
.withCaps(caps)
.withFloors(floors);
setCouponPricer(iborLeg, pricer);
return iborLeg;
}
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 capStrike, Rate floorStrike,
Volatility volatility) {
boost::shared_ptr<CapFloor> result;
switch (type) {
case CapFloor::Cap:
result = boost::shared_ptr<CapFloor>(
new Cap(leg, std::vector<Rate>(1, capStrike)));
break;
case CapFloor::Floor:
result = boost::shared_ptr<CapFloor>(
new Floor(leg, std::vector<Rate>(1, floorStrike)));
break;
case CapFloor::Collar:
result = boost::shared_ptr<CapFloor>(
new Collar(leg,
std::vector<Rate>(1, capStrike),
std::vector<Rate>(1, floorStrike)));
break;
default:
QL_FAIL("unknown cap/floor type");
}
result->setPricingEngine(makeEngine(volatility));
return result;
}
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(CapFlooredCouponTest)
void CapFlooredCouponTest::testLargeRates() {
BOOST_MESSAGE("Testing degenerate collared coupon...");
SavedSettings backup;
setup();
/* A vanilla floating leg and a capped floating leg with strike
equal to 100 and floor equal to 0 must have (about) the same NPV
(depending on variance: option expiry and volatility)
*/
std::vector<Rate> caps(length_,100.0);
std::vector<Rate> floors(length_,0.0);
Real tolerance = 1e-10;
// fixed leg with zero rate
Leg fixedLeg =
makeFixedLeg(startDate_,length_);
Leg floatLeg =
makeFloatingLeg(startDate_,length_);
Leg collaredLeg =
makeCapFlooredLeg(startDate_,length_,caps,floors,volatility_);
boost::shared_ptr<PricingEngine> engine(
new DiscountingSwapEngine(termStructure_));
Swap vanillaLeg(fixedLeg,floatLeg);
Swap collarLeg(fixedLeg,collaredLeg);
vanillaLeg.setPricingEngine(engine);
collarLeg.setPricingEngine(engine);
if (std::abs(vanillaLeg.NPV()-collarLeg.NPV())>tolerance) {
BOOST_MESSAGE("Lenght: " << length_ << " y" << "\n" <<
"Volatility: " << volatility_*100 << "%\n" <<
"Notional: " << nominal_ << "\n" <<
"Vanilla floating leg NPV: " << vanillaLeg.NPV()
<< "\n" <<
"Collared floating leg NPV (strikes 0 and 100): " << collarLeg.NPV()
<< "\n" <<
"Diff: " << std::abs(vanillaLeg.NPV()-collarLeg.NPV()));
}
}
void CapFlooredCouponTest::testDecomposition() {
BOOST_MESSAGE("Testing collared coupon against its decomposition...");
SavedSettings backup;
setup();
Real tolerance = 1e-12;
Real npvVanilla,npvCappedLeg,npvFlooredLeg,npvCollaredLeg,npvCap,npvFloor,npvCollar;
Real error;
Rate floorstrike = 0.05;
Rate capstrike = 0.10;
std::vector<Rate> caps(length_,capstrike);
std::vector<Rate> caps0 = std::vector<Rate>();
std::vector<Rate> floors(length_,floorstrike);
std::vector<Rate> floors0 = std::vector<Rate>();
Rate gearing_p = Rate(0.5);
Spread spread_p = Spread(0.002);
Rate gearing_n = Rate(-1.5);
Spread spread_n = Spread(0.12);
// fixed leg with zero rate
Leg fixedLeg =
makeFixedLeg(startDate_,length_);
// floating leg with gearing=1 and spread=0
Leg floatLeg =
makeFloatingLeg(startDate_,length_);
// floating leg with positive gearing (gearing_p) and spread<>0
Leg floatLeg_p =
makeFloatingLeg(startDate_,length_,gearing_p,spread_p);
// floating leg with negative gearing (gearing_n) and spread<>0
Leg floatLeg_n =
makeFloatingLeg(startDate_,length_,gearing_n,spread_n);
// Swap with null fixed leg and floating leg with gearing=1 and spread=0
Swap vanillaLeg(fixedLeg,floatLeg);
// Swap with null fixed leg and floating leg with positive gearing and spread<>0
Swap vanillaLeg_p(fixedLeg,floatLeg_p);
// Swap with null fixed leg and floating leg with negative gearing and spread<>0
Swap vanillaLeg_n(fixedLeg,floatLeg_n);
boost::shared_ptr<PricingEngine> engine(
new DiscountingSwapEngine(termStructure_));
vanillaLeg.setPricingEngine(engine);
vanillaLeg_p.setPricingEngine(engine);
vanillaLeg_n.setPricingEngine(engine);
/* CAPPED coupon - Decomposition of payoff
Payoff = Nom * Min(rate,strike) * accrualperiod =
= Nom * [rate + Min(0,strike-rate)] * accrualperiod =
= Nom * rate * accrualperiod - Nom * Max(rate-strike,0) * accrualperiod =
= VanillaFloatingLeg - Call
*/
// Case gearing = 1 and spread = 0
Leg cappedLeg =
makeCapFlooredLeg(startDate_,length_,caps,floors0,volatility_);
Swap capLeg(fixedLeg,cappedLeg);
capLeg.setPricingEngine(engine);
Cap cap(floatLeg, std::vector<Rate>(1, capstrike));
cap.setPricingEngine(makeEngine(volatility_));
npvVanilla = vanillaLeg.NPV();
npvCappedLeg = capLeg.NPV();
npvCap = cap.NPV();
error = std::abs(npvCappedLeg - (npvVanilla-npvCap));
if (error>tolerance) {
BOOST_ERROR("\nCapped Leg: gearing=1, spread=0%, strike=" << capstrike*100 <<
"%\n" <<
" Capped Floating Leg NPV: " << npvCappedLeg << "\n" <<
" Floating Leg NPV - Cap NPV: " << npvVanilla - npvCap << "\n" <<
" Diff: " << error );
}
/* gearing = 1 and spread = 0
FLOORED coupon - Decomposition of payoff
Payoff = Nom * Max(rate,strike) * accrualperiod =
= Nom * [rate + Max(0,strike-rate)] * accrualperiod =
= Nom * rate * accrualperiod + Nom * Max(strike-rate,0) * accrualperiod =
= VanillaFloatingLeg + Put
*/
Leg flooredLeg =
makeCapFlooredLeg(startDate_,length_,caps0,floors,volatility_);
Swap floorLeg(fixedLeg,flooredLeg);
floorLeg.setPricingEngine(engine);
Floor floor(floatLeg, std::vector<Rate>(1, floorstrike));
floor.setPricingEngine(makeEngine(volatility_));
npvFlooredLeg = floorLeg.NPV();
npvFloor = floor.NPV();
error = std::abs(npvFlooredLeg-(npvVanilla + npvFloor));
if (error>tolerance) {
BOOST_ERROR("Floored Leg: gearing=1, spread=0%, strike=" << floorstrike *100 <<
"%\n" <<
" Floored Floating Leg NPV: " << npvFlooredLeg << "\n" <<
" Floating Leg NPV + Floor NPV: " << npvVanilla + npvFloor << "\n" <<
" Diff: " << error );
}
/* gearing = 1 and spread = 0
COLLARED coupon - Decomposition of payoff
Payoff = Nom * Min(strikem,Max(rate,strikeM)) * accrualperiod =
= VanillaFloatingLeg - Collar
*/
Leg collaredLeg =
makeCapFlooredLeg(startDate_,length_,caps,floors,volatility_);
Swap collarLeg(fixedLeg,collaredLeg);
collarLeg.setPricingEngine(engine);
Collar collar(floatLeg,
std::vector<Rate>(1, capstrike),
std::vector<Rate>(1, floorstrike));
collar.setPricingEngine(makeEngine(volatility_));
npvCollaredLeg = collarLeg.NPV();
npvCollar = collar.NPV();
error = std::abs(npvCollaredLeg -(npvVanilla - npvCollar));
if (error>tolerance) {
BOOST_ERROR("\nCollared Leg: gearing=1, spread=0%, strike=" <<
floorstrike*100 << "% and " << capstrike*100 << "%\n" <<
" Collared Floating Leg NPV: " << npvCollaredLeg << "\n" <<
" Floating Leg NPV - Collar NPV: " << npvVanilla - npvCollar << "\n" <<
" Diff: " << error );
}
/* gearing = a and spread = b
CAPPED coupon - Decomposition of payoff
Payoff
= Nom * Min(a*rate+b,strike) * accrualperiod =
= Nom * [a*rate+b + Min(0,strike-a*rate-b)] * accrualperiod =
= Nom * a*rate+b * accrualperiod + Nom * Min(strike-b-a*rate,0) * accrualperiod
--> If a>0 (assuming positive effective strike):
Payoff = VanillaFloatingLeg - Call(a*rate+b,strike)
--> If a<0 (assuming positive effective strike):
Payoff = VanillaFloatingLeg + Nom * Min(strike-b+|a|*rate+,0) * accrualperiod =
= VanillaFloatingLeg + Put(|a|*rate+b,strike)
*/
// Positive gearing
Leg cappedLeg_p =
makeCapFlooredLeg(startDate_,length_,caps,floors0,
volatility_,gearing_p,spread_p);
Swap capLeg_p(fixedLeg,cappedLeg_p);
capLeg_p.setPricingEngine(engine);
Cap cap_p(floatLeg_p,std::vector<Rate>(1,capstrike));
cap_p.setPricingEngine(makeEngine(volatility_));
npvVanilla = vanillaLeg_p.NPV();
npvCappedLeg = capLeg_p.NPV();
npvCap = cap_p.NPV();
error = std::abs(npvCappedLeg - (npvVanilla-npvCap));
if (error>tolerance) {
BOOST_ERROR("\nCapped Leg: gearing=" << gearing_p << ", " <<
"spread= " << spread_p *100 <<
"%, strike=" << capstrike*100 << "%, " <<
"effective strike= " << (capstrike-spread_p)/gearing_p*100 <<
"%\n" <<
" Capped Floating Leg NPV: " << npvCappedLeg << "\n" <<
" Vanilla Leg NPV: " << npvVanilla << "\n" <<
" Cap NPV: " << npvCap << "\n" <<
" Floating Leg NPV - Cap NPV: " << npvVanilla - npvCap << "\n" <<
" Diff: " << error );
}
// Negative gearing
Leg cappedLeg_n =
makeCapFlooredLeg(startDate_,length_,caps,floors0,
volatility_,gearing_n,spread_n);
Swap capLeg_n(fixedLeg,cappedLeg_n);
capLeg_n.setPricingEngine(engine);
Floor floor_n(floatLeg,std::vector<Rate>(1,(capstrike-spread_n)/gearing_n));
floor_n.setPricingEngine(makeEngine(volatility_));
npvVanilla = vanillaLeg_n.NPV();
npvCappedLeg = capLeg_n.NPV();
npvFloor = floor_n.NPV();
error = std::abs(npvCappedLeg - (npvVanilla+ gearing_n*npvFloor));
if (error>tolerance) {
BOOST_ERROR("\nCapped Leg: gearing=" << gearing_n << ", " <<
"spread= " << spread_n *100 <<
"%, strike=" << capstrike*100 << "%, " <<
"effective strike= " << (capstrike-spread_n)/gearing_n*100 <<
"%\n" <<
" Capped Floating Leg NPV: " << npvCappedLeg << "\n" <<
" npv Vanilla: " << npvVanilla << "\n" <<
" npvFloor: " << npvFloor << "\n" <<
" Floating Leg NPV - Cap NPV: " << npvVanilla + gearing_n*npvFloor << "\n" <<
" Diff: " << error );
}
/* gearing = a and spread = b
FLOORED coupon - Decomposition of payoff
Payoff
= Nom * Max(a*rate+b,strike) * accrualperiod =
= Nom * [a*rate+b + Max(0,strike-a*rate-b)] * accrualperiod =
= Nom * a*rate+b * accrualperiod + Nom * Max(strike-b-a*rate,0) * accrualperiod
--> If a>0 (assuming positive effective strike):
Payoff = VanillaFloatingLeg + Put(a*rate+b,strike)
--> If a<0 (assuming positive effective strike):
Payoff = VanillaFloatingLeg + Nom * Max(strike-b+|a|*rate+,0) * accrualperiod =
= VanillaFloatingLeg - Call(|a|*rate+b,strike)
*/
// Positive gearing
Leg flooredLeg_p1 =
makeCapFlooredLeg(startDate_,length_,caps0,floors,
volatility_,gearing_p,spread_p);
Swap floorLeg_p1(fixedLeg,flooredLeg_p1);
floorLeg_p1.setPricingEngine(engine);
Floor floor_p1(floatLeg_p,std::vector<Rate>(1,floorstrike));
floor_p1.setPricingEngine(makeEngine(volatility_));
npvVanilla = vanillaLeg_p.NPV();
npvFlooredLeg = floorLeg_p1.NPV();
npvFloor = floor_p1.NPV();
error = std::abs(npvFlooredLeg - (npvVanilla+npvFloor));
if (error>tolerance) {
BOOST_ERROR("\nFloored Leg: gearing=" << gearing_p << ", "
<< "spread= " << spread_p *100<< "%, strike=" << floorstrike *100 << "%, "
<< "effective strike= " << (floorstrike-spread_p)/gearing_p*100
<< "%\n" <<
" Floored Floating Leg NPV: " << npvFlooredLeg
<< "\n" <<
" Floating Leg NPV + Floor NPV: " << npvVanilla + npvFloor
<< "\n" <<
" Diff: " << error );
}
// Negative gearing
Leg flooredLeg_n =
makeCapFlooredLeg(startDate_,length_,caps0,floors,
volatility_,gearing_n,spread_n);
Swap floorLeg_n(fixedLeg,flooredLeg_n);
floorLeg_n.setPricingEngine(engine);
Cap cap_n(floatLeg,std::vector<Rate>(1,(floorstrike-spread_n)/gearing_n));
cap_n.setPricingEngine(makeEngine(volatility_));
npvVanilla = vanillaLeg_n.NPV();
npvFlooredLeg = floorLeg_n.NPV();
npvCap = cap_n.NPV();
error = std::abs(npvFlooredLeg - (npvVanilla - gearing_n*npvCap));
if (error>tolerance) {
BOOST_ERROR("\nCapped Leg: gearing=" << gearing_n << ", " <<
"spread= " << spread_n *100 <<
"%, strike=" << floorstrike*100 << "%, " <<
"effective strike= " << (floorstrike-spread_n)/gearing_n*100 <<
"%\n" <<
" Capped Floating Leg NPV: " << npvFlooredLeg << "\n" <<
" Floating Leg NPV - Cap NPV: " << npvVanilla - gearing_n*npvCap << "\n" <<
" Diff: " << error );
}
/* gearing = a and spread = b
COLLARED coupon - Decomposition of payoff
Payoff = Nom * Min(caprate,Max(a*rate+b,floorrate)) * accrualperiod
--> If a>0 (assuming positive effective strike):
Payoff = VanillaFloatingLeg - Collar(a*rate+b, floorrate, caprate)
--> If a<0 (assuming positive effective strike):
Payoff = VanillaFloatingLeg + Collar(|a|*rate+b, caprate, floorrate)
*/
// Positive gearing
Leg collaredLeg_p =
makeCapFlooredLeg(startDate_,length_,caps,floors,
volatility_,gearing_p,spread_p);
Swap collarLeg_p1(fixedLeg,collaredLeg_p);
collarLeg_p1.setPricingEngine(engine);
Collar collar_p(floatLeg_p,
std::vector<Rate>(1,capstrike),
std::vector<Rate>(1,floorstrike));
collar_p.setPricingEngine(makeEngine(volatility_));
npvVanilla = vanillaLeg_p.NPV();
npvCollaredLeg = collarLeg_p1.NPV();
npvCollar = collar_p.NPV();
error = std::abs(npvCollaredLeg - (npvVanilla - npvCollar));
if (error>tolerance) {
BOOST_ERROR("\nCollared Leg: gearing=" << gearing_p << ", "
<< "spread= " << spread_p*100 << "%, strike="
<< floorstrike*100 << "% and " << capstrike*100
<< "%, "
<< "effective strike=" << (floorstrike-spread_p)/gearing_p*100
<< "% and " << (capstrike-spread_p)/gearing_p*100
<< "%\n" <<
" Collared Floating Leg NPV: " << npvCollaredLeg
<< "\n" <<
" Floating Leg NPV - Collar NPV: " << npvVanilla - npvCollar
<< "\n" <<
" Diff: " << error );
}
// Negative gearing
Leg collaredLeg_n =
makeCapFlooredLeg(startDate_,length_,caps,floors,
volatility_,gearing_n,spread_n);
Swap collarLeg_n1(fixedLeg,collaredLeg_n);
collarLeg_n1.setPricingEngine(engine);
Collar collar_n(floatLeg,
std::vector<Rate>(1,(floorstrike-spread_n)/gearing_n),
std::vector<Rate>(1,(capstrike-spread_n)/gearing_n));
collar_n.setPricingEngine(makeEngine(volatility_));
npvVanilla = vanillaLeg_n.NPV();
npvCollaredLeg = collarLeg_n1.NPV();
npvCollar = collar_n.NPV();
error = std::abs(npvCollaredLeg - (npvVanilla - gearing_n*npvCollar));
if (error>tolerance) {
BOOST_ERROR("\nCollared Leg: gearing=" << gearing_n << ", "
<< "spread= " << spread_n*100 << "%, strike="
<< floorstrike*100 << "% and " << capstrike*100
<< "%, "
<< "effective strike=" << (floorstrike-spread_n)/gearing_n*100
<< "% and " << (capstrike-spread_n)/gearing_n*100
<< "%\n" <<
" Collared Floating Leg NPV: " << npvCollaredLeg
<< "\n" <<
" Floating Leg NPV - Collar NPV: " << npvVanilla - gearing_n*npvCollar
<< "\n" <<
" Diff: " << error );
}
}
test_suite* CapFlooredCouponTest::suite() {
test_suite* suite = BOOST_TEST_SUITE("Capped/floored coupon tests");
suite->add(BOOST_TEST_CASE(&CapFlooredCouponTest::testLargeRates));
suite->add(BOOST_TEST_CASE(&CapFlooredCouponTest::testDecomposition));
return suite;
}
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