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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, 2008 StatPro Italia srl
Copyright (C) 2009 Chris Kenyon
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
<https://www.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 "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/cashflows/cashflows.hpp>
#include <ql/cashflows/cashflowvectors.hpp>
#include <ql/cashflows/inflationcouponpricer.hpp>
#include <ql/cashflows/yoyinflationcoupon.hpp>
#include <ql/indexes/inflation/euhicp.hpp>
#include <ql/indexes/inflation/ukrpi.hpp>
#include <ql/instruments/inflationcapfloor.hpp>
#include <ql/instruments/vanillaswap.hpp>
#include <ql/math/matrix.hpp>
#include <ql/models/marketmodels/correlations/expcorrelations.hpp>
#include <ql/models/marketmodels/models/flatvol.hpp>
#include <ql/pricingengines/blackformula.hpp>
#include <ql/pricingengines/inflation/inflationcapfloorengines.hpp>
#include <ql/pricingengines/swap/discountingswapengine.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/termstructures/inflation/inflationhelpers.hpp>
#include <ql/termstructures/inflation/piecewiseyoyinflationcurve.hpp>
#include <ql/termstructures/volatility/inflation/yoyinflationoptionletvolatilitystructure.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/time/calendars/unitedkingdom.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/time/daycounters/actualactual.hpp>
#include <ql/time/daycounters/thirty360.hpp>
#include <ql/time/schedule.hpp>
#include <ql/utilities/dataformatters.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
using std::fabs;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(InflationCapFlooredCouponTests)
struct Datum {
Date date;
Rate rate;
};
std::vector<ext::shared_ptr<BootstrapHelper<YoYInflationTermStructure> > >
makeHelpers(const std::vector<Datum>& iiData,
const ext::shared_ptr<YoYInflationIndex> &ii,
const Period &observationLag,
CPI::InterpolationType interpolation,
const Calendar &calendar,
const BusinessDayConvention &bdc,
const DayCounter &dc,
const Handle<YieldTermStructure>& discountCurve) {
std::vector<ext::shared_ptr<BootstrapHelper<YoYInflationTermStructure> > > instruments;
for (Datum datum : iiData) {
Date maturity = datum.date;
Handle<Quote> quote(ext::shared_ptr<Quote>(
new SimpleQuote(datum.rate/100.0)));
auto anInstrument = ext::make_shared<YearOnYearInflationSwapHelper>(
quote, observationLag, maturity,
calendar, bdc, dc, ii, interpolation, discountCurve);
instruments.push_back(anInstrument);
}
return instruments;
}
struct CommonVars {
// common data
Size length;
Date startDate;
Real volatility;
Frequency frequency;
std::vector<Real> nominals;
Calendar calendar;
BusinessDayConvention convention;
Natural fixingDays;
Date evaluationDate;
Natural settlementDays;
Date settlement;
Period observationLag;
DayCounter dc;
ext::shared_ptr<YoYInflationIndex> iir;
RelinkableHandle<YieldTermStructure> nominalTS;
ext::shared_ptr<YoYInflationTermStructure> yoyTS;
RelinkableHandle<YoYInflationTermStructure> hy;
// setup
CommonVars()
: nominals(1,1000000) {
// option variables
frequency = Annual;
// usual setup
volatility = 0.01;
length = 7;
calendar = UnitedKingdom();
convention = ModifiedFollowing;
Date today(13, August, 2007);
evaluationDate = calendar.adjust(today);
Settings::instance().evaluationDate() = evaluationDate;
settlementDays = 0;
fixingDays = 0;
settlement = calendar.advance(today,settlementDays,Days);
startDate = settlement;
dc = Thirty360(Thirty360::BondBasis);
// yoy index
// fixing data
Date from(1, January, 2005);
Date to(13, August, 2007);
Schedule rpiSchedule = MakeSchedule().from(from).to(to)
.withTenor(1*Months)
.withCalendar(UnitedKingdom())
.withConvention(ModifiedFollowing);
Real fixData[] = { 189.9, 189.9, 189.6, 190.5, 191.6, 192.0,
192.2, 192.2, 192.6, 193.1, 193.3, 193.6,
194.1, 193.4, 194.2, 195.0, 196.5, 197.7,
198.5, 198.5, 199.2, 200.1, 200.4, 201.1,
202.7, 201.6, 203.1, 204.4, 205.4, 206.2,
207.3, -999.0, -999 };
auto rpi = ext::make_shared<UKRPI>();
for (Size i=0; i<rpiSchedule.size();i++) {
rpi->addFixing(rpiSchedule[i], fixData[i]);
}
// link from yoy index to yoy TS
iir = ext::make_shared<YoYInflationIndex>(rpi, hy);
ext::shared_ptr<YieldTermStructure> nominalFF(
new FlatForward(evaluationDate, 0.05, ActualActual(ActualActual::ISDA)));
nominalTS.linkTo(nominalFF);
// now build the YoY inflation curve
Period observationLag = Period(2,Months);
std::vector<Datum> yyData = {
{ Date(13, August, 2008), 2.95 },
{ Date(13, August, 2009), 2.95 },
{ Date(13, August, 2010), 2.93 },
{ Date(15, August, 2011), 2.955 },
{ Date(13, August, 2012), 2.945 },
{ Date(13, August, 2013), 2.985 },
{ Date(13, August, 2014), 3.01 },
{ Date(13, August, 2015), 3.035 },
{ Date(13, August, 2016), 3.055 }, // note that
{ Date(13, August, 2017), 3.075 }, // some dates will be on
{ Date(13, August, 2019), 3.105 }, // holidays but the payment
{ Date(15, August, 2022), 3.135 }, // calendar will roll them
{ Date(13, August, 2027), 3.155 },
{ Date(13, August, 2032), 3.145 },
{ Date(13, August, 2037), 3.145 }
};
// now build the helpers ...
std::vector<ext::shared_ptr<BootstrapHelper<YoYInflationTermStructure> > > helpers =
makeHelpers(yyData, iir,
observationLag,
CPI::Flat,
calendar, convention, dc,
Handle<YieldTermStructure>(nominalTS));
Date baseDate = rpi->lastFixingDate();
Rate baseYYRate = yyData[0].rate/100.0;
auto pYYTS =
ext::make_shared<PiecewiseYoYInflationCurve<Linear>>(
evaluationDate, baseDate, baseYYRate, iir->frequency(), dc, helpers);
yoyTS = ext::dynamic_pointer_cast<YoYInflationTermStructure>(pYYTS);
// make sure that the index has the latest yoy term structure
hy.linkTo(pYYTS);
}
// utilities
Leg makeYoYLeg(const Date& startDate,
Integer length,
const Rate gearing = 1.0,
const Rate spread = 0.0) const {
ext::shared_ptr<YoYInflationIndex> ii =
ext::dynamic_pointer_cast<YoYInflationIndex>(iir);
Date endDate = calendar.advance(startDate,length*Years,Unadjusted);
Schedule schedule(startDate, endDate, Period(frequency), calendar,
Unadjusted,Unadjusted,// ref periods & acc periods
DateGeneration::Forward, false);
std::vector<Rate> gearingVector(length, gearing);
std::vector<Spread> spreadVector(length, spread);
Leg yoyLeg = yoyInflationLeg(schedule, calendar, ii, observationLag, CPI::Flat)
.withNotionals(nominals)
.withPaymentDayCounter(dc)
.withGearings(gearingVector)
.withSpreads(spreadVector)
.withPaymentAdjustment(convention);
return yoyLeg;
}
Leg makeFixedLeg(const Date& startDate, Integer length) const {
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)
.withNotionals(nominals)
.withCouponRates(coupons, dc);
}
Leg makeYoYCapFlooredLeg(Size which,
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) const {
Handle<YoYOptionletVolatilitySurface>
vol(ext::make_shared<ConstantYoYOptionletVolatility>(
volatility,
settlementDays,
calendar,
convention,
dc,
observationLag,
frequency,
iir->interpolated()));
ext::shared_ptr<YoYInflationCouponPricer> pricer;
switch (which) {
case 0:
pricer = ext::shared_ptr<YoYInflationCouponPricer>(
new BlackYoYInflationCouponPricer(vol, nominalTS));
break;
case 1:
pricer = ext::shared_ptr<YoYInflationCouponPricer>(
new UnitDisplacedBlackYoYInflationCouponPricer(vol, nominalTS));
break;
case 2:
pricer = ext::shared_ptr<YoYInflationCouponPricer>(
new BachelierYoYInflationCouponPricer(vol, nominalTS));
break;
default:
BOOST_FAIL("unknown coupon pricer request: which = "<<which
<<"should be 0=Black,1=DD,2=Bachelier");
break;
}
std::vector<Rate> gearingVector(length, gearing);
std::vector<Spread> spreadVector(length, spread);
ext::shared_ptr<YoYInflationIndex> ii =
ext::dynamic_pointer_cast<YoYInflationIndex>(iir);
Date endDate = calendar.advance(startDate,length*Years,Unadjusted);
Schedule schedule(startDate, endDate, Period(frequency), calendar,
Unadjusted,Unadjusted,// ref periods & acc periods
DateGeneration::Forward, false);
Leg yoyLeg = yoyInflationLeg(schedule, calendar, ii, observationLag, CPI::Flat)
.withNotionals(nominals)
.withPaymentDayCounter(dc)
.withPaymentAdjustment(convention)
.withGearings(gearingVector)
.withSpreads(spreadVector)
.withCaps(caps)
.withFloors(floors);
setCouponPricer(yoyLeg, pricer);
return yoyLeg;
}
ext::shared_ptr<PricingEngine> makeEngine(Volatility volatility, Size which) const {
ext::shared_ptr<YoYInflationIndex>
yyii = ext::dynamic_pointer_cast<YoYInflationIndex>(iir);
Handle<YoYOptionletVolatilitySurface>
vol(ext::make_shared<ConstantYoYOptionletVolatility>(
volatility,
settlementDays,
calendar,
convention,
dc,
observationLag,
frequency,
iir->interpolated()));
switch (which) {
case 0:
return ext::shared_ptr<PricingEngine>(
new YoYInflationBlackCapFloorEngine(iir, vol, nominalTS));
break;
case 1:
return ext::shared_ptr<PricingEngine>(
new YoYInflationUnitDisplacedBlackCapFloorEngine(iir, vol, nominalTS));
break;
case 2:
return ext::shared_ptr<PricingEngine>(
new YoYInflationBachelierCapFloorEngine(iir, vol, nominalTS));
break;
default:
BOOST_FAIL("unknown engine request: which = "<<which
<<"should be 0=Black,1=DD,2=Bachelier");
break;
}
// make compiler happy
QL_FAIL("never get here - no engine resolution");
}
ext::shared_ptr<YoYInflationCapFloor> makeYoYCapFloor(YoYInflationCapFloor::Type type,
const Leg& leg,
Rate strike,
Volatility volatility,
Size which) const {
ext::shared_ptr<YoYInflationCapFloor> result;
switch (type) {
case YoYInflationCapFloor::Cap:
result = ext::shared_ptr<YoYInflationCapFloor>(
new YoYInflationCap(leg, std::vector<Rate>(1, strike)));
break;
case YoYInflationCapFloor::Floor:
result = ext::shared_ptr<YoYInflationCapFloor>(
new YoYInflationFloor(leg, std::vector<Rate>(1, strike)));
break;
default:
QL_FAIL("unknown YoYInflation cap/floor type");
}
result->setPricingEngine(makeEngine(volatility, which));
return result;
}
};
BOOST_AUTO_TEST_CASE(testDecomposition) {
BOOST_TEST_MESSAGE("Testing collared coupon against its decomposition...");
CommonVars vars;
Real tolerance = 1e-10;
Real npvVanilla,npvCappedLeg,npvFlooredLeg,npvCollaredLeg,npvCap,npvFloor,npvCollar;
Real error;
Rate floorstrike = 0.05;
Rate capstrike = 0.10;
std::vector<Rate> caps(vars.length,capstrike);
std::vector<Rate> caps0 = std::vector<Rate>();
std::vector<Rate> floors(vars.length,floorstrike);
std::vector<Rate> floors0 = std::vector<Rate>();
Rate gearing_p = Rate(0.5);
auto spread_p = Spread(0.002);
Rate gearing_n = Rate(-1.5);
auto spread_n = Spread(0.12);
// fixed leg with zero rate
Leg fixedLeg =
vars.makeFixedLeg(vars.startDate,vars.length);
// floating leg with gearing=1 and spread=0
Leg floatLeg =
vars.makeYoYLeg(vars.startDate,vars.length);
// floating leg with positive gearing (gearing_p) and spread<>0
Leg floatLeg_p =
vars.makeYoYLeg(vars.startDate,vars.length,gearing_p,spread_p);
// floating leg with negative gearing (gearing_n) and spread<>0
Leg floatLeg_n =
vars.makeYoYLeg(vars.startDate,vars.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);
ext::shared_ptr<PricingEngine> engine(
new DiscountingSwapEngine(vars.nominalTS));
vanillaLeg.setPricingEngine(engine); // here use the autoset feature
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
//
Size whichPricer = 0;
// Case gearing = 1 and spread = 0
Leg cappedLeg =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,
caps,floors0,vars.volatility);
Swap capLeg(fixedLeg,cappedLeg);
capLeg.setPricingEngine(engine);
YoYInflationCap cap(floatLeg, std::vector<Rate>(1, capstrike));
cap.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg.NPV();
npvCappedLeg = capLeg.NPV();
npvCap = cap.NPV();
error = std::abs(npvCappedLeg - (npvVanilla-npvCap));
if (error>tolerance) {
BOOST_ERROR("\nYoY Capped 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 =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,
caps0,floors,vars.volatility);
Swap floorLeg(fixedLeg,flooredLeg);
floorLeg.setPricingEngine(engine);
YoYInflationFloor floor(floatLeg, std::vector<Rate>(1, floorstrike));
floor.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvFlooredLeg = floorLeg.NPV();
npvFloor = floor.NPV();
error = std::abs(npvFlooredLeg-(npvVanilla + npvFloor));
if (error>tolerance) {
BOOST_ERROR("YoY 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 =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,
caps,floors,vars.volatility);
Swap collarLeg(fixedLeg,collaredLeg);
collarLeg.setPricingEngine(engine);
YoYInflationCollar collar(floatLeg,
std::vector<Rate>(1, capstrike),
std::vector<Rate>(1, floorstrike));
collar.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvCollaredLeg = collarLeg.NPV();
npvCollar = collar.NPV();
error = std::abs(npvCollaredLeg -(npvVanilla - npvCollar));
if (error>tolerance) {
BOOST_ERROR("\nYoY Collared 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 =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps,floors0,
vars.volatility,gearing_p,spread_p);
Swap capLeg_p(fixedLeg,cappedLeg_p);
capLeg_p.setPricingEngine(engine);
YoYInflationCap cap_p(floatLeg_p,std::vector<Rate>(1,capstrike));
cap_p.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvCappedLeg = capLeg_p.NPV();
npvCap = cap_p.NPV();
error = std::abs(npvCappedLeg - (npvVanilla-npvCap));
if (error>tolerance) {
BOOST_ERROR("\nYoY Capped 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 =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps,floors0,
vars.volatility,gearing_n,spread_n);
Swap capLeg_n(fixedLeg,cappedLeg_n);
capLeg_n.setPricingEngine(engine);
YoYInflationFloor floor_n(floatLeg,std::vector<Rate>(1,(capstrike-spread_n)/gearing_n));
floor_n.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
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("\nYoY Capped 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 =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps0,floors,
vars.volatility,gearing_p,spread_p);
Swap floorLeg_p1(fixedLeg,flooredLeg_p1);
floorLeg_p1.setPricingEngine(engine);
YoYInflationFloor floor_p1(floatLeg_p,std::vector<Rate>(1,floorstrike));
floor_p1.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvFlooredLeg = floorLeg_p1.NPV();
npvFloor = floor_p1.NPV();
error = std::abs(npvFlooredLeg - (npvVanilla+npvFloor));
if (error>tolerance) {
BOOST_ERROR("\nYoY Floored 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 =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps0,floors,
vars.volatility,gearing_n,spread_n);
Swap floorLeg_n(fixedLeg,flooredLeg_n);
floorLeg_n.setPricingEngine(engine);
YoYInflationCap cap_n(floatLeg,std::vector<Rate>(1,(floorstrike-spread_n)/gearing_n));
cap_n.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
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("\nYoY Capped 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 =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps,floors,
vars.volatility,gearing_p,spread_p);
Swap collarLeg_p1(fixedLeg,collaredLeg_p);
collarLeg_p1.setPricingEngine(engine);
YoYInflationCollar collar_p(floatLeg_p,
std::vector<Rate>(1,capstrike),
std::vector<Rate>(1,floorstrike));
collar_p.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
npvVanilla = vanillaLeg_p.NPV();
npvCollaredLeg = collarLeg_p1.NPV();
npvCollar = collar_p.NPV();
error = std::abs(npvCollaredLeg - (npvVanilla - npvCollar));
if (error>tolerance) {
BOOST_ERROR("\nYoY Collared 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 =
vars.makeYoYCapFlooredLeg(whichPricer,vars.startDate,vars.length,caps,floors,
vars.volatility,gearing_n,spread_n);
Swap collarLeg_n1(fixedLeg,collaredLeg_n);
collarLeg_n1.setPricingEngine(engine);
YoYInflationCollar collar_n(floatLeg,
std::vector<Rate>(1,(floorstrike-spread_n)/gearing_n),
std::vector<Rate>(1,(capstrike-spread_n)/gearing_n));
collar_n.setPricingEngine(vars.makeEngine(vars.volatility,whichPricer));
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("\nYoY Collared 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 );
}
// remove circular refernce
vars.hy.reset();
}
BOOST_AUTO_TEST_CASE(testInstrumentEquality) {
BOOST_TEST_MESSAGE("Testing inflation capped/floored coupon against"
" inflation capfloor instrument...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
// vol is low ...
Rate strikes[] = { 0.01, 0.025, 0.029, 0.03, 0.031, 0.035, 0.07 };
// yoy inflation vol is generally very low
Volatility vols[] = { 0.001, 0.005, 0.010, 0.015, 0.020 };
// this is model independent
// capped coupon = fwd - cap, and fwd = swap(0)
// floored coupon = fwd + floor
for (Size whichPricer = 0; whichPricer < 3; whichPricer++) {
for (int& length : lengths) {
for (Real& strike : strikes) {
for (Real vol : vols) {
Leg leg = vars.makeYoYLeg(vars.evaluationDate, length);
ext::shared_ptr<Instrument> cap = vars.makeYoYCapFloor(
YoYInflationCapFloor::Cap, leg, strike, vol, whichPricer);
ext::shared_ptr<Instrument> floor = vars.makeYoYCapFloor(
YoYInflationCapFloor::Floor, leg, strike, vol, whichPricer);
Date from = vars.nominalTS->referenceDate();
Date to = from + length * Years;
Schedule yoySchedule = MakeSchedule().from(from).to(to)
.withTenor(1*Years)
.withCalendar(UnitedKingdom())
.withConvention(Unadjusted)
.backwards()
;
YearOnYearInflationSwap swap(Swap::Payer,
1000000.0,
yoySchedule,//fixed schedule, but same as yoy
0.0,//strikes[j],
vars.dc,
yoySchedule,
vars.iir,
vars.observationLag,
CPI::Flat,
0.0, //spread on index
vars.dc,
UnitedKingdom());
Handle<YieldTermStructure> hTS(vars.nominalTS);
ext::shared_ptr<PricingEngine> sppe(new DiscountingSwapEngine(hTS));
swap.setPricingEngine(sppe);
Leg leg2 = vars.makeYoYCapFlooredLeg(whichPricer, from, length,
std::vector<Rate>(length, strike), // cap
std::vector<Rate>(), // floor
vol,
1.0, // gearing
0.0); // spread
Leg leg3 = vars.makeYoYCapFlooredLeg(whichPricer, from, length,
std::vector<Rate>(), // cap
std::vector<Rate>(length, strike), // floor
vol,
1.0, // gearing
0.0); // spread
// N.B. nominals are 10e6
Real capped = CashFlows::npv(leg2,(**vars.nominalTS),false);
if ( fabs(capped - (swap.NPV() - cap->NPV())) > 1.0e-6) {
BOOST_FAIL("capped coupon != swap(0) - cap:\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " strike: " << io::rate(strike) << "\n"
<< " cap value: " << cap->NPV() << "\n"
<< " swap value: " << swap.NPV() << "\n"
<< " capped coupon " << capped);
}
// N.B. nominals are 10e6
Real floored = CashFlows::npv(leg3,(**vars.nominalTS),false);
if ( fabs(floored - (swap.NPV() + floor->NPV())) > 1.0e-6) {
BOOST_FAIL("floored coupon != swap(0) + floor :\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " strike: " << io::rate(strike) << "\n"
<< " floor value: " << floor->NPV() << "\n"
<< " swap value: " << swap.NPV() << "\n"
<< " floored coupon " << floored);
}
}
}
}
}
// remove circular refernce
vars.hy.reset();
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
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