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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(InflationCapFloorTests)
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,
CPI::InterpolationType interpolation,
const Period &observationLag,
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
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
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);
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,
CPI::Flat,
observationLag,
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 {
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);
return yoyInflationLeg(schedule, calendar, ii, observationLag, CPI::Flat)
.withNotionals(nominals)
.withPaymentDayCounter(dc)
.withPaymentAdjustment(convention);
}
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(testConsistency) {
BOOST_TEST_MESSAGE("Testing consistency between yoy inflation cap,"
" floor and collar...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
Rate cap_rates[] = { 0.01, 0.025, 0.029, 0.03, 0.031, 0.035, 0.07 };
Rate floor_rates[] = { 0.01, 0.025, 0.029, 0.03, 0.031, 0.035, 0.07 };
Volatility vols[] = { 0.001, 0.005, 0.010, 0.015, 0.020 };
for (Size whichPricer = 0; whichPricer < 3; whichPricer++) {
for (int& length : lengths) {
for (Real& cap_rate : cap_rates) {
for (Real& floor_rate : floor_rates) {
for (Real vol : vols) {
Leg leg = vars.makeYoYLeg(vars.evaluationDate, length);
ext::shared_ptr<YoYInflationCapFloor> cap = vars.makeYoYCapFloor(
YoYInflationCapFloor::Cap, leg, cap_rate, vol, whichPricer);
ext::shared_ptr<YoYInflationCapFloor> floor = vars.makeYoYCapFloor(
YoYInflationCapFloor::Floor, leg, floor_rate, vol, whichPricer);
YoYInflationCollar collar(leg, std::vector<Rate>(1, cap_rate),
std::vector<Rate>(1, floor_rate));
collar.setPricingEngine(vars.makeEngine(vol, whichPricer));
if (std::fabs((cap->NPV() - floor->NPV()) - collar.NPV()) > 1e-6) {
BOOST_FAIL("inconsistency between cap, floor and collar:\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " cap value: " << cap->NPV()
<< " at strike: " << io::rate(cap_rate) << "\n"
<< " floor value: " << floor->NPV()
<< " at strike: " << io::rate(floor_rate) << "\n"
<< " collar value: " << collar.NPV());
// test re-composition by optionlets, N.B. ONE per year
Real capletsNPV = 0.0;
std::vector<ext::shared_ptr<YoYInflationCapFloor> > caplets;
for (Integer m = 0; m < length * 1; m++) {
caplets.push_back(cap->optionlet(m));
caplets[m]->setPricingEngine(vars.makeEngine(vol, whichPricer));
capletsNPV += caplets[m]->NPV();
}
if (std::fabs(cap->NPV() - capletsNPV) > 1e-6) {
BOOST_FAIL("sum of caplet NPVs does not equal cap NPV:\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " cap value: " << cap->NPV()
<< " at strike: " << io::rate(cap_rate) << "\n"
<< " sum of caplets value: " << capletsNPV
<< " at strike (first): "
<< io::rate(caplets[0]->capRates()[0]) << "\n");
}
Real floorletsNPV = 0.0;
std::vector<ext::shared_ptr<YoYInflationCapFloor> > floorlets;
for (Integer m = 0; m < length * 1; m++) {
floorlets.push_back(floor->optionlet(m));
floorlets[m]->setPricingEngine(vars.makeEngine(vol, whichPricer));
floorletsNPV += floorlets[m]->NPV();
}
if (std::fabs(floor->NPV() - floorletsNPV) > 1e-6) {
BOOST_FAIL("sum of floorlet NPVs does not equal floor NPV:\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " cap value: " << floor->NPV()
<< " at strike: " << io::rate(floor_rate) << "\n"
<< " sum of floorlets value: " << floorletsNPV
<< " at strike (first): "
<< io::rate(floorlets[0]->floorRates()[0]) << "\n");
}
Real collarletsNPV = 0.0;
std::vector<ext::shared_ptr<YoYInflationCapFloor> > collarlets;
for (Integer m = 0; m < length * 1; m++) {
collarlets.push_back(collar.optionlet(m));
collarlets[m]->setPricingEngine(vars.makeEngine(vol, whichPricer));
collarletsNPV += collarlets[m]->NPV();
}
if (std::fabs(collar.NPV() - collarletsNPV) > 1e-6) {
BOOST_FAIL("sum of collarlet NPVs does not equal collar NPV:\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " cap value: " << collar.NPV()
<< " at strike floor: " << io::rate(floor_rate)
<< " at strike cap: " << io::rate(cap_rate) << "\n"
<< " sum of collarlets value: " << collarletsNPV
<< " at strike floor (first): "
<< io::rate(collarlets[0]->floorRates()[0])
<< " at strike cap (first): "
<< io::rate(collarlets[0]->capRates()[0]) << "\n");
}
}
}
}
}
}
} // pricer loop
// remove circular refernce
vars.hy.reset();
}
// Test inflation cap/floor parity, i.e. that cap-floor = swap, note that this
// is different from nominal because in nominal world standard cap/floors do
// not have the first optionlet. This is because they set in advance so
// there is no point. However, yoy inflation generally sets in arrears,
// (actually in arrears with a lag of a few months) thus the first optionlet
// is relevant. Hence we can do a parity test without a special definition
// of the YoY cap/floor instrument.
BOOST_AUTO_TEST_CASE(testParity) {
BOOST_TEST_MESSAGE("Testing yoy inflation cap/floor parity...");
CommonVars vars;
Integer lengths[] = { 1, 2, 3, 5, 7, 10, 15, 20 };
// vol is low ...
Rate strikes[] = { 0., 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 };
// cap-floor-swap parity is model-independent
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
strike, 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);
// N.B. nominals are 10e6
if (std::fabs((cap->NPV()-floor->NPV()) - swap.NPV()) > 1.0e-6) {
BOOST_FAIL("put/call parity violated:\n"
<< " length: " << length << " years\n"
<< " volatility: " << io::volatility(vol) << "\n"
<< " strike: " << io::rate(strike) << "\n"
<< " cap value: " << cap->NPV() << "\n"
<< " floor value: " << floor->NPV() << "\n"
<< " swap value: " << swap.NPV());
}
}
}
}
}
// remove circular refernce
vars.hy.reset();
}
BOOST_AUTO_TEST_CASE(testCachedValue) {
BOOST_TEST_MESSAGE("Testing Black yoy inflation cap/floor price"
" against cached values...");
CommonVars vars;
Size whichPricer = 0; // black
Real K = 0.0295; // one centi-point is fair rate error i.e. < 1 cp
Size j = 2;
Leg leg = vars.makeYoYLeg(vars.evaluationDate,j);
ext::shared_ptr<Instrument> cap
= vars.makeYoYCapFloor(YoYInflationCapFloor::Cap,leg, K, 0.01, whichPricer);
ext::shared_ptr<Instrument> floor
= vars.makeYoYCapFloor(YoYInflationCapFloor::Floor,leg, K, 0.01, whichPricer);
// close to atm prices
Real cachedCapNPVblack = 219.452;
Real cachedFloorNPVblack = 314.641;
// N.B. notionals are 10e6.
BOOST_CHECK_MESSAGE(fabs(cap->NPV()-cachedCapNPVblack)<0.02,"yoy cap cached NPV wrong "
<<cap->NPV()<<" should be "<<cachedCapNPVblack<<" Black pricer"
<<" diff was "<<(fabs(cap->NPV()-cachedCapNPVblack)));
BOOST_CHECK_MESSAGE(fabs(floor->NPV()-cachedFloorNPVblack)<0.02,"yoy floor cached NPV wrong "
<<floor->NPV()<<" should be "<<cachedFloorNPVblack<<" Black pricer"
<<" diff was "<<(fabs(floor->NPV()-cachedFloorNPVblack)));
whichPricer = 1; // dd
cap
= vars.makeYoYCapFloor(YoYInflationCapFloor::Cap,leg, K, 0.01, whichPricer);
floor
= vars.makeYoYCapFloor(YoYInflationCapFloor::Floor,leg, K, 0.01, whichPricer);
// close to atm prices
Real cachedCapNPVdd = 9114.61;
Real cachedFloorNPVdd = 9209.8;
// N.B. notionals are 10e6.
BOOST_CHECK_MESSAGE(fabs(cap->NPV()-cachedCapNPVdd)<0.22,"yoy cap cached NPV wrong "
<<cap->NPV()<<" should be "<<cachedCapNPVdd<<" dd Black pricer"
<<" diff was "<<(fabs(cap->NPV()-cachedCapNPVdd)));
BOOST_CHECK_MESSAGE(fabs(floor->NPV()-cachedFloorNPVdd)<0.22,"yoy floor cached NPV wrong "
<<floor->NPV()<<" should be "<<cachedFloorNPVdd<<" dd Black pricer"
<<" diff was "<<(fabs(floor->NPV()-cachedFloorNPVdd)));
whichPricer = 2; // bachelier
cap
= vars.makeYoYCapFloor(YoYInflationCapFloor::Cap,leg, K, 0.01, whichPricer);
floor
= vars.makeYoYCapFloor(YoYInflationCapFloor::Floor,leg, K, 0.01, whichPricer);
// close to atm prices
Real cachedCapNPVbac = 8852.4;
Real cachedFloorNPVbac = 8947.59;
// N.B. notionals are 10e6.
BOOST_CHECK_MESSAGE(fabs(cap->NPV()-cachedCapNPVbac)<0.22,"yoy cap cached NPV wrong "
<<cap->NPV()<<" should be "<<cachedCapNPVbac<<" bac Black pricer"
<<" diff was "<<(fabs(cap->NPV()-cachedCapNPVbac)));
BOOST_CHECK_MESSAGE(fabs(floor->NPV()-cachedFloorNPVbac)<0.22,"yoy floor cached NPV wrong "
<<floor->NPV()<<" should be "<<cachedFloorNPVbac<<" bac Black pricer"
<<" diff was "<<(fabs(floor->NPV()-cachedFloorNPVbac)));
// remove circular refernce
vars.hy.reset();
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
|
