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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2018 Sebastian Schlenkrich
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 "toplevelfixture.hpp"
#include "utilities.hpp"
#include <ql/cashflows/iborcoupon.hpp>
#include <ql/compounding.hpp>
#include <ql/experimental/basismodels/swaptioncfs.hpp>
#include <ql/experimental/basismodels/tenoroptionletvts.hpp>
#include <ql/experimental/basismodels/tenorswaptionvts.hpp>
#include <ql/indexes/ibor/euribor.hpp>
#include <ql/instruments/vanillaswap.hpp>
#include <ql/instruments/swaption.hpp>
#include <ql/pricingengines/swap/discountingswapengine.hpp>
#include <ql/termstructures/volatility/optionlet/strippedoptionlet.hpp>
#include <ql/termstructures/volatility/optionlet/strippedoptionletadapter.hpp>
#include <ql/termstructures/volatility/swaption/swaptionvolmatrix.hpp>
#include <ql/termstructures/yield/zerocurve.hpp>
#include <ql/math/interpolations/cubicinterpolation.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/daycounters/thirty360.hpp>
using namespace QuantLib;
using namespace boost::unit_test_framework;
BOOST_FIXTURE_TEST_SUITE(QuantLibTests, TopLevelFixture)
BOOST_AUTO_TEST_SUITE(BasisModelsTests)
// auxiliary data
Period termsData[] = {
Period(0, Days), Period(1, Years), Period(2, Years), Period(3, Years),
Period(5, Years), Period(7, Years), Period(10, Years), Period(15, Years),
Period(20, Years), Period(61, Years) // avoid extrapolation issues with 30y caplets
};
std::vector<Period> terms(termsData, termsData + 10);
Real discRatesData[] = {-0.00147407, -0.001761684, -0.001736745, -0.00119244, 0.000896055,
0.003537077, 0.007213824, 0.011391278, 0.013334611, 0.013982809};
std::vector<Real> discRates(discRatesData, discRatesData + 10);
Real proj3mRatesData[] = {-0.000483439, -0.000578569, -0.000383832, 0.000272656, 0.002478699,
0.005100113, 0.008750643, 0.012788095, 0.014534052, 0.014942896};
std::vector<Real> proj3mRates(proj3mRatesData, proj3mRatesData + 10);
Real proj6mRatesData[] = {0.000233608, 0.000218862, 0.000504018, 0.001240556, 0.003554415,
0.006153921, 0.009688264, 0.013521628, 0.015136391, 0.015377704};
std::vector<Real> proj6mRates(proj6mRatesData, proj6mRatesData + 10);
Handle<YieldTermStructure> getYTS(const std::vector<Period>& terms,
const std::vector<Real>& rates,
const Real spread = 0.0) {
Date today = Settings::instance().evaluationDate();
std::vector<Date> dates;
dates.reserve(terms.size());
for (auto term : terms)
dates.push_back(NullCalendar().advance(today, term, Unadjusted));
std::vector<Real> ratesPlusSpread(rates);
for (Real& k : ratesPlusSpread)
k += spread;
ext::shared_ptr<YieldTermStructure> ts =
ext::shared_ptr<YieldTermStructure>(new InterpolatedZeroCurve<Cubic>(
dates, ratesPlusSpread, Actual365Fixed(), NullCalendar()));
return RelinkableHandle<YieldTermStructure>(ts);
}
Period capletTermsData[] = {Period(1, Years), Period(2, Years), Period(3, Years),
Period(5, Years), Period(7, Years), Period(10, Years),
Period(15, Years), Period(20, Years), Period(25, Years),
Period(30, Years)};
std::vector<Period> capletTerms(capletTermsData, capletTermsData + 10);
Real capletStrikesData[] = {-0.0050, 0.0000, 0.0050, 0.0100, 0.0150, 0.0200, 0.0300, 0.0500};
std::vector<Real> capletStrikes(capletStrikesData, capletStrikesData + 8);
Handle<OptionletVolatilityStructure> getOptionletTS() {
Date today = Settings::instance().evaluationDate();
std::vector<Date> dates;
dates.reserve(capletTerms.size());
for (auto& capletTerm : capletTerms)
dates.push_back(TARGET().advance(today, capletTerm, Following));
// set up vol data manually
std::vector<std::vector<Real> > capletVols =
{
{0.003010094, 0.002628065, 0.00456118, 0.006731268, 0.008678572, 0.010570881, 0.014149552, 0.021000638},
{0.004173715, 0.003727039, 0.004180263, 0.005726083, 0.006905876, 0.008263514, 0.010555395, 0.014976523},
{0.005870143, 0.005334526, 0.005599775, 0.006633987, 0.007773317, 0.009036581, 0.011474391, 0.016277549},
{0.007458597, 0.007207522, 0.007263995, 0.007308727, 0.007813586, 0.008274858, 0.009743988, 0.012555171},
{0.007711531, 0.007608826, 0.007572816, 0.007684107, 0.007971932, 0.008283118, 0.009268828, 0.011574083},
{0.007619605, 0.007639059, 0.007719825, 0.007823373, 0.00800813, 0.008113384, 0.008616374, 0.009785436},
{0.007312199, 0.007352993, 0.007369116, 0.007468333, 0.007515657, 0.00767695, 0.008020447, 0.009072769},
{0.006905851, 0.006966315, 0.007056413, 0.007116494, 0.007259661, 0.00733308, 0.007667563, 0.008419696},
{0.006529553, 0.006630731, 0.006749022, 0.006858027, 0.007001959, 0.007139097, 0.007390404, 0.008036255},
{0.006225482, 0.006404012, 0.00651594, 0.006642273, 0.006640887, 0.006885713, 0.007093024, 0.00767373}
};
// create quotes
std::vector<std::vector<Handle<Quote> > > capletVolQuotes;
for (auto& capletVol : capletVols) {
std::vector<Handle<Quote> > row;
row.reserve(capletVol.size());
for (Real j : capletVol)
row.push_back(RelinkableHandle<Quote>(ext::shared_ptr<Quote>(new SimpleQuote(j))));
capletVolQuotes.push_back(row);
}
Handle<YieldTermStructure> curve3m = getYTS(terms, proj3mRates);
ext::shared_ptr<IborIndex> index(new Euribor3M(curve3m));
ext::shared_ptr<StrippedOptionletBase> tmp1(
new StrippedOptionlet(2, TARGET(), Following, index, dates, capletStrikes,
capletVolQuotes, Actual365Fixed(), Normal, 0.0));
ext::shared_ptr<StrippedOptionletAdapter> tmp2(new StrippedOptionletAdapter(tmp1));
return RelinkableHandle<OptionletVolatilityStructure>(tmp2);
}
Period swaptionVTSTermsData[] = {
Period(1, Years), Period(5, Years), Period(10, Years), Period(20, Years), Period(30, Years),
};
std::vector<Period> swaptionVTSTerms(swaptionVTSTermsData, swaptionVTSTermsData + 5);
Handle<SwaptionVolatilityStructure> getSwaptionVTS() {
std::vector<std::vector<Real> > swaptionVols =
{
{0.002616, 0.00468, 0.0056, 0.005852, 0.005823},
{0.006213, 0.00643, 0.006622, 0.006124, 0.005958},
{0.006658, 0.006723, 0.006602, 0.005802, 0.005464},
{0.005728, 0.005814, 0.005663, 0.004689, 0.004276},
{0.005041, 0.005059, 0.004746, 0.003927, 0.003608}
};
std::vector<std::vector<Handle<Quote> > > swaptionVolQuotes;
for (auto& swaptionVol : swaptionVols) {
std::vector<Handle<Quote> > row;
row.reserve(swaptionVol.size());
for (Real j : swaptionVol)
row.push_back(RelinkableHandle<Quote>(ext::shared_ptr<Quote>(new SimpleQuote(j))));
swaptionVolQuotes.push_back(row);
}
ext::shared_ptr<SwaptionVolatilityStructure> tmp(
new SwaptionVolatilityMatrix(TARGET(), Following, swaptionVTSTerms, swaptionVTSTerms,
swaptionVolQuotes, Actual365Fixed(), true, Normal));
return RelinkableHandle<SwaptionVolatilityStructure>(tmp);
}
void testSwaptioncfs(bool contTenorSpread) {
bool usingAtParCoupons = IborCoupon::Settings::instance().usingAtParCoupons();
// market data and floating rate index
Handle<YieldTermStructure> discYTS = getYTS(terms, discRates);
Handle<YieldTermStructure> proj6mYTS = getYTS(terms, proj6mRates);
ext::shared_ptr<IborIndex> euribor6m(new Euribor6M(proj6mYTS));
// Vanilla swap details
Date today = Settings::instance().evaluationDate();
Date swapStart = TARGET().advance(today, Period(5, Years), Following);
Date swapEnd = TARGET().advance(swapStart, Period(10, Years), Following);
Date exerciseDate = TARGET().advance(swapStart, Period(-2, Days), Preceding);
Schedule fixedSchedule(swapStart, swapEnd, Period(1, Years), TARGET(), ModifiedFollowing,
ModifiedFollowing, DateGeneration::Backward, false);
Schedule floatSchedule(swapStart, swapEnd, Period(6, Months), TARGET(), ModifiedFollowing,
ModifiedFollowing, DateGeneration::Backward, false);
ext::shared_ptr<VanillaSwap> swap(
new VanillaSwap(Swap::Payer, 10000.0, fixedSchedule, 0.03, Thirty360(Thirty360::BondBasis),
floatSchedule, euribor6m, 0.0, euribor6m->dayCounter()));
swap->setPricingEngine(ext::shared_ptr<PricingEngine>(new DiscountingSwapEngine(discYTS)));
// European exercise and swaption
ext::shared_ptr<Exercise> europeanExercise(new EuropeanExercise(exerciseDate));
ext::shared_ptr<Swaption> swaption(
new Swaption(swap, europeanExercise, Settlement::Physical));
// calculate basis model swaption cash flows, discount and conmpare with swap
SwaptionCashFlows cashFlows(swaption, discYTS, contTenorSpread);
// model time is always Act365Fixed
Time exerciseTime = Actual365Fixed().yearFraction(discYTS->referenceDate(),
swaption->exercise()->dates()[0]);
if (exerciseTime != cashFlows.exerciseTimes()[0])
BOOST_ERROR("Swaption cash flow exercise time does not coincide with manual calculation");
// there might be rounding errors
Real tol = 1.0e-8;
// (discounted) fixed leg coupons must match swap fixed leg NPV
Real fixedLeg = 0.0;
for (Size k = 0; k < cashFlows.fixedTimes().size(); ++k)
fixedLeg += cashFlows.fixedWeights()[k] * discYTS->discount(cashFlows.fixedTimes()[k]);
if (fabs(fixedLeg - (-swap->fixedLegNPV())) > tol) // note, '-1' because payer swap
BOOST_ERROR("Swaption cash flow fixed leg NPV does not match Vanillaswap fixed leg NPV"
<< "SwaptionCashFlows: " << fixedLeg << "\n"
<< "swap->fixedLegNPV: " << swap->fixedLegNPV() << "\n"
<< "Variance: " << swap->fixedLegNPV() - fixedLeg << "\n");
// (discounted) floating leg coupons must match swap floating leg NPV
Real floatLeg = 0.0;
for (Size k = 0; k < cashFlows.floatTimes().size(); ++k)
floatLeg += cashFlows.floatWeights()[k] * discYTS->discount(cashFlows.floatTimes()[k]);
if (fabs(floatLeg - swap->floatingLegNPV()) > tol)
BOOST_ERROR(
"Swaption cash flow floating leg NPV does not match Vanillaswap floating leg NPV.\n"
<< "SwaptionCashFlows: " << floatLeg << "\n"
<< "swap->floatingLegNPV: " << swap->floatingLegNPV() << "\n"
<< "Variance: " << swap->floatingLegNPV() - floatLeg << "\n");
// There should not be spread coupons in a single-curve setting.
// However, if indexed coupons are used the floating leg is not at par,
// so we need to relax the tolerance to a level at which it will only
// catch large errors.
Real tol2 = usingAtParCoupons ? tol : 0.02;
SwaptionCashFlows singleCurveCashFlows(swaption, proj6mYTS, contTenorSpread);
for (Size k = 1; k < singleCurveCashFlows.floatWeights().size() - 1; ++k) {
if (fabs(singleCurveCashFlows.floatWeights()[k]) > tol2)
BOOST_ERROR("Swaption cash flow floating leg spread does not vanish in "
"single-curve setting.\n"
<< "Cash flow index k: " << k << ", floatWeights: "
<< singleCurveCashFlows.floatWeights()[k] << "\n");
}
}
BOOST_AUTO_TEST_CASE(testSwaptioncfsContCompSpread) {
BOOST_TEST_MESSAGE(
"Testing deterministic tenor basis model with continuous compounded spreads...");
testSwaptioncfs(true);
}
BOOST_AUTO_TEST_CASE(testSwaptioncfsSimpleCompSpread) {
BOOST_TEST_MESSAGE("Testing deterministic tenor basis model with simple compounded spreads...");
testSwaptioncfs(false);
}
BOOST_AUTO_TEST_CASE(testTenoroptionletvts) {
BOOST_TEST_MESSAGE("Testing volatility transformation for caplets/floorlets...");
// market data and floating rate index
Real spread = 0.01;
Handle<YieldTermStructure> discYTS = getYTS(terms, discRates);
Handle<YieldTermStructure> proj3mYTS = getYTS(terms, proj3mRates);
Handle<YieldTermStructure> proj6mYTS = getYTS(terms, proj3mRates, spread);
ext::shared_ptr<IborIndex> euribor3m(new Euribor6M(proj3mYTS));
ext::shared_ptr<IborIndex> euribor6m(new Euribor6M(proj6mYTS));
// 3m optionlet VTS
Handle<OptionletVolatilityStructure> optionletVTS3m = getOptionletTS();
{
// we need a correlation structure
Real corrTimesRaw[] = {0.0, 50.0};
Real rhoInfDataRaw[] = {0.3, 0.3};
Real betaDataRaw[] = {0.9, 0.9};
std::vector<Real> corrTimes(corrTimesRaw, corrTimesRaw + 2);
std::vector<Real> rhoInfData(rhoInfDataRaw, rhoInfDataRaw + 2);
std::vector<Real> betaData(betaDataRaw, betaDataRaw + 2);
ext::shared_ptr<Interpolation> rho(
new LinearInterpolation(corrTimes.begin(), corrTimes.end(), rhoInfData.begin()));
ext::shared_ptr<Interpolation> beta(
new LinearInterpolation(corrTimes.begin(), corrTimes.end(), betaData.begin()));
ext::shared_ptr<TenorOptionletVTS::CorrelationStructure> corr(
new TenorOptionletVTS::TwoParameterCorrelation(rho, beta));
// now we can set up the new volTS and calculate volatilities
ext::shared_ptr<OptionletVolatilityStructure> optionletVTS6m(
new TenorOptionletVTS(optionletVTS3m, euribor3m, euribor6m, corr));
for (auto& capletTerm : capletTerms) {
for (Real& capletStrike : capletStrikes) {
Real vol3m = optionletVTS3m->volatility(capletTerm, capletStrike, true);
Real vol6m = optionletVTS6m->volatility(capletTerm, capletStrike, true);
Real vol6mShifted =
optionletVTS6m->volatility(capletTerm, capletStrike + spread, true);
// De-correlation yields that larger tenor shifted vols are smaller then shorter
// tenor vols
if (vol6mShifted - vol3m >
0.0001) // we leave 1bp tolerance due to simplified spread calculation
BOOST_ERROR("Shifted 6m vol significantly larger then 3m vol at\n"
<< "expiry term: " << capletTerm << ", strike: " << capletStrike
<< "\n"
<< "vol3m: " << vol3m << ", vol6m: " << vol6m
<< ", vol6mShifted: " << vol6mShifted << "\n");
}
}
}
{
// we need a correlation structure
Real corrTimesRaw[] = {0.0, 50.0};
Real rhoInfDataRaw[] = {0.0, 0.0};
Real betaDataRaw[] = {0.0, 0.0};
std::vector<Real> corrTimes(corrTimesRaw, corrTimesRaw + 2);
std::vector<Real> rhoInfData(rhoInfDataRaw, rhoInfDataRaw + 2);
std::vector<Real> betaData(betaDataRaw, betaDataRaw + 2);
ext::shared_ptr<Interpolation> rho(
new LinearInterpolation(corrTimes.begin(), corrTimes.end(), rhoInfData.begin()));
ext::shared_ptr<Interpolation> beta(
new LinearInterpolation(corrTimes.begin(), corrTimes.end(), betaData.begin()));
ext::shared_ptr<TenorOptionletVTS::CorrelationStructure> corr(
new TenorOptionletVTS::TwoParameterCorrelation(rho, beta));
// now we can set up the new volTS and calculate volatilities
ext::shared_ptr<OptionletVolatilityStructure> optionletVTS6m(
new TenorOptionletVTS(optionletVTS3m, euribor3m, euribor6m, corr));
for (Size i = 0; i < capletTerms.size(); ++i) {
for (Real& capletStrike : capletStrikes) {
Real vol3m = optionletVTS3m->volatility(capletTerms[i], capletStrike, true);
Real vol6m = optionletVTS6m->volatility(capletTerms[i], capletStrike, true);
Real vol6mShifted =
optionletVTS6m->volatility(capletTerms[i], capletStrike + spread, true);
// for perfect correlation shifted 6m vols should coincide with 3m vols
Real tol =
(i < 3) ? (0.001) :
(0.0001); // 10bp tol for smaller tenors and 1bp tol for larger tenors
if (fabs(vol6mShifted - vol3m) > tol)
BOOST_ERROR("Shifted 6m vol does not match 3m vol for perfect correlation at\n"
<< "expiry term: " << capletTerms[i] << ", strike: " << capletStrike
<< "\n"
<< "vol3m: " << vol3m << ", vol6m: " << vol6m
<< ", vol6mShifted: " << vol6mShifted << "\n");
}
}
}
}
BOOST_AUTO_TEST_CASE(testTenorswaptionvts) {
BOOST_TEST_MESSAGE("Testing volatility transformation for swaptions...");
// market data and floating rate index
Real spread = 0.01;
Handle<YieldTermStructure> discYTS = getYTS(terms, discRates);
Handle<YieldTermStructure> proj3mYTS = getYTS(terms, proj3mRates);
Handle<YieldTermStructure> proj6mYTS = getYTS(terms, proj3mRates, spread);
ext::shared_ptr<IborIndex> euribor3m(new Euribor6M(proj3mYTS));
ext::shared_ptr<IborIndex> euribor6m(new Euribor6M(proj6mYTS));
// Euribor6m ATM vols
Handle<SwaptionVolatilityStructure> euribor6mSwVTS = getSwaptionVTS();
{
ext::shared_ptr<TenorSwaptionVTS> euribor3mSwVTS(
new TenorSwaptionVTS(euribor6mSwVTS, discYTS, euribor6m, euribor3m, Period(1, Years),
Period(1, Years), Thirty360(Thirty360::BondBasis), Thirty360(Thirty360::BondBasis)));
// 6m vols should be slightly larger then 3m vols due to basis
for (Size i = 0; i < swaptionVTSTerms.size(); ++i) {
for (Size j = 0; j < swaptionVTSTerms.size(); ++j) {
Real vol6m = euribor6mSwVTS->volatility(swaptionVTSTerms[i], swaptionVTSTerms[j],
0.01, true);
Real vol3m = euribor3mSwVTS->volatility(swaptionVTSTerms[i], swaptionVTSTerms[j],
0.01, true);
if (vol3m > vol6m)
BOOST_ERROR("Euribor 6m must be larger than 3m vol at\n"
<< "expiry term: " << swaptionVTSTerms[i]
<< ", swap term: " << swaptionVTSTerms[j] << "\n"
<< "vol3m: " << vol3m << ", vol6m: " << vol6m << "\n");
}
}
}
{
ext::shared_ptr<TenorSwaptionVTS> euribor6mSwVTS2(
new TenorSwaptionVTS(euribor6mSwVTS, discYTS, euribor6m, euribor6m, Period(1, Years),
Period(1, Years), Thirty360(Thirty360::BondBasis), Thirty360(Thirty360::BondBasis)));
// 6m vols to 6m vols should yield initiial vols
for (Size i = 0; i < swaptionVTSTerms.size(); ++i) {
for (Size j = 0; j < swaptionVTSTerms.size(); ++j) {
Real vol6m = euribor6mSwVTS->volatility(swaptionVTSTerms[i], swaptionVTSTerms[j],
0.01, true);
Real vol6m2 = euribor6mSwVTS2->volatility(swaptionVTSTerms[i], swaptionVTSTerms[j],
0.01, true);
Real tol = 1.0e-8;
if (fabs(vol6m2 - vol6m) > tol)
BOOST_ERROR("Euribor 6m to 6m vols should not change at\n"
<< "expiry term: " << swaptionVTSTerms[i]
<< ", swap term: " << swaptionVTSTerms[j] << "\n"
<< "vol6m: " << vol6m << ", vol6m2: " << vol6m2
<< ", variance: " << (vol6m2 - vol6m) << "\n");
}
}
}
{
ext::shared_ptr<TenorSwaptionVTS> euribor3mSwVTS(
new TenorSwaptionVTS(euribor6mSwVTS, discYTS, euribor6m, euribor3m, Period(1, Years),
Period(1, Years), Thirty360(Thirty360::BondBasis), Thirty360(Thirty360::BondBasis)));
ext::shared_ptr<TenorSwaptionVTS> euribor6mSwVTS2(new TenorSwaptionVTS(
RelinkableHandle<SwaptionVolatilityStructure>(euribor3mSwVTS), discYTS, euribor3m,
euribor6m, Period(1, Years), Period(1, Years), Thirty360(Thirty360::BondBasis), Thirty360(Thirty360::BondBasis)));
// 6m vols to 6m vols should yield initiial vols
for (Size i = 0; i < swaptionVTSTerms.size(); ++i) {
for (Size j = 0; j < swaptionVTSTerms.size(); ++j) {
Real vol6m = euribor6mSwVTS->volatility(swaptionVTSTerms[i], swaptionVTSTerms[j],
0.01, true);
Real vol6m2 = euribor6mSwVTS2->volatility(swaptionVTSTerms[i], swaptionVTSTerms[j],
0.01, true);
Real tol = 1.0e-8;
if (fabs(vol6m2 - vol6m) > tol)
BOOST_ERROR("Euribor 6m to 3m to 6m vols should not change at\n"
<< "expiry term: " << swaptionVTSTerms[i]
<< ", swap term: " << swaptionVTSTerms[j] << "\n"
<< "vol6m: " << vol6m << ", vol6m2: " << vol6m2
<< ", variance: " << (vol6m2 - vol6m) << "\n");
}
}
}
}
BOOST_AUTO_TEST_SUITE_END()
BOOST_AUTO_TEST_SUITE_END()
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