blackswaptionenginedeltagamma.cpp

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/*
 Copyright (C) 2016 Quaternion Risk Management Ltd
 All rights reserved.
 
 This file is part of ORE, a free-software/open-source library
 for transparent pricing and risk analysis - http://opensourcerisk.org
 
 ORE is free software: you can redistribute it and/or modify it
 under the terms of the Modified BSD License.  You should have received a
 copy of the license along with this program.
 The license is also available online at <http://opensourcerisk.org>
 
 This program is distributed on the basis that it will form a useful
 contribution to risk analytics and model standardisation, 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 <boost/test/unit_test.hpp>
 
#include <qle/pricingengines/blackswaptionenginedeltagamma.hpp>
 
#include <ql/indexes/ibor/euribor.hpp>
#include <ql/instruments/makevanillaswap.hpp>
#include <ql/pricingengines/swaption/blackswaptionengine.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/yield/piecewisezerospreadedtermstructure.hpp>
 
#include <boost/make_shared.hpp>
#include <boost/timer/timer.hpp>
 
using namespace QuantLib;
using namespace QuantExt;
 
using namespace boost::unit_test_framework;
using std::vector;
 
namespace {
struct TestData {
    TestData() : refDate(Date(22, Aug, 2016)) {
        Settings::instance().evaluationDate() = refDate;
        baseDiscount = Handle<YieldTermStructure>(QuantLib::ext::make_shared<FlatForward>(
            refDate, Handle<Quote>(QuantLib::ext::make_shared<SimpleQuote>(0.02)), Actual365Fixed()));
        baseForward = Handle<YieldTermStructure>(QuantLib::ext::make_shared<FlatForward>(
            refDate, Handle<Quote>(QuantLib::ext::make_shared<SimpleQuote>(0.03)), Actual365Fixed()));
        pillarDates.push_back(refDate + 1 * Years);
        pillarDates.push_back(refDate + 2 * Years);
        pillarDates.push_back(refDate + 3 * Years);
        pillarDates.push_back(refDate + 4 * Years);
        pillarDates.push_back(refDate + 5 * Years);
        pillarDates.push_back(refDate + 7 * Years);
        pillarDates.push_back(refDate + 10 * Years);
        pillarDates.push_back(refDate + 15 * Years);
        pillarDates.push_back(refDate + 20 * Years);
        std::vector<Handle<Quote>> tmpDiscSpr, tmpFwdSpr;
        for (Size i = 0; i < pillarDates.size(); ++i) {
            QuantLib::ext::shared_ptr<SimpleQuote> qd = QuantLib::ext::make_shared<SimpleQuote>(0.0);
            QuantLib::ext::shared_ptr<SimpleQuote> qf = QuantLib::ext::make_shared<SimpleQuote>(0.0);
            discountSpreads.push_back(qd);
            forwardSpreads.push_back(qf);
            tmpDiscSpr.push_back(Handle<Quote>(qd));
            tmpFwdSpr.push_back(Handle<Quote>(qf));
            pillarTimes.push_back(baseDiscount->timeFromReference(pillarDates[i]));
        }
        discountCurve =
            Handle<YieldTermStructure>(QuantLib::ext::make_shared<InterpolatedPiecewiseZeroSpreadedTermStructure<Linear>>(
                baseDiscount, tmpDiscSpr, pillarDates));
        forwardCurve =
            Handle<YieldTermStructure>(QuantLib::ext::make_shared<InterpolatedPiecewiseZeroSpreadedTermStructure<Linear>>(
                baseForward, tmpFwdSpr, pillarDates));
        discountCurve->enableExtrapolation();
        forwardCurve->enableExtrapolation();
        forwardIndex = QuantLib::ext::make_shared<Euribor>(6 * Months, forwardCurve);
        lnVol = QuantLib::ext::make_shared<SimpleQuote>(0.20);
        slnVol = QuantLib::ext::make_shared<SimpleQuote>(0.10);
        nVol = QuantLib::ext::make_shared<SimpleQuote>(0.0075);
        slnShift = 0.03;
    }
    Date refDate;
    Handle<YieldTermStructure> baseDiscount, baseForward, discountCurve, forwardCurve;
    QuantLib::ext::shared_ptr<IborIndex> forwardIndex;
    std::vector<Date> pillarDates;
    std::vector<QuantLib::ext::shared_ptr<SimpleQuote>> discountSpreads, forwardSpreads;
    std::vector<Real> pillarTimes;
    QuantLib::ext::shared_ptr<SimpleQuote> lnVol, slnVol, nVol;
    Real slnShift;
}; // TestData
 
bool check(const Real reference, const Real value) {
    if (std::fabs(reference) >= 1E-4) {
        return std::fabs((reference - value) / reference) < 5E-2;
    } else {
        return std::fabs(reference - value) < 5E-5;
    }
}
 
class Timer {
    boost::timer::cpu_timer timer_;
    double elapsed_;
 
public:
    void start() { timer_ = boost::timer::cpu_timer(); }
    void stop() { elapsed_ = timer_.elapsed().wall * 1e-9; }
    double elapsed() const { return elapsed_; }
};
 
void performTest(const TestData& d, const QuantLib::ext::shared_ptr<PricingEngine>& engine0,
                 const QuantLib::ext::shared_ptr<PricingEngine>& engine, const bool receiveFixed, const Real spread,
                 const std::string& config) {
 
    BOOST_TEST_MESSAGE(
        "Testing npv, atm and vega calculation in BlackSwaptionEngineDeltaGamma against QuantLib engine (" << config
                                                                                                           << ")...");
 
    Size n = d.pillarTimes.size();
 
    QuantLib::ext::shared_ptr<VanillaSwap> swap = MakeVanillaSwap(11 * Years, d.forwardIndex, 0.04, 8 * Years)
                                              .receiveFixed(receiveFixed)
                                              .withNominal(10.0)
                                              .withFloatingLegSpread(spread);
    Date exerciseDate = d.refDate + 8 * Years;
    QuantLib::ext::shared_ptr<Exercise> exercise = QuantLib::ext::make_shared<EuropeanExercise>(exerciseDate);
    QuantLib::ext::shared_ptr<Swaption> swaption = QuantLib::ext::make_shared<Swaption>(swap, exercise);
 
    swaption->setPricingEngine(engine0);
    Real atm0 = swaption->result<Real>("atmForward");
    Real vega0 = swaption->result<Real>("vega");
    Real npv0 = swaption->NPV();
 
    swaption->setPricingEngine(engine);
    Real atm = swaption->result<Real>("atmForward");
    Matrix vega = swaption->result<Matrix>("vega");
    Real npv = swaption->NPV();
 
    // check vega matrix dimension
    if (vega.rows() != n || vega.columns() != n)
        BOOST_ERROR("vegaLn dimensions (" << vega.rows() << "x" << vega.columns() << ") are wrong, should be " << n
                                          << "x" << n);
    Real sumVega = 0.0;
    for (Size i = 0; i < n; ++i) {
        for (Size j = 0; j < n; ++j) {
            sumVega += vega[i][j];
        }
    }
 
    // check atm, npv, vega (sum, bucketing was inspected manually, it reuses the logic from gamma rebucketing)
    Real tol = 1E-8;
    if (std::fabs(atm0 - atm) > tol)
        BOOST_ERROR("atm (" << atm << ") can not be verified, expected " << atm0);
    if (std::fabs(npv0 - npv) > tol)
        BOOST_ERROR("npv (" << npv << ") can not be verified, expected " << npv0);
    if (std::fabs(vega0 - sumVega) > tol)
        BOOST_ERROR("vega (" << sumVega << ") can not be verified, expected " << vega0);
 
    BOOST_TEST_MESSAGE("Testing delta calculation in BlackSwaptionEngineDeltaGamma against bump and revalue results ("
                       << config << ")...");
 
    std::vector<Real> resultDeltaDsc = swaption->result<std::vector<Real>>("deltaDiscount");
    std::vector<Real> resultDeltaFwd = swaption->result<std::vector<Real>>("deltaForward");
    Matrix resultGamma = swaption->result<Matrix>("gamma");
 
    // bump and revalue checks
 
    // use QL engine to compute reference bump and revalue results
    swaption->setPricingEngine(engine0);
 
    // check results for correct dimensions
    if (resultDeltaDsc.size() != n)
        BOOST_ERROR("deltaDiscount result vector has a wrong dimension (" << resultDeltaDsc.size() << "), expected "
                                                                          << n);
    if (resultDeltaFwd.size() != n)
        BOOST_ERROR("deltaForward result vector has a wrong dimension (" << resultDeltaFwd.size() << "), expected "
                                                                         << n);
 
    if (resultGamma.rows() != 2 * n || resultGamma.columns() != 2 * n)
        BOOST_ERROR("gamma result vector has wrong dimensions (" << resultGamma.rows() << "x" << resultGamma.columns()
                                                                 << "), expected " << n << "x" << n);
 
    // delta (npv)
 
    const Real bump = 1E-7;
 
    for (Size i = 0; i < n; ++i) {
        d.discountSpreads[i]->setValue(bump);
        Real deltaDsc = (swaption->NPV() - npv0) / bump;
        d.discountSpreads[i]->setValue(0.0);
        d.forwardSpreads[i]->setValue(bump);
        Real deltaFwd = (swaption->NPV() - npv0) / bump;
        d.forwardSpreads[i]->setValue(0.0);
        if (!check(deltaDsc, resultDeltaDsc[i]))
            BOOST_ERROR("delta on pillar " << d.pillarTimes[i]
                                           << " (discount curve) could not be verified, analytical: "
                                           << resultDeltaDsc[i] << ", bump and revalue: " << deltaDsc);
        if (!check(deltaFwd, resultDeltaFwd[i]))
            BOOST_ERROR("delta on pillar " << d.pillarTimes[i] << " (forward curve) could not be verified, analytical: "
                                           << resultDeltaFwd[i] << ", bump and revalue: " << deltaFwd);
    }
 
    // gamma (npv)
 
    BOOST_TEST_MESSAGE("Testing gamma calculation in BlackSwaptionEngineDeltaGamma against bump and revalue results ("
                       << config << ")...");
 
    const Real bump2 = 1E-5;
    Matrix bumpGamma(n * 2, n * 2, 0.0);
 
    // dsc-dsc
    for (Size i = 0; i < n; ++i) {
        // j < i
        for (Size j = 0; j < i; ++j) {
            d.discountSpreads[i]->setValue(bump2);
            d.discountSpreads[j]->setValue(bump2);
            Real npvpp = swaption->NPV();
            d.discountSpreads[j]->setValue(0.0);
            Real npvp0 = swaption->NPV();
            d.discountSpreads[i]->setValue(0.0);
            d.discountSpreads[j]->setValue(bump2);
            Real npv0p = swaption->NPV();
            d.discountSpreads[j]->setValue(0.0);
            Real gamma = (npvpp - npvp0 - npv0p + npv0) / (bump2 * bump2);
            bumpGamma[i][j] = bumpGamma[j][i] = gamma;
        }
        // j == i
        d.discountSpreads[i]->setValue(2.0 * bump2);
        Real npvpp = swaption->NPV();
        d.discountSpreads[i]->setValue(bump2);
        Real npvp = swaption->NPV();
        d.discountSpreads[i]->setValue(0.0);
        Real gamma = (npvpp - 2.0 * npvp + npv0) / (bump2 * bump2);
        bumpGamma[i][i] = gamma;
    }
 
    // dsc-fwd
    for (Size i = 0; i < n; ++i) {
        // j <= i
        for (Size j = 0; j < n; ++j) {
            d.discountSpreads[i]->setValue(bump2);
            d.forwardSpreads[j]->setValue(bump2);
            Real npvpp = swaption->NPV();
            d.forwardSpreads[j]->setValue(0.0);
            Real npvp0 = swaption->NPV();
            d.discountSpreads[i]->setValue(0.0);
            d.forwardSpreads[j]->setValue(bump2);
            Real npv0p = swaption->NPV();
            d.forwardSpreads[j]->setValue(0.0);
            Real gamma = (npvpp - npvp0 - npv0p + npv0) / (bump2 * bump2);
            bumpGamma[i][n + j] = bumpGamma[n + j][i] = gamma;
        }
    }
 
    // fwd-fwd
    for (Size i = 0; i < n; ++i) {
        // j < i
        for (Size j = 0; j < i; ++j) {
            d.forwardSpreads[i]->setValue(bump2);
            d.forwardSpreads[j]->setValue(bump2);
            Real npvpp = swaption->NPV();
            d.forwardSpreads[j]->setValue(0.0);
            Real npvp0 = swaption->NPV();
            d.forwardSpreads[i]->setValue(0.0);
            d.forwardSpreads[j]->setValue(bump2);
            Real npv0p = swaption->NPV();
            d.forwardSpreads[j]->setValue(0.0);
            Real gamma = (npvpp - npvp0 - npv0p + npv0) / (bump2 * bump2);
            bumpGamma[n + i][n + j] = bumpGamma[n + j][n + i] = gamma;
        }
        // j == i
        d.forwardSpreads[i]->setValue(2.0 * bump2);
        Real npvpp = swaption->NPV();
        d.forwardSpreads[i]->setValue(bump2);
        Real npvp = swaption->NPV();
        d.forwardSpreads[i]->setValue(0.0);
        Real gamma = (npvpp - 2.0 * npvp + npv0) / (bump2 * bump2);
        bumpGamma[n + i][n + i] = gamma;
    }
 
    for (Size i = 0; i < 2 * n; ++i) {
        for (Size j = 0; j < 2 * n; ++j) {
            if (!check(bumpGamma[i][j], resultGamma[i][j]))
                BOOST_ERROR("gamma entry (" << i << "," << j << ") is " << resultGamma[i][j]
                                            << ", bump and revalue result is " << bumpGamma[i][j]);
        }
    }
 
    // totals (parallel shift over all curves)
    // this tests, if we have identified all non-zero first and second order partial derivatives
 
    for (Size i = 0; i < n; ++i) {
        d.discountSpreads[i]->setValue(bump);
        d.forwardSpreads[i]->setValue(bump);
    }
 
    Real totalDeltaBump = (swaption->NPV() - npv0) / bump;
 
    for (Size i = 0; i < n; ++i) {
        d.discountSpreads[i]->setValue(2.0 * bump2);
        d.forwardSpreads[i]->setValue(2.0 * bump2);
    }
    Real npvPP = swaption->NPV();
    for (Size i = 0; i < n; ++i) {
        d.discountSpreads[i]->setValue(bump2);
        d.forwardSpreads[i]->setValue(bump2);
    }
    Real npvP = swaption->NPV();
    for (Size i = 0; i < n; ++i) {
        d.discountSpreads[i]->setValue(0.0);
        d.forwardSpreads[i]->setValue(0.0);
    }
 
    Real totalGammaBump = (npvPP - 2.0 * npvP + npv0) / (bump2 * bump2);
 
    Real totalDelta = 0.0, totalGamma = 0.0;
    for (Size i = 0; i < n; ++i) {
        totalDelta += resultDeltaDsc[i];
        totalDelta += resultDeltaFwd[i];
    }
 
    for (Size i = 0; i < 2 * n; ++i) {
        for (Size j = 0; j < 2 * n; ++j) {
            totalGamma += resultGamma[i][j];
        }
    }
 
    if (!check(totalDeltaBump, totalDelta))
        BOOST_ERROR("total delta (" << totalDelta << ") can not be verified against bump and revalue result ("
                                    << totalDeltaBump << ")");
 
    if (!check(totalGammaBump, totalGamma))
        BOOST_ERROR("total gamma (" << totalGamma << ") can not be verified against bump and revalue result ("
                                    << totalGammaBump << ")");
 
} // performTest
 
} // anonymous namespace
 
BOOST_FIXTURE_TEST_SUITE(QuantExtTestSuite, qle::test::TopLevelFixture)
 
BOOST_AUTO_TEST_SUITE(BlackSwaptionEngineDeltaGammaTest)
 
BOOST_AUTO_TEST_CASE(testNpvDeltasGammaVegas) {
 
    TestData d;
 
    QuantLib::ext::shared_ptr<PricingEngine> engineLn0 =
        QuantLib::ext::make_shared<BlackSwaptionEngine>(d.discountCurve, Handle<Quote>(d.lnVol));
    QuantLib::ext::shared_ptr<PricingEngine> engineSln0 =
        QuantLib::ext::make_shared<BlackSwaptionEngine>(d.discountCurve, Handle<Quote>(d.slnVol), Actual365Fixed(), d.slnShift);
    QuantLib::ext::shared_ptr<PricingEngine> engineN0 =
        QuantLib::ext::make_shared<BachelierSwaptionEngine>(d.discountCurve, Handle<Quote>(d.nVol));
 
    QuantLib::ext::shared_ptr<PricingEngine> engineLn =
        QuantLib::ext::make_shared<BlackSwaptionEngineDeltaGamma>(d.discountCurve, Handle<Quote>(d.lnVol), Actual365Fixed(),
                                                          0.0, d.pillarTimes, d.pillarTimes, d.pillarTimes, true, true);
    QuantLib::ext::shared_ptr<PricingEngine> engineSln = QuantLib::ext::make_shared<BlackSwaptionEngineDeltaGamma>(
        d.discountCurve, Handle<Quote>(d.slnVol), Actual365Fixed(), d.slnShift, d.pillarTimes, d.pillarTimes,
        d.pillarTimes, true, true);
    QuantLib::ext::shared_ptr<PricingEngine> engineN =
        QuantLib::ext::make_shared<BachelierSwaptionEngineDeltaGamma>(d.discountCurve, Handle<Quote>(d.nVol), Actual365Fixed(),
                                                              d.pillarTimes, d.pillarTimes, d.pillarTimes, true, true);
 
    performTest(d, engineLn0, engineLn, false, 0.0, "lognormal model, payer");
    performTest(d, engineSln0, engineSln, false, 0.0, "shifted lognormal model, payer");
    performTest(d, engineN0, engineN, false, 0.0, "normal model, payer");
 
    performTest(d, engineLn0, engineLn, true, 0.0, "lognormal model, receiver");
    performTest(d, engineSln0, engineSln, true, 0.0, "shifted lognormal model, receiver");
    performTest(d, engineN0, engineN, true, 0.0, "normal model, receiver");
 
    // the tests with non-zero spread fail, fix it later in the engine, for now we check for zero spreads there
 
    // performTest(d, engineLn0, engineLn, false, 0.01, "lognormal model, payer, spread");
    // performTest(d, engineSln0, engineSln, false, 0.01, "shifted lognormal model, payer, spread");
    // performTest(d, engineN0, engineN, false, 0.01, "normal model, payer, spread");
 
    // performTest(d, engineLn0, engineLn, true, 0.01, "lognormal model, receiver, spread");
    // performTest(d, engineSln0, engineSln, true, 0.01, "shifted lognormal model, receiver, spread");
    // performTest(d, engineN0, engineN, true, 0.01, "normal model, receiver, spread");
 
    BOOST_CHECK(true);
}
 
BOOST_AUTO_TEST_SUITE_END()
 
BOOST_AUTO_TEST_SUITE_END()