forwardrateagreement_xad.cpp

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*
 Copyright (C) 2003, 2004 Ferdinando Ametrano
 Copyright (C) 2005, 2007 StatPro Italia srl
 Copyright (C) 2005 Joseph Wang
 Copyright (C) 2023, 2024 Xcelerit Computing Limited

 This file is part of QuantLib / XAD integration module.
 It is modified from 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_xad.hpp"
#include <ql/indexes/ibor/usdlibor.hpp>
#include <ql/instruments/forwardrateagreement.hpp>
#include <ql/termstructures/yield/zerocurve.hpp>
#include <ql/time/calendars/target.hpp>
#include <ql/time/calendars/unitedstates.hpp>
#include <ql/time/daycounters/actual360.hpp>
#include <ql/time/period.hpp>
#include <chrono>
#include <iomanip>
#include <iostream>
#include <vector>

using namespace QuantLib;
using namespace boost::unit_test_framework;

BOOST_FIXTURE_TEST_SUITE(QuantLibRisksTests, TopLevelFixture)

BOOST_AUTO_TEST_SUITE(ForwardRateAgreementXadTests)

namespace {

    struct ForwardRateAgreementData {
        Real nominal;
        Real spotRate1;
        Real spotRate2;
        Real spotRate3;
        Real rate;
    };

}

namespace {

    template <class PriceFunc>
    Real priceWithBumping(const ForwardRateAgreementData& value,
                          ForwardRateAgreementData& derivatives,
                          PriceFunc func) {
        // Bumping
        auto eps = 1e-7;
        auto data = value;
        auto v = func(data);

        data.nominal += 1;
        auto vplus = func(data);
        derivatives.nominal = (vplus - v) / 1;
        data = value;

        data.spotRate1 += eps;
        vplus = func(data);
        derivatives.spotRate1 = (vplus - v) / eps;
        data = value;

        data.spotRate2 += eps;
        vplus = func(data);
        derivatives.spotRate2 = (vplus - v) / eps;
        data = value;

        data.spotRate3 += eps;
        vplus = func(data);
        derivatives.spotRate3 = (vplus - v) / eps;
        data = value;

        data.rate += eps;
        vplus = func(data);
        derivatives.rate = (vplus - v) / eps;

        return v;
    }

    template <class PriceFunc>
    Real priceWithAAD(const ForwardRateAgreementData& values,
                      ForwardRateAgreementData& derivatives,
                      PriceFunc func) {
        // AAD
        using tape_type = Real::tape_type;
        tape_type tape;
        auto data = values;
        tape.registerInput(data.nominal);
        tape.registerInput(data.spotRate1);
        tape.registerInput(data.spotRate2);
        tape.registerInput(data.spotRate3);
        tape.registerInput(data.rate);
        tape.newRecording();

        auto price = func(data);

        tape.registerOutput(price);
        derivative(price) = 1.0;
        tape.computeAdjoints();

        derivatives.nominal = derivative(data.nominal);
        derivatives.spotRate1 = derivative(data.spotRate1);
        derivatives.spotRate2 = derivative(data.spotRate2);
        derivatives.spotRate3 = derivative(data.spotRate3);
        derivatives.rate = derivative(data.rate);

        return price;
    }
}

namespace {
    Real priceForwardRateAgreement(const ForwardRateAgreementData& value) {
        Date today(30, June, 2020);
        Settings::instance().evaluationDate() = today;

        std::vector<Date> spotDates;
        spotDates.push_back(Date(30, June, 2020));
        spotDates.push_back(Date(31, December, 2020));
        spotDates.push_back(Date(30, June, 2021));
        std::vector<Real> spotRates;
        spotRates.push_back(value.spotRate1);
        spotRates.push_back(value.spotRate2);
        spotRates.push_back(value.spotRate3);

        DayCounter dayConvention = Actual360();
        Calendar calendar = UnitedStates(UnitedStates::GovernmentBond);
        Date startDate = calendar.advance(today, Period(3, Months));
        Date maturityDate = calendar.advance(startDate, Period(3, Months));

        Compounding compounding = Simple;
        Frequency compoundingFrequency = Annual;

        Handle<YieldTermStructure> spotCurve(
            ext::make_shared<ZeroCurve>(spotDates, spotRates, dayConvention, calendar, Linear(),
                                        compounding, compoundingFrequency));
        spotCurve->enableExtrapolation();

        auto index = ext::make_shared<USDLibor>(Period(3, Months), spotCurve);
        index->addFixing(Date(26, June, 2020), 0.05);

        ForwardRateAgreement fra(index, startDate, maturityDate, Position::Long, value.rate,
                                 value.nominal, spotCurve);

        return fra.NPV();
    }
}

BOOST_AUTO_TEST_CASE(testForwardRateAgreementDerivatives) {

    SavedSettings save;
    BOOST_TEST_MESSAGE("Testing forward rate agreement derivatives...");

    // input
    auto data = ForwardRateAgreementData{100000, 0.5, 0.5, 0.5, 0.06};

    // bumping
    auto derivatives_bumping = ForwardRateAgreementData{};
    auto expected = priceWithBumping(data, derivatives_bumping, priceForwardRateAgreement);

    // aad
    auto derivatives_aad = ForwardRateAgreementData{};
    auto actual = priceWithAAD(data, derivatives_aad, priceForwardRateAgreement);

    // compare
    QL_CHECK_CLOSE(expected, actual, 1e-9);
    QL_CHECK_CLOSE(derivatives_bumping.nominal, derivatives_aad.nominal, 1e-3);
    QL_CHECK_CLOSE(derivatives_bumping.spotRate1, derivatives_aad.spotRate1, 1e-3);
    QL_CHECK_CLOSE(derivatives_bumping.spotRate2, derivatives_aad.spotRate2, 1e-3);
    QL_CHECK_CLOSE(derivatives_bumping.spotRate3, derivatives_aad.spotRate3, 1e-3);
    QL_CHECK_CLOSE(derivatives_bumping.rate, derivatives_aad.rate, 1e-3);
}

BOOST_AUTO_TEST_SUITE_END()

BOOST_AUTO_TEST_SUITE_END()