barrieroption_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/instruments/barrieroption.hpp>
#include <ql/pricingengines/barrier/analyticbarrierengine.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/time/calendars/nullcalendar.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(BarrierOptionXadTest)

namespace {

    struct BarrierOptionData {
        Option::Type type;
        Real strike;
        Real u;       // underlying
        Rate r;       // risk-free rate
        Real b;       // barrier
        Volatility v; // volatility
    };

}
namespace {

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

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

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

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

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

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

        return v;
    }

    template <class PriceFunc>
    Real
    priceWithAAD(const BarrierOptionData& values, BarrierOptionData& derivatives, PriceFunc func) {
        // AAD
        using tape_type = Real::tape_type;
        tape_type tape;
        auto data = values;
        tape.registerInput(data.strike);
        tape.registerInput(data.u);
        tape.registerInput(data.r);
        tape.registerInput(data.b);
        tape.registerInput(data.v);
        tape.newRecording();

        auto price = func(data);

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

        derivatives.strike = derivative(data.strike);
        derivatives.u = derivative(data.u);
        derivatives.r = derivative(data.r);
        derivatives.b = derivative(data.u);
        derivatives.v = derivative(data.b);

        return price;
    }
}

namespace {
    Real priceBarrierOption(const BarrierOptionData& value) {
        Date today(29, May, 2006);
        Settings::instance().evaluationDate() = today;

        // the option to replicate
        Barrier::Type barrierType = Barrier::DownOut;
        Real barrier = 70.0;
        Real rebate = 0.0;
        Option::Type type = Option::Put;
        Real underlying = 100.0;
        auto underlyingH = ext::make_shared<SimpleQuote>(underlying);
        Real strike = 100.0;
        Real r = 0.04;
        Real v = 0.20;
        auto riskFreeRate = ext::make_shared<SimpleQuote>(r);
        auto volatility = ext::make_shared<SimpleQuote>(v);
        Date maturity = today + 1 * Years;

        DayCounter dayCounter = Actual365Fixed();

        Handle<Quote> h1(riskFreeRate);
        Handle<Quote> h2(volatility);
        Handle<YieldTermStructure> flatRate(
            ext::make_shared<FlatForward>(0, NullCalendar(), h1, dayCounter));
        Handle<BlackVolTermStructure> flatVol(
            ext::make_shared<BlackConstantVol>(0, NullCalendar(), h2, dayCounter));

        // instantiate the option
        auto exercise = ext::make_shared<EuropeanExercise>(maturity);
        auto payoff = ext::make_shared<PlainVanillaPayoff>(type, strike);

        auto bsProcess =
            ext::make_shared<BlackScholesProcess>(Handle<Quote>(underlyingH), flatRate, flatVol);


        /// option
        auto referenceOption =
            ext::make_shared<BarrierOption>(barrierType, barrier, rebate, payoff, exercise);

        referenceOption->setPricingEngine(ext::make_shared<AnalyticBarrierEngine>(bsProcess));

        return referenceOption->NPV();
    }
}

BOOST_AUTO_TEST_CASE(testBarrierOptionDerivatives) {

    SavedSettings save;
    BOOST_TEST_MESSAGE("Testing barrier options derivatives...");

    // input
    auto data = BarrierOptionData{Option::Call, 100.00, 90.00, 0.10, 0.10, 0.10};

    // bumping
    auto derivatives_bumping = BarrierOptionData{};
    auto expected = priceWithBumping(data, derivatives_bumping, priceBarrierOption);

    // aad
    auto derivatives_aad = BarrierOptionData{};
    auto actual = priceWithAAD(data, derivatives_aad, priceBarrierOption);

    // compare
    QL_CHECK_CLOSE(expected, actual, 1e-9);
    QL_CHECK_CLOSE(derivatives_bumping.strike, derivatives_aad.strike, 1e-7);
    QL_CHECK_CLOSE(derivatives_bumping.u, derivatives_aad.u, 1e-7);
    QL_CHECK_CLOSE(derivatives_bumping.r, derivatives_aad.r, 1e-7);
    QL_CHECK_CLOSE(derivatives_bumping.b, derivatives_aad.b, 1e-7);
    QL_CHECK_CLOSE(derivatives_bumping.v, derivatives_aad.v, 1e-7);
}

BOOST_AUTO_TEST_SUITE_END()

BOOST_AUTO_TEST_SUITE_END()