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

/*

 Copyright (C) 2007 Klaus Spanderen

 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.

*/

/*! \file analyticbsmhullwhiteengine.hpp

    \brief analytic Black-Scholes engines including stochastic interest rates

*/

#include <ql/pricingengines/vanilla/analyticbsmhullwhiteengine.hpp>

#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>

#include <ql/termstructures/volatility/equityfx/blackvoltermstructure.hpp>

#include <utility>

namespace QuantLib {

    namespace {

        class ShiftedBlackVolTermStructure : public BlackVolTermStructure {

          public:

            ShiftedBlackVolTermStructure(

                Real varianceOffset,

                const Handle<BlackVolTermStructure> & volTS)

                : BlackVolTermStructure(volTS->referenceDate(),

                                        volTS->calendar(),

                                        Following,

                                        volTS->dayCounter()),

                  varianceOffset_(varianceOffset),

                  volTS_(volTS) { }

            Real minStrike() const override { return volTS_->minStrike(); }

            Real maxStrike() const override { return volTS_->maxStrike(); }

            Date maxDate() const override { return volTS_->maxDate(); }

          protected:

            Real blackVarianceImpl(Time t, Real strike) const override {

                return volTS_->blackVariance(t, strike, true)+varianceOffset_;

            }

            Volatility blackVolImpl(Time t, Real strike) const override {

                Time nonZeroMaturity = (t==0.0 ? 0.00001 : t);

                Real var = blackVarianceImpl(nonZeroMaturity, strike);

                return std::sqrt(var/nonZeroMaturity);

            }

          private:

            const Real varianceOffset_;

            const Handle<BlackVolTermStructure> volTS_;

        };

    }

    AnalyticBSMHullWhiteEngine::AnalyticBSMHullWhiteEngine(

        Real equityShortRateCorrelation,

        ext::shared_ptr<GeneralizedBlackScholesProcess> process,

        const ext::shared_ptr<HullWhite>& model)

    : GenericModelEngine<HullWhite, VanillaOption::arguments, VanillaOption::results>(model),

      rho_(equityShortRateCorrelation), process_(std::move(process)) {

        QL_REQUIRE(process_, "no Black-Scholes process specified");

        QL_REQUIRE(!model_.empty(), "no Hull-White model specified");

        registerWith(process_);

    }

    void AnalyticBSMHullWhiteEngine::calculate() const {

        QL_REQUIRE(process_->x0() > 0.0, "negative or null underlying given");

        const ext::shared_ptr<StrikedTypePayoff> payoff =

            ext::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);

        QL_REQUIRE(payoff, "non-striked payoff given");

        const ext::shared_ptr<Exercise> exercise = arguments_.exercise;

        Time t = process_->riskFreeRate()->dayCounter().yearFraction(

                                    process_->riskFreeRate()->referenceDate(),

                                    exercise->lastDate());

        const Real a = model_->params()[0];

        const Real sigma = model_->params()[1];

        const Real eta =

            process_->blackVolatility()->blackVol(exercise->lastDate(),

                                                  payoff->strike());

        Real varianceOffset;

        if (a*t > std::pow(QL_EPSILON, 0.25)) {

            const Real v = sigma*sigma/(a*a)

                *(t + 2/a*std::exp(-a*t) - 1/(2*a)*std::exp(-2*a*t) - 3/(2*a));

            const Real mu = 2*rho_*sigma*eta/a*(t-1/a*(1-std::exp(-a*t)));

            varianceOffset = v + mu;

        }

        else {

            // low-a algebraic limit

            const Real v = sigma*sigma*t*t*t*(1/3.0-0.25*a*t+7/60.0*a*a*t*t);

            const Real mu = rho_*sigma*eta*t*t*(1-a*t/3.0+a*a*t*t/12.0);

            varianceOffset = v + mu;

        }

        Handle<BlackVolTermStructure> volTS(

             ext::make_shared<ShiftedBlackVolTermStructure>(varianceOffset,

                                               process_->blackVolatility()));

        auto adjProcess = ext::make_shared<GeneralizedBlackScholesProcess>(process_->stateVariable(),

                                                   process_->dividendYield(),

                                                   process_->riskFreeRate(),

                                                   volTS);

        auto bsmEngine = ext::make_shared<AnalyticEuropeanEngine>(adjProcess);

        VanillaOption(payoff, exercise).setupArguments(

                                                   bsmEngine->getArguments());

        bsmEngine->calculate();

        results_ = *dynamic_cast<const OneAssetOption::results*>(

                                                    bsmEngine->getResults());

    }

}