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

/*

 Copyright (C) 2009 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 fdmblackscholesmesher.cpp

    \brief 1-d mesher for the Black-Scholes process (in ln(S))

*/

#include <ql/processes/blackscholesprocess.hpp>

#include <ql/termstructures/yieldtermstructure.hpp>

#include <ql/termstructures/yield/quantotermstructure.hpp>

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

#include <ql/math/distributions/normaldistribution.hpp>

#include <ql/methods/finitedifferences/utilities/fdmquantohelper.hpp>

#include <ql/methods/finitedifferences/meshers/uniform1dmesher.hpp>

#include <ql/methods/finitedifferences/meshers/concentrating1dmesher.hpp>

#include <ql/methods/finitedifferences/meshers/fdmblackscholesmesher.hpp>

namespace QuantLib {

    FdmBlackScholesMesher::FdmBlackScholesMesher(

        Size size,

        const ext::shared_ptr<GeneralizedBlackScholesProcess>& process,

        Time maturity, Real strike,

        Real xMinConstraint, Real xMaxConstraint,

        Real eps, Real scaleFactor,

        const std::pair<Real, Real>& cPoint,

        const DividendSchedule& dividendSchedule,

        const ext::shared_ptr<FdmQuantoHelper>& fdmQuantoHelper,

        Real spotAdjustment)

    : Fdm1dMesher(size) {

        const Real S = process->x0();

        QL_REQUIRE(S > 0.0, "negative or null underlying given");

        std::vector<std::pair<Time, Real> > intermediateSteps;

        for (const auto& i : dividendSchedule) {

            const Time t = process->time(i->date());

            if (t <= maturity && t >= 0.0)

                intermediateSteps.emplace_back(process->time(i->date()), i->amount());

        }

        const Size intermediateTimeSteps = std::max<Size>(2, Size(24.0*maturity));

        for (Size i=0; i < intermediateTimeSteps; ++i)

            intermediateSteps.emplace_back((i + 1) * (maturity / intermediateTimeSteps), 0.0);

        std::sort(intermediateSteps.begin(), intermediateSteps.end());

        const Handle<YieldTermStructure> rTS = process->riskFreeRate();

        const Handle<YieldTermStructure> qTS =

            (fdmQuantoHelper) != nullptr ?

                Handle<YieldTermStructure>(ext::make_shared<QuantoTermStructure>(

                    process->dividendYield(), process->riskFreeRate(),

                    Handle<YieldTermStructure>(fdmQuantoHelper->fTS_), process->blackVolatility(),

                    strike, Handle<BlackVolTermStructure>(fdmQuantoHelper->fxVolTS_),

                    fdmQuantoHelper->exchRateATMlevel_, fdmQuantoHelper->equityFxCorrelation_)) :

                process->dividendYield();

        Time lastDivTime = 0.0;

        Real fwd = S + spotAdjustment;

        Real mi = fwd, ma = fwd;

        for (auto& intermediateStep : intermediateSteps) {

            const Time divTime = intermediateStep.first;

            const Real divAmount = intermediateStep.second;

            fwd = fwd / rTS->discount(divTime) * rTS->discount(lastDivTime)

                      * qTS->discount(divTime) / qTS->discount(lastDivTime);

            mi  = std::min(mi, fwd); ma = std::max(ma, fwd);

            fwd-= divAmount;

            mi  = std::min(mi, fwd); ma = std::max(ma, fwd);

            lastDivTime = divTime;

        }

        // Set the grid boundaries

        const Real normInvEps = InverseCumulativeNormal()(1-eps);

        const Real sigmaSqrtT 

            = process->blackVolatility()->blackVol(maturity, strike)

                                                        *std::sqrt(maturity);

        Real xMin = std::log(mi) - sigmaSqrtT*normInvEps*scaleFactor;

        Real xMax = std::log(ma) + sigmaSqrtT*normInvEps*scaleFactor;

        if (xMinConstraint != Null<Real>()) {

            xMin = xMinConstraint;

        }

        if (xMaxConstraint != Null<Real>()) {

            xMax = xMaxConstraint;

        }

        ext::shared_ptr<Fdm1dMesher> helper;

        if (   cPoint.first != Null<Real>() 

            && std::log(cPoint.first) >=xMin && std::log(cPoint.first) <=xMax) {

            helper = ext::shared_ptr<Fdm1dMesher>(

                new Concentrating1dMesher(xMin, xMax, size, 

                    std::pair<Real,Real>(std::log(cPoint.first),

                                         cPoint.second)));

        }

        else {

            helper = ext::shared_ptr<Fdm1dMesher>(

                                        new Uniform1dMesher(xMin, xMax, size));

        }

        locations_ = helper->locations();

        for (Size i=0; i < locations_.size(); ++i) {

            dplus_[i]  = helper->dplus(i);

            dminus_[i] = helper->dminus(i);

        }

    }

    ext::shared_ptr<GeneralizedBlackScholesProcess> 

    FdmBlackScholesMesher::processHelper(const Handle<Quote>& s0,

                                         const Handle<YieldTermStructure>& rTS,

                                         const Handle<YieldTermStructure>& qTS,

                                         Volatility vol) {

        return ext::make_shared<GeneralizedBlackScholesProcess>(

                s0, qTS, rTS,

                Handle<BlackVolTermStructure>(

                    ext::shared_ptr<BlackVolTermStructure>(

                        new BlackConstantVol(rTS->referenceDate(),

                                             Calendar(),

                                             vol,

                                             rTS->dayCounter()))));

    }

}