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

/*

 Copyright (C) 2013 Yue Tian

 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.

*/

#include <ql/experimental/barrieroption/vannavolgabarrierengine.hpp>

#include <ql/experimental/barrieroption/vannavolgainterpolation.hpp>

#include <ql/math/matrix.hpp>

#include <ql/pricingengines/barrier/analyticbarrierengine.hpp>

#include <ql/pricingengines/blackdeltacalculator.hpp>

#include <ql/pricingengines/blackformula.hpp>

#include <ql/quotes/simplequote.hpp>

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

#include <ql/time/calendars/nullcalendar.hpp>

#include <utility>

using std::pow;

using std::log;

using std::sqrt;

namespace QuantLib {

    VannaVolgaBarrierEngine::VannaVolgaBarrierEngine(Handle<DeltaVolQuote> atmVol,

                                                     Handle<DeltaVolQuote> vol25Put,

                                                     Handle<DeltaVolQuote> vol25Call,

                                                     Handle<Quote> spotFX,

                                                     Handle<YieldTermStructure> domesticTS,

                                                     Handle<YieldTermStructure> foreignTS,

                                                     const bool adaptVanDelta,

                                                     const Real bsPriceWithSmile)

    : atmVol_(std::move(atmVol)), vol25Put_(std::move(vol25Put)), vol25Call_(std::move(vol25Call)),

      T_(atmVol_->maturity()), spotFX_(std::move(spotFX)), domesticTS_(std::move(domesticTS)),

      foreignTS_(std::move(foreignTS)), adaptVanDelta_(adaptVanDelta),

      bsPriceWithSmile_(bsPriceWithSmile) {

        QL_REQUIRE(vol25Put_->delta() == -0.25, "25 delta put is required by vanna volga method");

        QL_REQUIRE(vol25Call_->delta() == 0.25, "25 delta call is required by vanna volga method");

        QL_REQUIRE(vol25Put_->maturity() == vol25Call_->maturity() &&

                       vol25Put_->maturity() == atmVol_->maturity(),

                   "Maturity of 3 vols are not the same");

        QL_REQUIRE(!domesticTS_.empty(), "domestic yield curve is not defined");

        QL_REQUIRE(!foreignTS_.empty(), "foreign yield curve is not defined");

        registerWith(atmVol_);

        registerWith(vol25Put_);

        registerWith(vol25Call_);

        registerWith(spotFX_);

        registerWith(domesticTS_);

        registerWith(foreignTS_);

    }

    void VannaVolgaBarrierEngine::calculate() const {

        QL_REQUIRE(arguments_.barrierType == Barrier::UpIn || arguments_.barrierType == Barrier::UpOut ||

            arguments_.barrierType == Barrier::DownIn || arguments_.barrierType == Barrier::DownOut,

            "Invalid barrier type");

        const Real sigmaShift_vega = 0.0001;

        const Real sigmaShift_volga = 0.0001;

        const Real spotShift_delta = 0.0001 * spotFX_->value();

        const Real sigmaShift_vanna = 0.0001;

        Handle<Quote> x0Quote(

            ext::make_shared<SimpleQuote>(spotFX_->value())); //used for shift

        Handle<Quote> atmVolQuote(

            ext::make_shared<SimpleQuote>(atmVol_->value())); //used for shift

        ext::shared_ptr<BlackVolTermStructure> blackVolTS =

            ext::make_shared<BlackConstantVol>(

                Settings::instance().evaluationDate(),

                NullCalendar(), atmVolQuote, Actual365Fixed());

        ext::shared_ptr<BlackScholesMertonProcess> stochProcess =

            ext::make_shared<BlackScholesMertonProcess>(

                                 x0Quote,

                                 foreignTS_,

                                 domesticTS_,

                                 Handle<BlackVolTermStructure>(blackVolTS));

        ext::shared_ptr<PricingEngine> engineBS =

            ext::make_shared<AnalyticBarrierEngine>(stochProcess);

        BlackDeltaCalculator blackDeltaCalculatorAtm(

                        Option::Call, atmVol_->deltaType(), x0Quote->value(),

                        domesticTS_->discount(T_), foreignTS_->discount(T_),

                        atmVol_->value() * sqrt(T_));

        Real atmStrike = blackDeltaCalculatorAtm.atmStrike(atmVol_->atmType());

        Real call25Vol = vol25Call_->value();

        Real put25Vol = vol25Put_->value();

        BlackDeltaCalculator blackDeltaCalculatorPut25(Option::Put, vol25Put_->deltaType(), x0Quote->value(), 

                                                      domesticTS_->discount(T_), foreignTS_->discount(T_),

                                                      put25Vol * sqrt(T_));

        Real put25Strike = blackDeltaCalculatorPut25.strikeFromDelta(-0.25);

        BlackDeltaCalculator blackDeltaCalculatorCall25(Option::Call, vol25Call_->deltaType(), x0Quote->value(), 

                                                      domesticTS_->discount(T_), foreignTS_->discount(T_),

                                                      call25Vol * sqrt(T_));

        Real call25Strike = blackDeltaCalculatorCall25.strikeFromDelta(0.25);

        //here use vanna volga interpolated smile to price vanilla

        std::vector<Real> strikes;

        std::vector<Real> vols;

        strikes.push_back(put25Strike);

        vols.push_back(put25Vol);

        strikes.push_back(atmStrike);

        vols.push_back(atmVol_->value());

        strikes.push_back(call25Strike);

        vols.push_back(call25Vol);

        VannaVolga vannaVolga(x0Quote->value(), domesticTS_->discount(T_), foreignTS_->discount(T_), T_);

        Interpolation interpolation = vannaVolga.interpolate(strikes.begin(), strikes.end(), vols.begin());

        interpolation.enableExtrapolation();

        const ext::shared_ptr<StrikedTypePayoff> payoff =

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

        Real strikeVol = interpolation(payoff->strike());

        //vanilla option price

        Real forward = x0Quote->value() * foreignTS_->discount(T_) / domesticTS_->discount(T_);

        Real vanillaOption = blackFormula(payoff->optionType(), payoff->strike(), 

                                      forward, 

                                      strikeVol * sqrt(T_),

                                      domesticTS_->discount(T_));

        results_.additionalResults["Forward"] = forward;

        results_.additionalResults["StrikeVol"] = strikeVol;

        //spot > barrier up&out 0

        if(x0Quote->value() >= arguments_.barrier && arguments_.barrierType == Barrier::UpOut){

            results_.value = 0.0;

            results_.additionalResults["VanillaPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;

            results_.additionalResults["BarrierInPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;

            results_.additionalResults["BarrierOutPrice"] = Real(0.0);

        }

        //spot > barrier up&in vanilla

        else if(x0Quote->value() >= arguments_.barrier && arguments_.barrierType == Barrier::UpIn){

            results_.value = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;

            results_.additionalResults["VanillaPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;

            results_.additionalResults["BarrierInPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;

            results_.additionalResults["BarrierOutPrice"] = Real(0.0);

        }

        //spot < barrier down&out 0

        else if(x0Quote->value() <= arguments_.barrier && arguments_.barrierType == Barrier::DownOut){

            results_.value = 0.0;

            results_.additionalResults["VanillaPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;

            results_.additionalResults["BarrierInPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;

            results_.additionalResults["BarrierOutPrice"] = Real(0.0);

        }

        //spot < barrier down&in vanilla

        else if(x0Quote->value() <= arguments_.barrier && arguments_.barrierType == Barrier::DownIn){

            results_.value = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;

            results_.additionalResults["VanillaPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;

            results_.additionalResults["BarrierInPrice"] = adaptVanDelta_? bsPriceWithSmile_ : vanillaOption;

            results_.additionalResults["BarrierOutPrice"] = Real(0.0);

        }

        else{

            //set up BS barrier option pricing

            //only calculate out barrier option price

            // in barrier price = vanilla - out barrier

            Barrier::Type barrierType;

            if(arguments_.barrierType == Barrier::UpOut)

                barrierType = arguments_.barrierType;

            else if(arguments_.barrierType == Barrier::UpIn)

                barrierType = Barrier::UpOut;

            else if(arguments_.barrierType == Barrier::DownOut)

                barrierType = arguments_.barrierType;

            else

                barrierType = Barrier::DownOut;

            BarrierOption barrierOption(barrierType,

                                        arguments_.barrier,

                                        arguments_.rebate,

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

                                        arguments_.exercise);

            barrierOption.setPricingEngine(engineBS);

            //BS price with atm vol

            Real priceBS = barrierOption.NPV();

            Real price25CallBS = blackFormula(Option::Call,call25Strike,

                                              forward, 

                                              atmVol_->value() * sqrt(T_),

                                              domesticTS_->discount(T_));

            Real price25PutBS = blackFormula(Option::Put,put25Strike,

                                              forward,

                                              atmVol_->value() * sqrt(T_),

                                              domesticTS_->discount(T_));

            //market price

            Real price25CallMkt = blackFormula(Option::Call,call25Strike,

                                              forward, 

                                              call25Vol * sqrt(T_),

                                              domesticTS_->discount(T_));

            Real price25PutMkt = blackFormula(Option::Put,put25Strike,

                                              forward,

                                              put25Vol * sqrt(T_),

                                              domesticTS_->discount(T_));

            //Analytical Black Scholes formula for vanilla option

            NormalDistribution norm;

            Real d1atm = (std::log(forward/atmStrike) 

                           + 0.5*std::pow(atmVolQuote->value(),2.0) * T_)/(atmVolQuote->value() * sqrt(T_));

            Real vegaAtm_Analytical = x0Quote->value() * norm(d1atm) * sqrt(T_) * foreignTS_->discount(T_);

            Real vannaAtm_Analytical = vegaAtm_Analytical/x0Quote->value() *(1.0 - d1atm/(atmVolQuote->value()*sqrt(T_)));

            Real volgaAtm_Analytical = vegaAtm_Analytical * d1atm * (d1atm - atmVolQuote->value() * sqrt(T_))/atmVolQuote->value();

            Real d125call = (std::log(forward/call25Strike) 

                           + 0.5*std::pow(atmVolQuote->value(),2.0) * T_)/(atmVolQuote->value() * sqrt(T_));

            Real vega25Call_Analytical = x0Quote->value() * norm(d125call) * sqrt(T_) * foreignTS_->discount(T_);

            Real vanna25Call_Analytical = vega25Call_Analytical/x0Quote->value() *(1.0 - d125call/(atmVolQuote->value()*sqrt(T_)));

            Real volga25Call_Analytical = vega25Call_Analytical * d125call * (d125call - atmVolQuote->value() * sqrt(T_))/atmVolQuote->value();

            Real d125Put = (std::log(forward/put25Strike) 

                           + 0.5*std::pow(atmVolQuote->value(),2.0) * T_)/(atmVolQuote->value() * sqrt(T_));

            Real vega25Put_Analytical = x0Quote->value() * norm(d125Put) * sqrt(T_) * foreignTS_->discount(T_);

            Real vanna25Put_Analytical = vega25Put_Analytical/x0Quote->value() *(1.0 - d125Put/(atmVolQuote->value()*sqrt(T_)));

            Real volga25Put_Analytical = vega25Put_Analytical * d125Put * (d125Put - atmVolQuote->value() * sqrt(T_))/atmVolQuote->value();

            //BS vega

            ext::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value() + sigmaShift_vega);

            barrierOption.recalculate();

            Real vegaBarBS = (barrierOption.NPV() - priceBS)/sigmaShift_vega;

            ext::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value() - sigmaShift_vega);//setback

            //BS volga

            //vegaBar2

            //base NPV

            ext::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value() + sigmaShift_volga);

            barrierOption.recalculate();

            Real priceBS2 = barrierOption.NPV();

            //shifted npv

            ext::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value() + sigmaShift_vega);

            barrierOption.recalculate();

            Real vegaBarBS2 = (barrierOption.NPV() - priceBS2)/sigmaShift_vega;

            Real volgaBarBS = (vegaBarBS2 - vegaBarBS)/sigmaShift_volga;

            ext::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value() 

                                                                                               - sigmaShift_volga 

                                                                                               - sigmaShift_vega);//setback

            //BS Delta

            //base delta

            ext::static_pointer_cast<SimpleQuote> (x0Quote.currentLink())->setValue(x0Quote->value() + spotShift_delta);//shift forth

            barrierOption.recalculate();

            Real priceBS_delta1 = barrierOption.NPV();

            ext::static_pointer_cast<SimpleQuote> (x0Quote.currentLink())->setValue(x0Quote->value() - 2 * spotShift_delta);//shift back

            barrierOption.recalculate();

            Real priceBS_delta2 = barrierOption.NPV();

            ext::static_pointer_cast<SimpleQuote> (x0Quote.currentLink())->setValue(x0Quote->value() +  spotShift_delta);//set back

            Real deltaBar1 = (priceBS_delta1 - priceBS_delta2)/(2.0*spotShift_delta);

            //shifted delta

            ext::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value() + sigmaShift_vanna);//shift sigma

            ext::static_pointer_cast<SimpleQuote> (x0Quote.currentLink())->setValue(x0Quote->value() + spotShift_delta);//shift forth

            barrierOption.recalculate();

            priceBS_delta1 = barrierOption.NPV();

            ext::static_pointer_cast<SimpleQuote> (x0Quote.currentLink())->setValue(x0Quote->value() - 2 * spotShift_delta);//shift back

            barrierOption.recalculate();

            priceBS_delta2 = barrierOption.NPV();

            ext::static_pointer_cast<SimpleQuote> (x0Quote.currentLink())->setValue(x0Quote->value() +  spotShift_delta);//set back

            Real deltaBar2 = (priceBS_delta1 - priceBS_delta2)/(2.0*spotShift_delta);

            Real vannaBarBS = (deltaBar2 - deltaBar1)/sigmaShift_vanna;

            ext::static_pointer_cast<SimpleQuote> (atmVolQuote.currentLink())->setValue(atmVolQuote->value() - sigmaShift_vanna);//set back

            //Matrix

            Matrix A(3,3,0.0);

            //analytical

            A[0][0] = vegaAtm_Analytical;

            A[0][1] = vega25Call_Analytical;

            A[0][2] = vega25Put_Analytical;

            A[1][0] = vannaAtm_Analytical;

            A[1][1] = vanna25Call_Analytical;

            A[1][2] = vanna25Put_Analytical;

            A[2][0] = volgaAtm_Analytical;

            A[2][1] = volga25Call_Analytical;

            A[2][2] = volga25Put_Analytical;

            Array b(3,0.0);

            b[0] = vegaBarBS;

            b[1] = vannaBarBS;

            b[2] = volgaBarBS;

            Array q = inverse(A) * b;

            //touch probability

            CumulativeNormalDistribution cnd;

            Real mu = domesticTS_->zeroRate(T_, Continuous).rate() - foreignTS_->zeroRate(T_, Continuous).rate() - pow(atmVol_->value(), 2.0)/2.0;

            Real h2 = (log(arguments_.barrier/x0Quote->value()) + mu*T_)/(atmVol_->value()*sqrt(T_));

            Real h2Prime = (log(x0Quote->value()/arguments_.barrier) + mu*T_)/(atmVol_->value()*sqrt(T_));

            Real probTouch = 0.0;

            if(arguments_.barrierType == Barrier::UpIn || arguments_.barrierType == Barrier::UpOut)

                probTouch = cnd(h2Prime) + pow(arguments_.barrier/x0Quote->value(), 2.0*mu/pow(atmVol_->value(), 2.0))*cnd(-h2);

            else

                probTouch = cnd(-h2Prime) + pow(arguments_.barrier/x0Quote->value(), 2.0*mu/pow(atmVol_->value(), 2.0))*cnd(h2);

            Real p_survival = 1.0 - probTouch;

            Real lambda = p_survival ;

            Real adjust = q[1]*(price25CallMkt - price25CallBS)

                        + q[2]*(price25PutMkt - price25PutBS);

            Real outPrice = priceBS + lambda*adjust;//

            Real inPrice;

            //adapt Vanilla delta

            if (adaptVanDelta_) {

                outPrice += lambda*(bsPriceWithSmile_ - vanillaOption);

                //capfloored by (0, vanilla)

                outPrice = std::max(0.0, std::min(bsPriceWithSmile_, outPrice));

                inPrice = bsPriceWithSmile_ - outPrice;

            }

            else{

                //capfloored by (0, vanilla)

                outPrice = std::max(0.0, std::min(vanillaOption, outPrice));

                inPrice = vanillaOption - outPrice;

            }

            if(arguments_.barrierType == Barrier::DownOut || arguments_.barrierType == Barrier::UpOut)

                results_.value = outPrice;

            else

                results_.value = inPrice;

            results_.additionalResults["VanillaPrice"] = vanillaOption;

            results_.additionalResults["BarrierInPrice"] = inPrice;

            results_.additionalResults["BarrierOutPrice"] = outPrice;

            results_.additionalResults["lambda"] = lambda;

         }

    }

}