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

/*

 Copyright (C) 2011, 2012, 2013, 2023 Andre Miemiec

 Copyright (C) 2012 Samuel Tebege

 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/cashflows/cashflows.hpp>

#include <ql/cashflows/couponpricer.hpp>

#include <ql/exercise.hpp>

#include <ql/experimental/swaptions/haganirregularswaptionengine.hpp>

#include <ql/instruments/swaption.hpp>

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

#include <ql/math/interpolations/linearinterpolation.hpp>

#include <ql/math/matrixutilities/svd.hpp>

#include <ql/math/solvers1d/bisection.hpp>

#include <ql/math/solvers1d/brent.hpp>

#include <ql/pricingengines/swap/discountingswapengine.hpp>

#include <ql/pricingengines/swaption/blackswaptionengine.hpp>

#include <utility>

namespace QuantLib {

    //////////////////////////////////////////////////////////////////////////

    // Implementation of helper class HaganIrregularSwaptionEngine::Basket  //

    //////////////////////////////////////////////////////////////////////////

    HaganIrregularSwaptionEngine::Basket::Basket(

        ext::shared_ptr<IrregularSwap> swap,

        Handle<YieldTermStructure> termStructure,

        Handle<SwaptionVolatilityStructure> volatilityStructure)

    : swap_(std::move(swap)), termStructure_(std::move(termStructure)),

      volatilityStructure_(std::move(volatilityStructure)) {

        engine_ = ext::shared_ptr<PricingEngine>(new DiscountingSwapEngine(termStructure_));

        // store swap npv

        swap_->setPricingEngine(engine_);

        targetNPV_ = swap_->NPV();

        // build standard swaps

        const Leg& fixedLeg = swap_->fixedLeg();

        const Leg& floatLeg = swap_->floatingLeg();

        Leg fixedCFS, floatCFS;

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

            // retrieve fixed rate coupon from fixed leg

            ext::shared_ptr<FixedRateCoupon> coupon =

                ext::dynamic_pointer_cast<FixedRateCoupon>(fixedLeg[i]);

            QL_REQUIRE(coupon, "dynamic cast of fixed leg coupon failed.");

            expiries_.push_back(coupon->date());

            ext::shared_ptr<FixedRateCoupon> newCpn = ext::make_shared<FixedRateCoupon>(

                coupon->date(), 1.0, coupon->rate(), coupon->dayCounter(),

                coupon->accrualStartDate(), coupon->accrualEndDate(),

                coupon->referencePeriodStart(), coupon->referencePeriodEnd());

            fixedCFS.push_back(newCpn);

            annuities_.push_back(10000 * CashFlows::bps(fixedCFS, **termStructure_, true));

            floatCFS.clear();

            for (const auto& j : floatLeg) {

                // retrieve ibor coupon from floating leg

                ext::shared_ptr<IborCoupon> coupon = ext::dynamic_pointer_cast<IborCoupon>(j);

                QL_REQUIRE(coupon, "dynamic cast of float leg coupon failed.");

                if (coupon->date() <= expiries_[i]) {

                    ext::shared_ptr<IborCoupon> newCpn = ext::make_shared<IborCoupon>(

                        coupon->date(), 1.0, coupon->accrualStartDate(), coupon->accrualEndDate(),

                        coupon->fixingDays(), coupon->iborIndex(), 1.0, coupon->spread(),

                        coupon->referencePeriodStart(), coupon->referencePeriodEnd(),

                        coupon->dayCounter(), coupon->isInArrears());

                    if (!newCpn->isInArrears())

                        newCpn->setPricer(

                            ext::shared_ptr<FloatingRateCouponPricer>(new BlackIborCouponPricer()));

                    floatCFS.push_back(newCpn);

                }

            }

            Real floatLegNPV = CashFlows::npv(floatCFS, **termStructure_, true);

            fairRates_.push_back(floatLegNPV / annuities_[i]);

        }

    }

    // computes a replication of the swap in terms of a basket of vanilla swaps

    // by solving a linear system of equation

    Array HaganIrregularSwaptionEngine::Basket::compute(Rate lambda) const {

        // update members

        lambda_ = lambda;

        Size n = swap_->fixedLeg().size();

        // build linear system of equations

        Matrix arr(n, n, 0.0);

        Array rhs(n);

        // fill the matrix describing the linear system of equations by looping over rows

        for (Size r = 0; r < n; ++r) {

            ext::shared_ptr<FixedRateCoupon> cpn_r =

                ext::dynamic_pointer_cast<FixedRateCoupon>(swap_->fixedLeg()[r]);

            QL_REQUIRE(cpn_r, "Cast to fixed rate coupon failed.");

            // looping over columns

            for (Size c = r; c < n; ++c) {

                // set homogenous part of lse

                arr[r][c] = (fairRates_[c] + lambda_) * cpn_r->accrualPeriod();

            }

            // add nominal repayment for i-th swap

            arr[r][r] += 1;

        }

        for (Size r = 0; r < n; ++r) {

            ext::shared_ptr<FixedRateCoupon> cpn_r =

                ext::dynamic_pointer_cast<FixedRateCoupon>(swap_->fixedLeg()[r]);

            // set inhomogenity of lse

            Real N_r = cpn_r->nominal();

            if (r < n - 1) {

                ext::shared_ptr<FixedRateCoupon> cpn_rp1 =

                    ext::dynamic_pointer_cast<FixedRateCoupon>(swap_->fixedLeg()[r + 1]);

                Real N_rp1 = cpn_rp1->nominal();

                rhs[r] = N_r * (cpn_r->rate()) * cpn_r->accrualPeriod() + (N_r - N_rp1);

            } else {

                rhs[r] = N_r * (cpn_r->rate()) * cpn_r->accrualPeriod() + N_r;

            }

        }

        SVD svd(arr);

        return svd.solveFor(rhs);

    }

    Real HaganIrregularSwaptionEngine::Basket::operator()(Rate lambda) const {

        Array weights = compute(lambda);

        Real defect = -targetNPV_;

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

            defect -= Integer(swap_->type()) * lambda * weights[i] * annuities_[i];

        return defect;

    }

    // creates a standard swap by deducing its conventions from market data objects

    ext::shared_ptr<VanillaSwap> HaganIrregularSwaptionEngine::Basket::component(Size i) const {

        ext::shared_ptr<IborCoupon> iborCpn =

            ext::dynamic_pointer_cast<IborCoupon>(swap_->floatingLeg()[0]);

        QL_REQUIRE(iborCpn, "dynamic cast of float leg coupon failed. Can't find index.");

        ext::shared_ptr<IborIndex> iborIndex = iborCpn->iborIndex();

        Period dummySwapLength = Period(1, Years);

        ext::shared_ptr<VanillaSwap> memberSwap_ =

            MakeVanillaSwap(dummySwapLength, iborIndex)

                .withType(swap_->type())

                .withEffectiveDate(swap_->startDate())

                .withTerminationDate(expiries_[i])

                .withRule(DateGeneration::Backward)

                .withDiscountingTermStructure(termStructure_);

        Real stdAnnuity = 10000 * CashFlows::bps(memberSwap_->fixedLeg(), **termStructure_, true);

        // compute annuity transformed rate

        Rate transformedRate = (fairRates_[i] + lambda_) * annuities_[i] / stdAnnuity;

        memberSwap_ = MakeVanillaSwap(dummySwapLength, iborIndex, transformedRate)

                          .withType(swap_->type())

                          .withEffectiveDate(swap_->startDate())

                          .withTerminationDate(expiries_[i])

                          .withRule(DateGeneration::Backward)

                          .withDiscountingTermStructure(termStructure_);

        return memberSwap_;

    }

    ///////////////////////////////////////////////////////////

    // Implementation of class HaganIrregularSwaptionEngine  //

    ///////////////////////////////////////////////////////////

    HaganIrregularSwaptionEngine::HaganIrregularSwaptionEngine(

        Handle<SwaptionVolatilityStructure> volatilityStructure,

        Handle<YieldTermStructure> termStructure)

    : termStructure_(std::move(termStructure)),

      volatilityStructure_(std::move(volatilityStructure)) {

        registerWith(termStructure_);

        registerWith(volatilityStructure_);

    }

    void HaganIrregularSwaptionEngine::calculate() const {

        // check exercise type

        ext::shared_ptr<Exercise> exercise_ = this->arguments_.exercise;

        QL_REQUIRE(exercise_->type() == QuantLib::Exercise::European, "swaption must be european");

        // extract the underlying irregular swap

        ext::shared_ptr<IrregularSwap> swap_ = this->arguments_.swap;

        // Reshuffle spread from float to fixed (, i.e. remove spread from float side by finding the

        // adjusted fixed coupon such that the NPV of the swap stays constant).

        Leg fixedLeg = swap_->fixedLeg();

        Real fxdLgBPS = CashFlows::bps(fixedLeg, **termStructure_, true);

        Leg floatLeg = swap_->floatingLeg();

        Real fltLgNPV = CashFlows::npv(floatLeg, **termStructure_, true);

        Real fltLgBPS = CashFlows::bps(floatLeg, **termStructure_, true);

        Leg floatCFS, fixedCFS;

        floatCFS.clear();

        for (auto& j : floatLeg) {

            // retrieve ibor coupon from floating leg

            ext::shared_ptr<IborCoupon> coupon = ext::dynamic_pointer_cast<IborCoupon>(j);

            QL_REQUIRE(coupon, "dynamic cast of float leg coupon failed.");

            ext::shared_ptr<IborCoupon> newCpn = ext::make_shared<IborCoupon>(

                coupon->date(), coupon->nominal(), coupon->accrualStartDate(),

                coupon->accrualEndDate(), coupon->fixingDays(), coupon->iborIndex(),

                coupon->gearing(), 0.0, coupon->referencePeriodStart(),

                coupon->referencePeriodEnd(), coupon->dayCounter(), coupon->isInArrears());

            if (!newCpn->isInArrears())

                newCpn->setPricer(

                    ext::shared_ptr<FloatingRateCouponPricer>(new BlackIborCouponPricer()));

            floatCFS.push_back(newCpn);

        }

        Real sprdLgNPV = fltLgNPV - CashFlows::npv(floatCFS, **termStructure_, true);

        Rate avgSpread = sprdLgNPV / fltLgBPS / 10000;

        Rate cpn_adjustment = avgSpread * fltLgBPS / fxdLgBPS;

        fixedCFS.clear();

        for (auto& i : fixedLeg) {

            // retrieve fixed rate coupon from fixed leg

            ext::shared_ptr<FixedRateCoupon> coupon = ext::dynamic_pointer_cast<FixedRateCoupon>(i);

            QL_REQUIRE(coupon, "dynamic cast of fixed leg coupon failed.");

            ext::shared_ptr<FixedRateCoupon> newCpn = ext::make_shared<FixedRateCoupon>(

                coupon->date(), coupon->nominal(), coupon->rate() - cpn_adjustment,

                coupon->dayCounter(), coupon->accrualStartDate(), coupon->accrualEndDate(),

                coupon->referencePeriodStart(), coupon->referencePeriodEnd());

            fixedCFS.push_back(newCpn);

        }

        // this is the irregular swap with spread removed

        swap_ = ext::make_shared<IrregularSwap>(arguments_.swap->type(), fixedCFS, floatCFS);

        // Sets up the basket by implementing the methodology described in

        // P.S.Hagan "Callable Swaps and Bermudan 'Exercise into Swaptions'"

        Basket basket(swap_, termStructure_, volatilityStructure_);

        ///////////////////////////////////////////////////////////////////////////////////////////////////

        // find lambda //

        ///////////////////////////////////////////////////////////////////////////////////////////////////

        Bisection s1d;

        Rate minLambda = -0.5;

        Rate maxLambda = 0.5;

        s1d.setMaxEvaluations(10000);

        s1d.setLowerBound(minLambda);

        s1d.setUpperBound(maxLambda);

        s1d.solve(basket, 1.0e-8, 0.01, minLambda, maxLambda);

        /////////////////////////////////////////////////////////////////////////////////////////////////

        //  compute the price of the irreg swaption as the sum of the prices of the regular

        //  swaptions  //

        /////////////////////////////////////////////////////////////////////////////////////////////////

        results_.value = HKPrice(basket, exercise_);

    }

    /////////////////////////////////////////////////////////////////////////////////////////

    // Computes irregular swaption price according to P.J. Hunt, J.E. Kennedy:             //

    // "Implied interest rate pricing models", Finance Stochast. 2, 275-293 (1998)         //

    /////////////////////////////////////////////////////////////////////////////////////////

    Real HaganIrregularSwaptionEngine::HKPrice(Basket& basket,

                                               ext::shared_ptr<Exercise>& exercise) const {

        // Swaption Engine: assumes that the swaptions exercise date equals the swap start date

        QL_REQUIRE((volatilityStructure_->volatilityType() == Normal),

                   "swaptionEngine: only normal volatility implemented.");

        ext::shared_ptr<PricingEngine> swaptionEngine = ext::shared_ptr<PricingEngine>(

            new BachelierSwaptionEngine(termStructure_, volatilityStructure_));

        // retrieve weights of underlying swaps

        Array weights = basket.weights();

        Real npv = 0.0;

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

            ext::shared_ptr<VanillaSwap> pvSwap_ = basket.component(i);

            Swaption swaption = Swaption(pvSwap_, exercise);

            swaption.setPricingEngine(swaptionEngine);

            npv += weights[i] * swaption.NPV();

        }

        return npv;

    }

}