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

/*

Copyright (C) 2018 Sebastian Schlenkrich

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

<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.

*/

/*! \file tenoroptionletvts.hpp

    \brief caplet volatility term structure based on volatility transformation

*/

#ifndef quantlib_tenoroptionletvts_hpp

#define quantlib_tenoroptionletvts_hpp

#include <ql/indexes/iborindex.hpp>

#include <ql/math/interpolation.hpp>

#include <ql/termstructures/volatility/optionlet/optionletvolatilitystructure.hpp>

#include <ql/termstructures/volatility/smilesection.hpp>

#include <ql/time/dategenerationrule.hpp>

#include <utility>

namespace QuantLib {

    class TenorOptionletVTS : public OptionletVolatilityStructure {

      public:

        class CorrelationStructure; // declaration below

      protected:

        class TenorOptionletSmileSection : public SmileSection {

          protected:

            ext::shared_ptr<CorrelationStructure> correlation_;

            std::vector<ext::shared_ptr<SmileSection> > baseSmileSection_;

            std::vector<Time> startTimeBase_; // for correlation parametrisation

            std::vector<Real> fraRateBase_;

            Real fraRateTarg_;

            std::vector<Real> v_;

            // implement transformation formula

            Volatility volatilityImpl(Rate strike) const override;

          public:

            // constructor includes actual transformation details

            TenorOptionletSmileSection(const TenorOptionletVTS& volTS, Time optionTime);

            // further SmileSection interface methods

            Real minStrike() const override {

                return baseSmileSection_[0]->minStrike() + fraRateTarg_ - fraRateBase_[0];

            }

            Real maxStrike() const override {

                return baseSmileSection_[0]->maxStrike() + fraRateTarg_ - fraRateBase_[0];

            }

            Real atmLevel() const override { return fraRateTarg_; }

        };

        Handle<OptionletVolatilityStructure> baseVTS_;

        ext::shared_ptr<IborIndex> baseIndex_;

        ext::shared_ptr<IborIndex> targIndex_;

        ext::shared_ptr<CorrelationStructure> correlation_;

      public:

        // functor interface for parametric correlation

        class CorrelationStructure {

          public:

            // return the correlation between two FRA rates starting at start1 and start2

            virtual Real operator()(const Time& start1, const Time& start2) const = 0;

            virtual ~CorrelationStructure() = default;

            ;

        };

        // very basic choice for correlation structure

        class TwoParameterCorrelation : public CorrelationStructure {

          protected:

            ext::shared_ptr<Interpolation> rhoInf_;

            ext::shared_ptr<Interpolation> beta_;

          public:

            TwoParameterCorrelation(ext::shared_ptr<Interpolation> rhoInf,

                                    ext::shared_ptr<Interpolation> beta)

            : rhoInf_(std::move(rhoInf)), beta_(std::move(beta)) {}

            Real operator()(const Time& start1, const Time& start2) const override {

                Real rhoInf = (*rhoInf_)(start1);

                Real beta = (*beta_)(start1);

                Real rho = rhoInf + (1.0 - rhoInf) * exp(-beta * fabs(start2 - start1));

                return rho;

            }

        };

        // constructor

        TenorOptionletVTS(const Handle<OptionletVolatilityStructure>& baseVTS,

                          ext::shared_ptr<IborIndex> baseIndex,

                          ext::shared_ptr<IborIndex> targIndex,

                          ext::shared_ptr<CorrelationStructure> correlation);

        // Termstructure interface

        //! the latest date for which the curve can return values

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

        // VolatilityTermstructure interface

        //! implements the actual smile calculation in derived classes

        ext::shared_ptr<SmileSection> smileSectionImpl(Time optionTime) const override {

            return ext::shared_ptr<SmileSection>(new TenorOptionletSmileSection(*this, optionTime));

        }

        //! implements the actual volatility calculation in derived classes

        Volatility volatilityImpl(Time optionTime, Rate strike) const override {

            return smileSection(optionTime)->volatility(strike);

        }

        //! the minimum strike for which the term structure can return vols

        Rate minStrike() const override { return baseVTS_->minStrike(); }

        //! the maximum strike for which the term structure can return vols

        Rate maxStrike() const override { return baseVTS_->maxStrike(); }

        // the methodology is designed for normal volatilities

        VolatilityType volatilityType() const override { return Normal; }

    };

    typedef TenorOptionletVTS::CorrelationStructure TenorOptionletVTSCorrelationStructure;

}

#endif