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

/*

 Copyright (C) 2006, 2007 Ferdinando Ametrano

 Copyright (C) 2006 Cristina Duminuco

 Copyright (C) 2005, 2006 Klaus Spanderen

 Copyright (C) 2007 Giorgio Facchinetti

 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/termstructures/volatility/abcd.hpp>

#include <ql/math/comparison.hpp>

#include <algorithm>

namespace QuantLib {

    AbcdFunction::AbcdFunction(Real a, Real b, Real c, Real d)

    : AbcdMathFunction(a, b, c, d) {}

    Real AbcdFunction::volatility(Time tMin, Time tMax, Time T) const {

        if (tMax==tMin)

            return instantaneousVolatility(tMax, T);

        QL_REQUIRE(tMax>tMin, "tMax must be > tMin");

        return std::sqrt(variance(tMin, tMax, T)/(tMax-tMin));

    }

    Real AbcdFunction::variance(Time tMin, Time tMax, Time T) const {

        return covariance(tMin, tMax, T, T);

    }

    Real AbcdFunction::covariance(Time t, Time T, Time S) const {

        return (*this)(T-t) * (*this)(S-t);

    }

    Real AbcdFunction::covariance(Time t1, Time t2, Time T, Time S) const {

        QL_REQUIRE(t1<=t2,

                   "integrations bounds (" << t1 <<

                   "," << t2 << ") are in reverse order");

        Time cutOff = std::min(S,T);

        if (t1>=cutOff) {

            return 0.0;

        } else {

            cutOff = std::min(t2, cutOff);

            return primitive(cutOff, T, S) - primitive(t1, T, S);

        }

    }

    // INSTANTANEOUS

    Real AbcdFunction::instantaneousVolatility(Time u, Time T) const {

        return std::sqrt(instantaneousVariance(u, T));

    }

    Real AbcdFunction::instantaneousVariance(Time u, Time T) const {

        return instantaneousCovariance(u, T, T);

    }

    Real AbcdFunction::instantaneousCovariance(Time u, Time T, Time S) const {

        return (*this)(T-u)*(*this)(S-u);

    }

    // PRIMITIVE

    Real AbcdFunction::primitive(Time t, Time T, Time S) const {

        if (T<t || S<t) return 0.0;

        if (close(c_,0.0)) {

            Real v = a_+d_;

            return t*(v*v+v*b_*S+v*b_*T-v*b_*t+b_*b_*S*T-0.5*b_*b_*t*(S+T)+b_*b_*t*t/3.0);

        }

        Real k1=std::exp(c_*t), k2=std::exp(c_*S), k3=std::exp(c_*T);

        return (b_*b_*(-1 - 2*c_*c_*S*T - c_*(S + T)

                     + k1*k1*(1 + c_*(S + T - 2*t) + 2*c_*c_*(S - t)*(T - t)))

                + 2*c_*c_*(2*d_*a_*(k2 + k3)*(k1 - 1)

                         +a_*a_*(k1*k1 - 1)+2*c_*d_*d_*k2*k3*t)

                + 2*b_*c_*(a_*(-1 - c_*(S + T) + k1*k1*(1 + c_*(S + T - 2*t)))

                         -2*d_*(k3*(1 + c_*S) + k2*(1 + c_*T)

                               - k1*k3*(1 + c_*(S - t))

                               - k1*k2*(1 + c_*(T - t)))

                         )

                ) / (4*c_*c_*c_*k2*k3);

    }

//===========================================================================//

//                               AbcdSquared                                //

//===========================================================================//

    AbcdSquared::AbcdSquared(Real a, Real b, Real c, Real d, Time T, Time S)

    : abcd_(new AbcdFunction(a,b,c,d)),

      T_(T), S_(S) {}

    Real AbcdSquared::operator()(Time t) const {

        return abcd_->covariance(t, T_, S_);

    }

}