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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2014 Peter Caspers
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 zabr.hpp
\brief ZABR functions
Reference: Andreasen, Huge: ZABR - Expansions for the masses, Preliminary
Version, December 2011, http://ssrn.com/abstract=1980726
*/
#ifndef quantlib_zabr_hpp
#define quantlib_zabr_hpp
#include <ql/types.hpp>
#include <ql/math/statistics/incrementalstatistics.hpp>
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <ql/math/interpolations/cubicinterpolation.hpp>
#include <ql/math/interpolations/bicubicsplineinterpolation.hpp>
#include <vector>
namespace QuantLib {
class ZabrModel {
public:
ZabrModel(Real expiryTime, Real forward, Real alpha, Real beta, Real nu, Real rho, Real gamma);
Real localVolatility(Real f) const;
std::vector<Real> localVolatility(const std::vector<Real> &f) const;
Real fdPrice(Real strike) const;
std::vector<Real> fdPrice(const std::vector<Real> &strikes) const;
Real fullFdPrice(Real strike) const;
Real lognormalVolatility(Real strike) const;
std::vector<Real> lognormalVolatility(const std::vector<Real> &strikes) const;
Real normalVolatility(Real strike) const;
std::vector<Real> normalVolatility(const std::vector<Real> &strikes) const;
Real forward() const { return forward_; }
Real expiryTime() const { return expiryTime_; }
Real alpha() const { return alpha_; }
Real beta() const { return beta_; }
Real nu() const { return nu_; }
Real rho() const { return rho_; }
Real gamma() const { return gamma_; }
private:
const Real expiryTime_, forward_;
const Real alpha_, beta_, nu_, rho_,
gamma_; // nu_ here is a tranformed version of the input nu !
Real x(Real strike) const;
std::vector<Real> x(const std::vector<Real> &strikes) const;
Real y(Real strike) const;
Real F(Real y, Real u) const;
Real lognormalVolatilityHelper(Real strike, Real x) const;
Real normalVolatilityHelper(Real strike, Real x) const;
Real localVolatilityHelper(Real f, Real x) const;
};
}
#endif
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