fdmzabrop.hpp

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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
 <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 fdmzabrop.hpp
    \brief Zabr linear pricing operator
*/
 
#ifndef quantlib_fdm_zabr_op_hpp
#define quantlib_fdm_zabr_op_hpp
 
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/firstderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/triplebandlinearop.hpp>
#include <ql/methods/finitedifferences/operators/ninepointlinearop.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearopcomposite.hpp>
 
namespace QuantLib {
 
class FdmZabrUnderlyingPart {
  public:
    FdmZabrUnderlyingPart(
        const ext::shared_ptr<FdmMesher>& mesher, Real beta, Real nu, Real rho, Real gamma);
 
    void setTime(Time t1, Time t2);
    const TripleBandLinearOp &getMap() const;
 
  protected:
    const Array volatilityValues_;
    const Array forwardValues_;
    TripleBandLinearOp mapT_;
 
    const ext::shared_ptr<FdmMesher> mesher_;
};
 
class FdmZabrVolatilityPart {
  public:
    FdmZabrVolatilityPart(
        const ext::shared_ptr<FdmMesher>& mesher, Real beta, Real nu, Real rho, Real gamma);
 
    void setTime(Time t1, Time t2);
    const TripleBandLinearOp &getMap() const;
 
  protected:
    const Array volatilityValues_;
    const Array forwardValues_;
    TripleBandLinearOp mapT_;
 
    const ext::shared_ptr<FdmMesher> mesher_;
};
 
class FdmZabrOp : public FdmLinearOpComposite {
  public:
    FdmZabrOp(const ext::shared_ptr<FdmMesher>& mesher,
              Real beta,
              Real nu,
              Real rho,
              Real gamma = 1.0); // gamma=1.0 recovers the classic sabr model
 
    Size size() const override;
    void setTime(Time t1, Time t2) override;
 
    Array apply(const Array& r) const override;
    Array apply_mixed(const Array& r) const override;
 
    Array apply_direction(Size direction, const Array& r) const override;
    Array solve_splitting(Size direction, const Array& r, Real s) const override;
    Array preconditioner(const Array& r, Real s) const override;
 
    std::vector<SparseMatrix> toMatrixDecomp() const override;
 
  private:
    const Array volatilityValues_;
    const Array forwardValues_;
    NinePointLinearOp dxyMap_;
    FdmZabrUnderlyingPart dxMap_;
    FdmZabrVolatilityPart dyMap_;
};
}
 
#endif