fdmsabrop.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2018 Klaus Spanderen
 
 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 fdmsabrop.hpp
    \brief FDM operator for the SABR model
*/
 
#ifndef quantlib_fdm_sabr_op_hpp
#define quantlib_fdm_sabr_op_hpp
 
#include <ql/methods/finitedifferences/operators/ninepointlinearop.hpp>
#include <ql/methods/finitedifferences/operators/triplebandlinearop.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearopcomposite.hpp>
 
namespace QuantLib {
 
    //! SABR model with absorbing boundary at f=0
    /*! \f[
         df_t = \alpha_t f_t^\beta \mathrm{d}W_t  \\
         d\alpha_t = \nu \alpha_t \mathrm{d}Z_t \\
         \rho \mathrm{d}t = < \mathrm{d}W_t, \mathrm{d}Z_t >
        \f]
    */
 
 
    class FdmMesher;
    class YieldTermStructure;
 
    class FdmSabrOp : public FdmLinearOpComposite {
      public:
        FdmSabrOp(const ext::shared_ptr<FdmMesher>& mesher,
                  ext::shared_ptr<YieldTermStructure> rTS,
                  Real f0,
                  Real alpha,
                  Real beta,
                  Real nu,
                  Real rho);
 
        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 ext::shared_ptr<YieldTermStructure> rTS_;
 
        const TripleBandLinearOp dffMap_;
        const TripleBandLinearOp dxMap_, dxxMap_;
        const NinePointLinearOp correlationMap_;
 
        TripleBandLinearOp mapF_, mapA_;
    };
}
 
#endif