eulerdiscretization.hpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2004, 2005 StatPro Italia srl
 
 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 eulerdiscretization.hpp
    \brief Euler discretization for stochastic processes
*/
 
#ifndef quantlib_euler_discretization_hpp
#define quantlib_euler_discretization_hpp
 
#include <ql/stochasticprocess.hpp>
 
namespace QuantLib {
 
    //! Euler discretization for stochastic processes
    /*! \ingroup processes */
    class EulerDiscretization
        : public StochasticProcess::discretization,
          public StochasticProcess1D::discretization {
      public:
 
        /*! Returns an approximation of the drift defined as
            \f$ \mu(t_0, \mathbf{x}_0) \Delta t \f$.
        */
        Array drift(const StochasticProcess&, Time t0, const Array& x0, Time dt) const override;
        /*! Returns an approximation of the drift defined as
            \f$ \mu(t_0, x_0) \Delta t \f$.
        */
        Real drift(const StochasticProcess1D&, Time t0, Real x0, Time dt) const override;
 
        /*! Returns an approximation of the diffusion defined as
            \f$ \sigma(t_0, \mathbf{x}_0) \sqrt{\Delta t} \f$.
        */
        Matrix diffusion(const StochasticProcess&, Time t0, const Array& x0, Time dt) const override;
        /*! Returns an approximation of the diffusion defined as
            \f$ \sigma(t_0, x_0) \sqrt{\Delta t} \f$.
        */
        Real diffusion(const StochasticProcess1D&, Time t0, Real x0, Time dt) const override;
 
        /*! Returns an approximation of the covariance defined as
            \f$ \sigma(t_0, \mathbf{x}_0)^2 \Delta t \f$.
        */
        Matrix covariance(const StochasticProcess&, Time t0, const Array& x0, Time dt) const override;
        /*! Returns an approximation of the variance defined as
            \f$ \sigma(t_0, x_0)^2 \Delta t \f$.
        */
        Real variance(const StochasticProcess1D&, Time t0, Real x0, Time dt) const override;
    };
 
}
 
 
#endif