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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
<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 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
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