StochasticProcess1D (3) - Linux Manuals

StochasticProcess1D: 1-dimensional stochastic process

NAME

QuantLib::StochasticProcess1D - 1-dimensional stochastic process

SYNOPSIS

#include <ql/stochasticprocess.hpp>

Inherits QuantLib::StochasticProcess.

Inherited by HelperProcess, ForwardMeasureProcess1D, GeneralizedBlackScholesProcess, GeometricBrownianMotionProcess, HullWhiteProcess, Merton76Process, OrnsteinUhlenbeckProcess, and SquareRootProcess.

Classes

class discretization
discretization of a 1-D stochastic process

Public Member Functions

1-D stochastic process interface

virtual Real x0 () const =0
returns the initial value of the state variable
virtual Real drift (Time t, Real x) const =0
returns the drift part of the equation, i.e. $ mu(t, x_t) $
virtual Real diffusion (Time t, Real x) const =0
returns the diffusion part of the equation, i.e. $ igma(t, x_t) $
virtual Real expectation (Time t0, Real x0, Time dt) const

virtual Real stdDeviation (Time t0, Real x0, Time dt) const

virtual Real variance (Time t0, Real x0, Time dt) const

virtual Real evolve (Time t0, Real x0, Time dt, Real dw) const

virtual Real apply (Real x0, Real dx) const

Protected Member Functions

StochasticProcess1D (const boost::shared_ptr< discretization > &)

Protected Attributes

boost::shared_ptr< discretization > discretization_

Detailed Description

1-dimensional stochastic process

This class describes a stochastic process governed by [ dx_t = mu(t, x_t)dt + igma(t, x_t)dW_t. ]

Member Function Documentation

virtual Real expectation (Time t0, Real x0, Time dt) const [virtual]

returns the expectation $ E(x_{t_0 + Delta t} | x_{t_0} = x_0) $ of the process after a time interval $ Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.

Reimplemented in HullWhiteProcess, HullWhiteForwardProcess, and OrnsteinUhlenbeckProcess.

virtual Real stdDeviation (Time t0, Real x0, Time dt) const [virtual]

returns the standard deviation $ S(x_{t_0 + Delta t} | x_{t_0} = x_0) $ of the process after a time interval $ Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.

Reimplemented in HullWhiteProcess, HullWhiteForwardProcess, and OrnsteinUhlenbeckProcess.

virtual Real variance (Time t0, Real x0, Time dt) const [virtual]

returns the variance $ V(x_{t_0 + Delta t} | x_{t_0} = x_0) $ of the process after a time interval $ Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.

Reimplemented in HullWhiteProcess, HullWhiteForwardProcess, and OrnsteinUhlenbeckProcess.

virtual Real evolve (Time t0, Real x0, Time dt, Real dw) const [virtual]

returns the asset value after a time interval $ Delta t $ according to the given discretization. By default, it returns [ E(x_0,t_0,Delta t) + S(x_0,t_0,Delta t) dot Delta w ] where $ E $ is the expectation and $ S $ the standard deviation.

Reimplemented in ExtendedBlackScholesMertonProcess.

virtual Real apply (Real x0, Real dx) const [virtual]

applies a change to the asset value. By default, it returns $ x + Delta x $.

Reimplemented in GeneralizedBlackScholesProcess, and Merton76Process.

Author

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