1-dimensional stochastic process More...

#include <ql/stochasticprocess.hpp>

Inheritance diagram for StochasticProcess1D:

Classes
class	discretization
	discretization of a 1-D stochastic process More...

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. $\sigma(t, x_t)$

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

Public Member Functions inherited from StochasticProcess
virtual Size	factors () const
	returns the number of independent factors of the process

virtual Time	time (const Date &) const

void	update ()

Public Member Functions inherited from Observer
	Observer (const Observer &)

Observer &	operator= (const Observer &)

std::pair< std::set < boost::shared_ptr < Observable > >::iterator, bool >	registerWith (const boost::shared_ptr< Observable > &)

Size	unregisterWith (const boost::shared_ptr< Observable > &)

void	unregisterWithAll ()

Public Member Functions inherited from Observable
	Observable (const Observable &)

Observable &	operator= (const Observable &)

void	notifyObservers ()

Protected Member Functions
	StochasticProcess1D (const boost::shared_ptr< discretization > &)

Protected Member Functions inherited from StochasticProcess
	StochasticProcess (const boost::shared_ptr< discretization > &)

Protected Attributes
boost::shared_ptr< discretization >	discretization_

Protected Attributes inherited from StochasticProcess
boost::shared_ptr< discretization >	discretization_

Detailed Description

1-dimensional stochastic process

This class describes a stochastic process governed by

$dx_t = \mu(t, x_t)dt + \sigma(t, x_t)dW_t.$

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 HullWhiteForwardProcess, GeneralizedBlackScholesProcess, ExtendedOrnsteinUhlenbeckProcess, GeneralizedOrnsteinUhlenbeckProcess, OrnsteinUhlenbeckProcess, and HullWhiteProcess.

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 HullWhiteForwardProcess, ExtendedOrnsteinUhlenbeckProcess, GemanRoncoroniProcess, GeneralizedOrnsteinUhlenbeckProcess, OrnsteinUhlenbeckProcess, and HullWhiteProcess.

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.