CoxIngersollRossProcess Class Reference

CoxIngersollRoss process class. More...

#include <ql/processes/coxingersollrossprocess.hpp>

Inheritance diagram for CoxIngersollRossProcess:

Public Member Functions
	CoxIngersollRossProcess (Real speed, Volatility vol, Real x0=0.0, Real level=0.0)
Real	drift (Time t, Real x) const override
	returns the drift part of the equation, i.e. \( \mu(t, x_t) \)
Real	diffusion (Time t, Real x) const override
	returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \)
Real	expectation (Time t0, Real x0, Time dt) const override
Real	stdDeviation (Time t0, Real x0, Time dt) const override
Real	x0 () const override
	returns the initial value of the state variable
Real	speed () const
Real	volatility () const
Real	level () const
Real	variance (Time t0, Real x0, Time dt) const override
Real	evolve (Time t0, Real x0, Time dt, Real dw) const override
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 () override
Public Member Functions inherited from Observer
	Observer (const Observer &)
Observer &	operator= (const Observer &)
std::pair< iterator, bool >	registerWith (const ext::shared_ptr< Observable > &)
void	registerWithObservables (const ext::shared_ptr< Observer > &)
Size	unregisterWith (const ext::shared_ptr< Observable > &)
void	unregisterWithAll ()
virtual void	deepUpdate ()
Public Member Functions inherited from Observable
	Observable (const Observable &)
Observable &	operator= (const Observable &)
	Observable (Observable &&)=delete
Observable &	operator= (Observable &&)=delete
void	notifyObservers ()

Additional Inherited Members
Public Types inherited from Observer
typedef set_type::iterator	iterator
	StochasticProcess1D (ext::shared_ptr< discretization >)
	StochasticProcess (ext::shared_ptr< discretization >)
ext::shared_ptr< discretization >	discretization_
ext::shared_ptr< discretization >	discretization_

Detailed Description

CoxIngersollRoss process class.

This class describes the CoxIngersollRoss process governed by

\[ dx(t) = k (\theta - x(t)) dt + \sigma \sqrt{x(t)} dW(t). \]

The process is discretized using the Quadratic Exponential scheme. For details see Leif Andersen, Efficient Simulation of the Heston Stochastic Volatility Model.

Member Function Documentation

drift()

Real drift ( Time t, Real x ) const

overridevirtual

returns the drift part of the equation, i.e. \( \mu(t, x_t) \)

Implements StochasticProcess1D.

diffusion()

Real diffusion ( Time t, Real x ) const

overridevirtual

returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \)

Implements StochasticProcess1D.

expectation()

Real expectation ( Time t0, Real x0, Time dt ) const

overridevirtual

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 from StochasticProcess1D.

stdDeviation()

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

overridevirtual

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 from StochasticProcess1D.

x0()

Real x0 ( ) const

overridevirtual

returns the initial value of the state variable

Implements StochasticProcess1D.

variance()

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

overridevirtual

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 from StochasticProcess1D.

evolve()

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

overridevirtual

returns the asset value after a time interval \( \Delta t \) according to the given discretization. By default, it returns

\[E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w \]

where \( E \) is the expectation and \( S \) the standard deviation.

Reimplemented from StochasticProcess1D.