HestonProcess Class Reference

Square-root stochastic-volatility Heston process. More...

#include <ql/processes/hestonprocess.hpp>

Inheritance diagram for HestonProcess:

Public Types
enum	Discretization {   PartialTruncation , FullTruncation , Reflection , NonCentralChiSquareVariance ,   QuadraticExponential , QuadraticExponentialMartingale , BroadieKayaExactSchemeLobatto , BroadieKayaExactSchemeLaguerre ,   BroadieKayaExactSchemeTrapezoidal }
Public Types inherited from Observer
typedef set_type::iterator	iterator

Public Member Functions
	HestonProcess (Handle< YieldTermStructure > riskFreeRate, Handle< YieldTermStructure > dividendYield, Handle< Quote > s0, Real v0, Real kappa, Real theta, Real sigma, Real rho, Discretization d=QuadraticExponentialMartingale)
Size	size () const override
	returns the number of dimensions of the stochastic process
Size	factors () const override
	returns the number of independent factors of the process
Array	initialValues () const override
	returns the initial values of the state variables
Array	drift (Time t, const Array &x) const override
	returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)
Matrix	diffusion (Time t, const Array &x) const override
	returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \)
Array	apply (const Array &x0, const Array &dx) const override
Array	evolve (Time t0, const Array &x0, Time dt, const Array &dw) const override
Real	v0 () const
Real	rho () const
Real	kappa () const
Real	theta () const
Real	sigma () const
const Handle< Quote > &	s0 () const
const Handle< YieldTermStructure > &	dividendYield () const
const Handle< YieldTermStructure > &	riskFreeRate () const
Time	time (const Date &) const override
Real	pdf (Real x, Real v, Time t, Real eps=1e-3) const
Public Member Functions inherited from StochasticProcess
virtual Array	expectation (Time t0, const Array &x0, Time dt) const
virtual Matrix	stdDeviation (Time t0, const Array &x0, Time dt) const
virtual Matrix	covariance (Time t0, const Array &x0, Time dt) 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
	StochasticProcess (ext::shared_ptr< discretization >)
ext::shared_ptr< discretization >	discretization_

Detailed Description

Square-root stochastic-volatility Heston process.

This class describes the square root stochastic volatility process governed by

\[\begin{array}{rcl} dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \\ dv(t, S) &=& \kappa (\theta - v) dt + \sigma \sqrt{v} dW_2 \\ dW_1 dW_2 &=& \rho dt \end{array} \]

Member Function Documentation

size()

Size size ( ) const

overridevirtual

returns the number of dimensions of the stochastic process

Implements StochasticProcess.

factors()

Size factors ( ) const

overridevirtual

returns the number of independent factors of the process

Reimplemented from StochasticProcess.

initialValues()

Array initialValues ( ) const

overridevirtual

returns the initial values of the state variables

Implements StochasticProcess.

drift()

Array drift ( Time t, const Array & x ) const

overridevirtual

returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)

Implements StochasticProcess.

diffusion()

Matrix diffusion ( Time t, const Array & x ) const

overridevirtual

returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \)

Implements StochasticProcess.

apply()

Array apply ( const Array & x0, const Array & dx ) const

overridevirtual

applies a change to the asset value. By default, it returns \( \mathrm{x} + \Delta \mathrm{x} \).

Reimplemented from StochasticProcess.

evolve()

Array evolve ( Time t0, const Array & x0, Time dt, const Array & dw ) const

overridevirtual

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

\[E(\mathrm{x}_0,t_0,\Delta t) + S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} \]

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

Reimplemented from StochasticProcess.

time()

Time time ( const Date & ) const

overridevirtual

returns the time value corresponding to the given date in the reference system of the stochastic process.

Note

As a number of processes might not need this functionality, a default implementation is given which raises an exception.

Reimplemented from StochasticProcess.