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 boost::unordered_set< ext::shared_ptr< Observable > >	set_type

typedef set_type::iterator	iterator

Public Member Functions
	HestonProcess (const Handle< YieldTermStructure > &riskFreeRate, const Handle< YieldTermStructure > &dividendYield, const Handle< Quote > &s0, Real v0, Real kappa, Real theta, Real sigma, Real rho, Discretization d=QuadraticExponentialMartingale)

Size	size () const
	returns the number of dimensions of the stochastic process

Size	factors () const
	returns the number of independent factors of the process

Disposable< Array >	initialValues () const
	returns the initial values of the state variables

Disposable< Array >	drift (Time t, const Array &x) const
	returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)

Disposable< Matrix >	diffusion (Time t, const Array &x) const
	returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \)

Disposable< Array >	apply (const Array &x0, const Array &dx) const

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

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

Real	pdf (Real x, Real v, Time t, Real eps=1e-3) const

Public Member Functions inherited from StochasticProcess
virtual Disposable< Array >	expectation (Time t0, const Array &x0, Time dt) const

virtual Disposable< Matrix >	stdDeviation (Time t0, const Array &x0, Time dt) const

virtual Disposable< Matrix >	covariance (Time t0, const Array &x0, Time dt) const

void	update ()

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 &)

void	notifyObservers ()

Additional Inherited Members
Protected Member Functions inherited from StochasticProcess
	StochasticProcess ()

	StochasticProcess (const ext::shared_ptr< discretization > &)

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

Detailed Description

Square-root stochastic-volatility Heston process.

This class describes the square root stochastic volatility process governed by

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

Examples: EquityOption.cpp.

Member Function Documentation

◆ apply()

Disposable<Array> apply	(	const Array &	x0,
		const Array &	dx
	)		const

virtual

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

Reimplemented from StochasticProcess.

◆ evolve()

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

virtual

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

virtual

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.

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ apply()

◆ evolve()

◆ time()