Stochastic-volatility GJR-GARCH(1,1) process. More...

#include <ql/processes/gjrgarchprocess.hpp>

Inheritance diagram for GJRGARCHProcess:

Collaboration diagram for GJRGARCHProcess:

Public Types
enum	Discretization { PartialTruncation , FullTruncation , Reflection }

Public Types inherited from Observer
typedef set_type::iterator	iterator

Public Member Functions
	GJRGARCHProcess (Handle< YieldTermStructure > riskFreeRate, Handle< YieldTermStructure > dividendYield, Handle< Quote > s0, Real v0, Real omega, Real alpha, Real beta, Real gamma, Real lambda, Real daysPerYear=252.0, Discretization d=FullTruncation)

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

Array	initialValues () const override
	returns the initial values of the state variables More...

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

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

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	lambda () const

Real	omega () const

Real	alpha () const

Real	beta () const

Real	gamma () const

Real	daysPerYear () const

const Handle< Quote > &	s0 () const

const Handle< YieldTermStructure > &	dividendYield () const

const Handle< YieldTermStructure > &	riskFreeRate () const

Time	time (const Date &) const override

Public Member Functions inherited from StochasticProcess
	~StochasticProcess () override=default

virtual Size	factors () const
	returns the number of independent factors of the process More...

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 ()=default

	Observer (const Observer &)

Observer &	operator= (const Observer &)

virtual	~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	update ()=0

virtual void	deepUpdate ()

Public Member Functions inherited from Observable
	Observable ()

	Observable (const Observable &)

Observable &	operator= (const Observable &)

	Observable (Observable &&)=delete

Observable &	operator= (Observable &&)=delete

virtual	~Observable ()=default

void	notifyObservers ()

Private Attributes
Handle< YieldTermStructure >	riskFreeRate_

Handle< YieldTermStructure >	dividendYield_

Handle< Quote >	s0_

Real	v0_

Real	omega_

Real	alpha_

Real	beta_

Real	gamma_

Real	lambda_

Real	daysPerYear_

Discretization	discretization_

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

	StochasticProcess (ext::shared_ptr< discretization >)

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

Detailed Description

Stochastic-volatility GJR-GARCH(1,1) process.

This class describes the stochastic volatility process governed by

\[ \begin{array}{rcl} dS(t, S) &=& \mu S dt + \sqrt{v} S dW_1 \\ dv(t, S) &=& (\omega + (\beta + \alpha * q_{2} + \gamma * q_{3} - 1) v) dt + (\alpha \sigma_{12} + \gamma \sigma_{13}) v dW_1 + \sqrt{\alpha^{2} (\sigma^{2}_{2} - \sigma^{2}_{12}) + \gamma^{2} (\sigma^{2}_{3} - \sigma^{2}_{13}) + 2 \alpha \gamma (\sigma_{23} - \sigma_{12} \sigma_{13})} v dW_2 \ \ N = normalCDF(\lambda) \\ n &=& \exp{-\lambda^{2}/2} / \sqrt{2 \pi} \\ q_{2} &=& 1 + \lambda^{2} \\ q_{3} &=& \lambda n + N + \lambda^2 N \\ \sigma^{2}_{2} = 2 + 4 \lambda^{4} \\ \sigma^{2}_{3} = \lambda^{3} n + 5 \lambda n + 3N + \lambda^{4} N + 6 \lambda^{2} N -\\lambda^{2} n^{2} - N^{2} - \lambda^{4} N^{2} - 2 \lambda n N - 2 \lambda^{3} nN - 2 \lambda^{2} N^{2} \ \ \sigma_{12} = -2 \lambda \\ \sigma_{13} = -2 n - 2 \lambda N \\ \sigma_{23} = 2N + \sigma_{12} \sigma_{13} \\ \end{array} \]

Definition at line 64 of file gjrgarchprocess.hpp.

Member Enumeration Documentation

◆ Discretization

enum Discretization

Enumerator
PartialTruncation
FullTruncation
Reflection

Definition at line 66 of file gjrgarchprocess.hpp.

Constructor & Destructor Documentation

◆ GJRGARCHProcess()

GJRGARCHProcess	(	Handle< YieldTermStructure >	riskFreeRate,
		Handle< YieldTermStructure >	dividendYield,
		Handle< Quote >	s0,
		Real	v0,
		Real	omega,
		Real	alpha,
		Real	beta,
		Real	gamma,
		Real	lambda,
		Real	daysPerYear = `252.0`,
		Discretization	d = `FullTruncation`
	)

Definition at line 29 of file gjrgarchprocess.cpp.

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Member Function Documentation

◆ size()

Size size ( ) const

overridevirtual

returns the number of dimensions of the stochastic process

Implements StochasticProcess.

Definition at line 49 of file gjrgarchprocess.cpp.

◆ initialValues()

Array initialValues ( ) const

overridevirtual

returns the initial values of the state variables

Implements StochasticProcess.

Definition at line 53 of file gjrgarchprocess.cpp.

◆ 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.

Definition at line 57 of file gjrgarchprocess.cpp.

◆ 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.

Definition at line 76 of file gjrgarchprocess.cpp.

◆ 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.

Definition at line 114 of file gjrgarchprocess.cpp.

◆ 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.

Definition at line 119 of file gjrgarchprocess.cpp.

◆ v0()

Real v0 ( ) const

Definition at line 88 of file gjrgarchprocess.hpp.

◆ lambda()

Real lambda ( ) const

Definition at line 89 of file gjrgarchprocess.hpp.

◆ omega()

Real omega ( ) const

Definition at line 90 of file gjrgarchprocess.hpp.

◆ alpha()

Real alpha ( ) const

Definition at line 91 of file gjrgarchprocess.hpp.

◆ beta()

Real beta ( ) const

Definition at line 92 of file gjrgarchprocess.hpp.

◆ gamma()

Real gamma ( ) const

Definition at line 93 of file gjrgarchprocess.hpp.

◆ daysPerYear()

Real daysPerYear ( ) const

Definition at line 94 of file gjrgarchprocess.hpp.

◆ s0()

const Handle< Quote > & s0 ( ) const

Definition at line 190 of file gjrgarchprocess.cpp.

◆ dividendYield()

const Handle< YieldTermStructure > & dividendYield ( ) const

Definition at line 194 of file gjrgarchprocess.cpp.

◆ riskFreeRate()

const Handle< YieldTermStructure > & riskFreeRate ( ) const

Definition at line 198 of file gjrgarchprocess.cpp.

◆ 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.

Definition at line 202 of file gjrgarchprocess.cpp.

Member Data Documentation

◆ riskFreeRate_

Handle<YieldTermStructure> riskFreeRate_

private

Definition at line 103 of file gjrgarchprocess.hpp.

◆ dividendYield_

Handle<YieldTermStructure> dividendYield_

private

Definition at line 103 of file gjrgarchprocess.hpp.

◆ s0_

Handle<Quote> s0_

private

Definition at line 104 of file gjrgarchprocess.hpp.

◆ v0_

Real v0_

private

Definition at line 105 of file gjrgarchprocess.hpp.

◆ omega_

Real omega_

private

Definition at line 105 of file gjrgarchprocess.hpp.

◆ alpha_

Real alpha_

private

Definition at line 105 of file gjrgarchprocess.hpp.

◆ beta_

Real beta_

private

Definition at line 105 of file gjrgarchprocess.hpp.

◆ gamma_

Real gamma_

private

Definition at line 105 of file gjrgarchprocess.hpp.

◆ lambda_

Real lambda_

private

Definition at line 105 of file gjrgarchprocess.hpp.

◆ daysPerYear_

Real daysPerYear_

private

Definition at line 105 of file gjrgarchprocess.hpp.

◆ discretization_

Discretization discretization_

private

Definition at line 106 of file gjrgarchprocess.hpp.

Public Types

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Member Enumeration Documentation

◆ Discretization

Constructor & Destructor Documentation

◆ GJRGARCHProcess()

Member Function Documentation

◆ size()

◆ initialValues()

◆ drift()

◆ diffusion()

◆ apply()

◆ evolve()

◆ v0()

◆ lambda()

◆ omega()

◆ alpha()

◆ beta()

◆ gamma()

◆ daysPerYear()

◆ s0()

◆ dividendYield()

◆ riskFreeRate()

◆ time()

Member Data Documentation

◆ riskFreeRate_

◆ dividendYield_

◆ s0_

◆ v0_

◆ omega_

◆ alpha_

◆ beta_

◆ gamma_

◆ lambda_

◆ daysPerYear_

◆ discretization_