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QuantLib::GJRGARCHProcess – Stochastic-volatility GJR-GARCH(1,1) process.

Synopsis

GJRGARCHProcess(const Handle<YieldTermStructure> &riskFreeRate, const Handle<YieldTermStructure> &dividendYield, const 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

    returns the number of dimensions of the stochastic 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.$ igma(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 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

Inherits QuantLib::StochasticProcess.

Public Types

enum Discretization { PartialTruncation, FullTruncation, Reflection }

Public Member Functions

GJRGARCHProcess(const Handle<YieldTermStructure> &riskFreeRate, const Handle<YieldTermStructure> &dividendYield, const 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

    returns the number of dimensions of the stochastic 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.$ igma(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 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

Detailed Description

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

This class describes the stochastic volatility process governed by [ r Function Documentation"

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.

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) dot Delta mathrm{w} ] where $ E $ is the expectation and $ S $ the standard deviation.

Reimplemented from StochasticProcess.

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.

Author

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