umontreal.iro.lecuyer.stochprocess

Class GeometricVarianceGammaProcess

java.lang.Object

umontreal.iro.lecuyer.stochprocess.StochasticProcess

umontreal.iro.lecuyer.stochprocess.GeometricVarianceGammaProcess

public class GeometricVarianceGammaProcess
extends StochasticProcess

This class represents a geometric variance gamma process S(t) (see). This stochastic process is defined by the equation

S(t) = S(0) exp(μt + X(t;σ, ν, θ) + ωt),

where X is a variance gamma process and

ω = (1/ν) ln(1 - θν - σ²ν/2).

Constructor Summary

Constructors

Constructor and Description
GeometricVarianceGammaProcess(double s0, double theta, double sigma, double nu, double mu, RandomStream stream) Constructs a new GeometricVarianceGammaProcess with parameters θ = theta, σ = sigma, ν = nu, μ = mu and initial value S(t0) = s0.
GeometricVarianceGammaProcess(double s0, double mu, VarianceGammaProcess vargamma) Constructs a new GeometricVarianceGammaProcess.

Method Summary

Modifier and Type	Method and Description
double[]	generatePath() Generates, returns, and saves the sample path {X(t0), X(t1),…, X(td)}.
double[]	generatePath(double[] uniform01)
double	getCurrentUpperBound()
double	getMu() Returns the value of the parameter μ.
double	getNu() Returns the value of the parameter ν.
double	getOmega() Returns the value of the quantity ω defined in.
double	getSigma() Returns the value of the parameter σ.
RandomStream	getStream() Returns the random stream of the underlying generator.
double	getTheta() Returns the value of the parameter θ.
VarianceGammaProcess	getVarianceGammaProcess() Returns a reference to the variance gamma process X defined in the constructor.
double	nextObservation() Generates and returns the next observation X(tj) of the stochastic process.
void	resetStartProcess() Resets the GeometricaVarianceGammaProcess, but also applies the resetStartProcess method to the VarianceGammaProcess object used to generate this process.
void	setParams(double s0, double theta, double sigma, double nu, double mu) Sets the parameters S(t0) = s0, θ = theta, σ = sigma, ν = nu and μ = mu of the process.
void	setStream(RandomStream stream) Resets the random stream of the underlying generator to stream.

Methods inherited from class umontreal.iro.lecuyer.stochprocess.StochasticProcess

generatePath, getArrayMappingCounterToIndex, getCurrentObservation, getCurrentObservationIndex, getNbObservationTimes, getObservation, getObservationTimes, getPath, getSubpath, getX0, hasNextObservation, setObservationTimes, setObservationTimes, setX0

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

GeometricVarianceGammaProcess

public GeometricVarianceGammaProcess(double s0,
                                     double theta,
                                     double sigma,
                                     double nu,
                                     double mu,
                                     RandomStream stream)

Constructs a new GeometricVarianceGammaProcess with parameters θ = theta, σ = sigma, ν = nu, μ = mu and initial value S(t₀) = s0. The stream is used to generate the VarianceGammaProcess object used to implement X in.

GeometricVarianceGammaProcess

public GeometricVarianceGammaProcess(double s0,
                                     double mu,
                                     VarianceGammaProcess vargamma)

Constructs a new GeometricVarianceGammaProcess. The parameters θ, σ, ν are set to the parameters of the VarianceGammaProcess vargamma. The parameter μ is set to mu and the initial values S(t₀) = s0.

Method Detail

nextObservation

public double nextObservation()

Description copied from class: StochasticProcess

Generates and returns the next observation X(t_j) of the stochastic process. The processes are usually sampled sequentially, i.e. if the last observation generated was for time t_j-1, the next observation returned will be for time t_j. In some cases, subclasses extending this abstract class may use non-sequential sampling algorithms (such as bridge sampling). The order of generation of the t_j's is then specified by the subclass. All the processes generated using principal components analysis (PCA) do not have this method.

Overrides:

nextObservation in class StochasticProcess

generatePath

public double[] generatePath()

Description copied from class: StochasticProcess

Generates, returns, and saves the sample path {X(t₀), X(t₁),…, X(t_d)}. It can then be accessed via getPath, getSubpath, or getObservation. The generation method depends on the process type.

Specified by:

generatePath in class StochasticProcess

generatePath

public double[] generatePath(double[] uniform01)

getCurrentUpperBound

public double getCurrentUpperBound()

resetStartProcess

public void resetStartProcess()

Resets the GeometricaVarianceGammaProcess, but also applies the resetStartProcess method to the VarianceGammaProcess object used to generate this process.

Overrides:

resetStartProcess in class StochasticProcess

setParams

public void setParams(double s0,
                      double theta,
                      double sigma,
                      double nu,
                      double mu)

Sets the parameters S(t₀) = s0, θ = theta, σ = sigma, ν = nu and μ = mu of the process. Warning: This method will recompute some quantities stored internally, which may be slow if called repeatedly.

getTheta

public double getTheta()

Returns the value of the parameter θ.

getMu

public double getMu()

Returns the value of the parameter μ.

getNu

public double getNu()

Returns the value of the parameter ν.

getSigma

public double getSigma()

Returns the value of the parameter σ.

getOmega

public double getOmega()

Returns the value of the quantity ω defined in.

getVarianceGammaProcess

public VarianceGammaProcess getVarianceGammaProcess()

Returns a reference to the variance gamma process X defined in the constructor.

setStream

public void setStream(RandomStream stream)

Description copied from class: StochasticProcess

Resets the random stream of the underlying generator to stream.

Specified by:

setStream in class StochasticProcess

getStream

public RandomStream getStream()

Description copied from class: StochasticProcess

Returns the random stream of the underlying generator.

Specified by:

getStream in class StochasticProcess