umontreal.iro.lecuyer.stochprocess

Class VarianceGammaProcessDiff

java.lang.Object

umontreal.iro.lecuyer.stochprocess.StochasticProcess

umontreal.iro.lecuyer.stochprocess.VarianceGammaProcess

umontreal.iro.lecuyer.stochprocess.VarianceGammaProcessDiff

Direct Known Subclasses:

VarianceGammaProcessDiffPCA

public class VarianceGammaProcessDiff
extends VarianceGammaProcess

This class represents a variance gamma (VG) process {S(t) = X(t;θ, σ, ν) : t >= 0}. This process is generated using difference of gamma sampling (see), which uses the representation of the VG process as the difference of two independent GammaProcess'es (see):

X(t;θ, σ, ν) : = X(0) + Γ⁺(t;μ_p, ν_p) - Γ^-(t;μ_n, ν_n)

where X(0) is a constant corresponding to the initial value of the process and

μp	=	(1/2)( &thetas;^2 + 2σ^2/ν)1/2 + θ/2
μn	=	(1/2)( &thetas;^2 + 2σ^2/ν)1/2 - θ/2
νp	=	((1/2)(&thetas;^2 + 2σ^2/ν)1/2 + θ/2)2ν
νn	=	((1/2)(&thetas;^2 - 2σ^2/ν)1/2 + θ/2)2ν

Field Summary

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

path

Constructor Summary

Constructors

Constructor and Description
VarianceGammaProcessDiff(double s0, double theta, double sigma, double nu, GammaProcess gpos, GammaProcess gneg) Same as above.
VarianceGammaProcessDiff(double s0, double theta, double sigma, double nu, RandomStream stream) Constructs a new VarianceGammaProcessDiff with parameters θ = theta, σ = sigma, ν = nu and initial value S(t0) = s0.

Method Summary

Methods

Modifier and Type	Method and Description
double[]	generatePath() Generates, returns and saves the path.
double[]	generatePath(double[] uniform01) Similar to the usual generatePath(), but here the uniform random numbers used for the simulation must be provided to the method.
GammaProcess	getGneg() Returns a reference to the GammaProcess object gneg used to generate the Γ- component of the process.
GammaProcess	getGpos() Returns a reference to the GammaProcess object gpos used to generate the Γ+ component of the process.
double	nextObservation() Generates the observation for the next time.
void	resetStartProcess() Sets the observation times on the VarianceGammaProcessDiff as usual, but also applies the resetStartProcess method to the two GammaProcess objects used to generate this process.
void	setObservationTimes(double[] t, int d) Sets the observation times on the VarianceGammaProcesDiff as usual, but also sets the observation times of the underlying GammaProcess'es.
void	setStream(RandomStream stream) Sets the RandomStream of the two GammaProcess'es to the same stream.

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

getBrownianMotion, getGammaProcess, getNu, getSigma, getStream, getTheta, setParams

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

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

Methods inherited from class java.lang.Object

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

Constructor Detail

VarianceGammaProcessDiff

public VarianceGammaProcessDiff(double s0,
                        double theta,
                        double sigma,
                        double nu,
                        RandomStream stream)

Constructs a new VarianceGammaProcessDiff with parameters θ = theta, σ = sigma, ν = nu and initial value S(t₀) = s0. stream is used by two instances of GammaProcess, Γ⁺ and Γ^-, respectively. The other parameters are as in the class VarianceGammaProcess. The GammaProcess objects for Γ⁺ and Γ^- are constructed using the parameters from and their initial values Γ⁺(t₀) and Γ^-(t₀) are set to 0.

VarianceGammaProcessDiff

public VarianceGammaProcessDiff(double s0,
                        double theta,
                        double sigma,
                        double nu,
                        GammaProcess gpos,
                        GammaProcess gneg)

Same as above. To avoid confusion, the parameters of the GammaProcess objects for Γ⁺ and Γ^- are set to those of and their initial values Γ⁺(t₀) and Γ^-(t₀) are set to 0. Also, since there is only one RandomStream in the other constructor, only the RandomStream included in the GammaProcess gpos is kept, as the RandomStream of gneg is the same.

Method Detail

nextObservation

public double nextObservation()

Description copied from class: VarianceGammaProcess

Generates the observation for the next time. It also works with bridge sampling; however both BrownianMotionBridge and GammaProcessBridge must be used in the constructor in that case. Furthermore, for bridge sampling, the order of the observations is that of the bridge, not sequential order.

Overrides:

nextObservation in class VarianceGammaProcess

generatePath

public double[] generatePath()

Generates, returns and saves the path. To do so, the path of Γ⁺ is first generated and then the path of Γ^-. This is not the optimal way of proceeding in order to reduce the variance in QMC simulations; for that, use generatePath(double[] uniform01) instead.

Overrides:

generatePath in class VarianceGammaProcess

generatePath

public double[] generatePath(double[] uniform01)

Similar to the usual generatePath(), but here the uniform random numbers used for the simulation must be provided to the method. This allows to properly use the uniform random variates in QMC simulations. This method divides the table of uniform random numbers uniform01 in two smaller tables, the first one containing the odd indices of uniform01 are used to generate the path of Γ⁺ and the even indices are used to generate the path of Γ^-. This way of proceeding further reduces the variance for QMC simulations.

Overrides:

generatePath in class VarianceGammaProcess

resetStartProcess

public void resetStartProcess()

Sets the observation times on the VarianceGammaProcessDiff as usual, but also applies the resetStartProcess method to the two GammaProcess objects used to generate this process.

Overrides:

resetStartProcess in class VarianceGammaProcess

getGpos

public GammaProcess getGpos()

Returns a reference to the GammaProcess object gpos used to generate the Γ⁺ component of the process.

getGneg

public GammaProcess getGneg()

Returns a reference to the GammaProcess object gneg used to generate the Γ^- component of the process.

setObservationTimes

public void setObservationTimes(double[] t,
                       int d)

Sets the observation times on the VarianceGammaProcesDiff as usual, but also sets the observation times of the underlying GammaProcess'es.

Overrides:

setObservationTimes in class VarianceGammaProcess

setStream

public void setStream(RandomStream stream)

Sets the RandomStream of the two GammaProcess'es to the same stream.

Overrides:

setStream in class VarianceGammaProcess