umontreal.iro.lecuyer.stochprocess

Class GeometricNormalInverseGaussianProcess

java.lang.Object

umontreal.iro.lecuyer.stochprocess.StochasticProcess

umontreal.iro.lecuyer.stochprocess.GeometricLevyProcess

umontreal.iro.lecuyer.stochprocess.GeometricNormalInverseGaussianProcess

public class GeometricNormalInverseGaussianProcess
extends GeometricLevyProcess

. The geometric normal inverse gaussian (GNIG) process is the exponentiation of a NormalInverseGaussianProcess:

S(t) = S₀exp((r - ω_RN)t + NIG(t;α, β, μ, δ)),

where r is the interest rate. It is a strictly positive process, which is useful in finance. There is also a neutral correction in the exponential, ω_RN = μ + δγ - δ(α^2-(1+β)^2)^1/2, which takes into account the market price of risk. The underlying NIG process must start at zero, NIG(t₀) = 0 and the initial time should also be set to zero, t₀ = 0, both for the NIG and GNIG.

Field Summary

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

path

Constructor Summary

Constructors

Constructor and Description
GeometricNormalInverseGaussianProcess(double s0, double muGeom, double alpha, double beta, double mu, double delta, RandomStream streamBrownian, InverseGaussianProcess igP) Constructs a new GeometricNormalInverseGaussianProcess.
GeometricNormalInverseGaussianProcess(double s0, double muGeom, double alpha, double beta, double mu, double delta, RandomStream streamBrownian, NormalInverseGaussianProcess nigP) Constructs a new GeometricNormalInverseGaussianProcess.
GeometricNormalInverseGaussianProcess(double s0, double muGeom, double alpha, double beta, double mu, double delta, RandomStream streamBrownian, RandomStream streamNIG1, RandomStream streamNIG2, java.lang.String igType) Constructs a new GeometricNormalInverseGaussianProcess.
GeometricNormalInverseGaussianProcess(double s0, double muGeom, double alpha, double beta, double mu, double delta, RandomStream streamAll, java.lang.String igType) Constructs a new GeometricNormalInverseGaussianProcess.

Method Summary

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

generatePath, getLevyProcess, getMuGeom, getOmega, getStream, nextObservation, resetRiskNeutralCorrection, resetStartProcess, setMuGeom, setObservationTimes, setStream

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

GeometricNormalInverseGaussianProcess

public GeometricNormalInverseGaussianProcess(double s0,
                                     double muGeom,
                                     double alpha,
                                     double beta,
                                     double mu,
                                     double delta,
                                     RandomStream streamBrownian,
                                     NormalInverseGaussianProcess nigP)

Constructs a new GeometricNormalInverseGaussianProcess. The parameters of the NIG process will be overwritten by the parameters given to the GNIG, with the initial value of the NIG set to 0. The observation times of the NIG will also be changed to those of the GNIG.

GeometricNormalInverseGaussianProcess

public GeometricNormalInverseGaussianProcess(double s0,
                                     double muGeom,
                                     double alpha,
                                     double beta,
                                     double mu,
                                     double delta,
                                     RandomStream streamBrownian,
                                     InverseGaussianProcess igP)

Constructs a new GeometricNormalInverseGaussianProcess. The process igP will be used internally by the underlying NormalInverseGaussianProcess.

GeometricNormalInverseGaussianProcess

public GeometricNormalInverseGaussianProcess(double s0,
                                     double muGeom,
                                     double alpha,
                                     double beta,
                                     double mu,
                                     double delta,
                                     RandomStream streamBrownian,
                                     RandomStream streamNIG1,
                                     RandomStream streamNIG2,
                                     java.lang.String igType)

Constructs a new GeometricNormalInverseGaussianProcess. The drift of the geometric term, muGeom, is usually the interest rate r. s0 is the initial value of the process and the other four parameters are the parameters of the underlying NormalInverseGaussianProcess process.

GeometricNormalInverseGaussianProcess

public GeometricNormalInverseGaussianProcess(double s0,
                                     double muGeom,
                                     double alpha,
                                     double beta,
                                     double mu,
                                     double delta,
                                     RandomStream streamAll,
                                     java.lang.String igType)

Constructs a new GeometricNormalInverseGaussianProcess. The String igType corresponds to the type of InverseGaussianProcess that will be used by the underlying NormalInverseGaussianProcess. All RandomStream's used to generate the underlying NormalInverseGaussianProcess and its underlying InverseGaussianProcess are set to the same given streamAll.