umontreal.iro.lecuyer.stochprocess

Class GeometricBrownianMotion

java.lang.Object

umontreal.iro.lecuyer.stochprocess.StochasticProcess

umontreal.iro.lecuyer.stochprocess.GeometricBrownianMotion

public class GeometricBrownianMotion
extends StochasticProcess

. Represents a geometric Brownian motion (GBM) process {S(t), t >= 0}, which evolves according to the stochastic differential equation

dS(t) = μS(t)dt + σS(t)dB(t),

where μ and σ are the drift and volatility parameters, and {B(t), t >= 0} is a standard Brownian motion (for which B(t)∼N(0, t)). This process can also be written as the exponential of a Brownian motion:

S(t) = S(0)exp[(μ - σ²/2)t + σtB(t)] = S(0)exp[X(t)],

where X(t) = (μ - σ²/2)t + σtB(t). The GBM process is simulated by simulating the BM process X and taking the exponential. This BM process is stored internally.

Field Summary

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

path

Constructor Summary

Constructors

Constructor and Description
GeometricBrownianMotion(double s0, double mu, double sigma, BrownianMotion bm) Constructs a new GeometricBrownianMotion with parameters μ = mu, σ = sigma, and S(t0) = s0, using bm as the underlying BrownianMotion.
GeometricBrownianMotion(double s0, double mu, double sigma, RandomStream stream) Same as GeometricBrownianMotion (s0, mu, sigma, new BrownianMotion (0.0, 0.0, 1.0, stream)).

Method Summary

Methods

Modifier and Type	Method and Description
double[]	generatePath() Generates, returns, and saves the sample path {X(t0), X(t1),…, X(td)}.
double[]	generatePath(RandomStream stream) Same as generatePath(), but first resets the stream to stream.
BrownianMotion	getBrownianMotion() Returns a reference to the BrownianMotion object used to generate the process.
NormalGen	getGen() Returns the NormalGen used.
double	getMu() Returns the value of μ.
double	getSigma() Returns the value of σ.
RandomStream	getStream() Returns the RandomStream for the underlying Brownian motion.
double	nextObservation() Generates and returns the next observation X(tj) of the stochastic process.
void	resetStartProcess() Same as in StochasticProcess, but also invokes resetStartProcess for the underlying BrownianMotion object.
void	setObservationTimes(double[] t, int d) Sets the observation times of the process to a copy of T, with t0 = T[0] and td = T[d].
void	setParams(double s0, double mu, double sigma) Sets the parameters S(t0) = s0, μ = mu and σ = sigma of the process.
void	setStream(RandomStream stream) Resets the RandomStream for the underlying Brownian motion to stream.

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

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

GeometricBrownianMotion

public GeometricBrownianMotion(double s0,
                       double mu,
                       double sigma,
                       RandomStream stream)

Same as GeometricBrownianMotion (s0, mu, sigma, new BrownianMotion (0.0, 0.0, 1.0, stream)).

GeometricBrownianMotion

public GeometricBrownianMotion(double s0,
                       double mu,
                       double sigma,
                       BrownianMotion bm)

Constructs a new GeometricBrownianMotion with parameters μ = mu, σ = sigma, and S(t₀) = s0, using bm as the underlying BrownianMotion. The parameters of bm are automatically reset to μ - σ²/2 and σ, regardless of the original parameters of bm. The observation times are the same as those of bm. The generation method depends on that of bm (sequential, bridge sampling, PCA, etc.).

Method Detail

setObservationTimes

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

Description copied from class: StochasticProcess

Sets the observation times of the process to a copy of T, with t₀ = T[0] and t_d = T[d]. The size of T must be d + 1.

Overrides:

setObservationTimes in class StochasticProcess

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(RandomStream stream)

Description copied from class: StochasticProcess

Same as generatePath(), but first resets the stream to stream.

Overrides:

generatePath in class StochasticProcess

resetStartProcess

public void resetStartProcess()

Same as in StochasticProcess, but also invokes resetStartProcess for the underlying BrownianMotion object.

Overrides:

resetStartProcess in class StochasticProcess

setParams

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

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

setStream

public void setStream(RandomStream stream)

Resets the RandomStream for the underlying Brownian motion to stream.

Specified by:

setStream in class StochasticProcess

getStream

public RandomStream getStream()

Returns the RandomStream for the underlying Brownian motion.

Specified by:

getStream in class StochasticProcess

getMu

public double getMu()

Returns the value of μ.

getSigma

public double getSigma()

Returns the value of σ.

getGen

public NormalGen getGen()

Returns the NormalGen used.

getBrownianMotion

public BrownianMotion getBrownianMotion()

Returns a reference to the BrownianMotion object used to generate the process.