Finance - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Finance : Stochastic Processes : Finance/GammaProcess

Finance

  

GammaProcess

  

create new Gamma process

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

GammaProcess(mu, sigma)

Parameters

mu

-

real constant; mean parameter

sigma

-

real constant; variance parameter

Description

• 

The GammaProcess command creates a Gamma process with the specified parameters. The Gamma process Gt with mean parameter mu and variance parameter sigma is a continuous-time process with stationary, independent gamma increments such that for any 0<h, Gt&plus;hGt has a Gamma distribution with shape parameter μ2hσ and scale parameter σμ.

• 

The parameter mu is the mean. The parameter sigma is the variance.

Examples

withFinance&colon;

&mu;1&colon;&sigma;3&colon;

GGammaProcess&mu;&comma;&sigma;&colon;

PathPlotGt&comma;t&equals;0..3&comma;timesteps&equals;100&comma;replications&equals;10&comma;thickness&equals;3&comma;axes&equals;BOXED&comma;gridlines&equals;true

ExpectedValueG3&comma;replications&equals;104

value&equals;2.376349494&comma;standarderror&equals;0.01792180394

(1)

SSampleValuesG2G1.98&comma;timesteps&equals;102&comma;replications&equals;103

S:= 1 .. 1000 ArrayData Type: float8Storage: rectangularOrder: C_order

(2)

The variance gamma process, introduced by Madan and Seneta, is the difference of two independent gamma processes representing the up and down movements of the underlying asset.

XuGammaProcess1&comma;3&colon;

XdGammaProcess0.9&comma;3&colon;

Xt&rarr;XutXdt

X:=t&rarr;XutXdt

(3)

PathPlotXt&comma;t&equals;0..3&comma;timesteps&equals;20&comma;replications&equals;5&comma;thickness&equals;2&comma;axes&equals;BOXED&comma;gridlines&equals;true

References

  

Glasserman, P., Monte Carlo Methods in Financial Engineering. New York: Springer-Verlag, 2004.

Compatibility

• 

The Finance[GammaProcess] command was introduced in Maple 15.

• 

For more information on Maple 15 changes, see Updates in Maple 15.

See Also

Finance[BlackScholesProcess]

Finance[CEVProcess]

Finance[Diffusion]

Finance[Drift]

Finance[ExpectedValue]

Finance[GeometricBrownianMotion]

Finance[ItoProcess]

Finance[PathPlot]

Finance[SamplePath]

Finance[SampleValues]

Finance[StochasticProcesses]

Finance[WienerProcess]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam