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Finance[GammaProcess] - create new Gamma process

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;

G:=GammaProcess&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)

S:=SampleValuesG2G1.98&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.

Xu:=GammaProcess1&comma;3&colon;

Xd:=GammaProcess0.9&comma;3&colon;

X:=t&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

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]

References

  

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


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