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Finance

  

HullWhiteModel

  

create Hull-White interest rate model

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

HullWhiteModel(theta, alpha, sigma)

Parameters

theta

-

observed term structure of interest rates

alpha

-

speed of mean reversion

sigma

-

volatility

Description

• 

The HullWhiteModel command creates a Hull-White model with the specified parameters. Under this model the short rate process rt has the following dynamics with respect to the risk-neutral measure

drt=θtαrtdt+σdWt

where α and σ are non-negative constants and W(t) is a Wiener process modeling the random market risk factor.

Examples

withFinance:

times0.08,0.24,0.48,1.0,2.0,5.0,10.0,30.0

times:=0.08,0.24,0.48,1.0,2.0,5.0,10.0,30.0

(1)

rates0.03,0.032,0.035,0.04,0.045,0.05,0.053,0.055

rates:=0.03,0.032,0.035,0.04,0.045,0.05,0.053,0.055

(2)

RZeroCurvetimes,rates

R:=moduleend module

(3)

plotR,0..30,axes=BOXED,thickness=2,gridlines=true

MHullWhiteModelR,1.0,0.02

M:=moduleend module

(4)

XShortRateProcessM

X:=_R

(5)

PathPlotXt,t=0..1,timesteps=50,replications=20,axes=BOXED,thickness=2,color=red..blue,gridlines=true

Here is the corresponding short-rate tree.

TShortRateTreeM,20,20

T:=moduleend module

(6)

TreePlotT,axes=BOXED,thickness=2,gridlines=true

References

  

Brigo, D., Mercurio, F., Interest Rate Models: Theory and Practice, New York: Springer-Verlag, 2001.

  

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

  

Hull, J., Options, Futures, and Other Derivatives, 5th. edition, Upper Saddle River, New Jersey: Prentice Hall, 2003.

  

Vasicek, O.A., An Equilibrium Characterization of the Term Structure, Journal of Financial Economics, 5 (1977), pp 177-188.

Compatibility

• 

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

• 

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

See Also

Finance[BlackScholesProcess]

Finance[CoxIngersollRossModel]

Finance[OrnsteinUhlenbeckProcess]

Finance[PathGenerator]

Finance[SamplePath]

Finance[ShortRateProcess]

Finance[ShortRateTree]

Finance[VasicekModel]

 


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