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Finance

  

VasicekModel

  

define Vasicek interest rate model

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

VasicekModel(r0, mu, theta, sigma)

Parameters

r0

-

initial interest rate

mu

-

long-running mean

theta

-

speed of mean reversion

sigma

-

volatility

Description

• 

The VasicekModel command creates a Vasicek 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=θμλσ+θrtdt+σdWt

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

Examples

withFinance:

First define a Vasicek model with parameters r0=0.03, μ=0.05, θ=0.3 and σ=0.02.

modelVasicekModel0.03,0.05,0.3,0.02

model:=moduleend module

(1)

The following is the corresponding stochastic process.

rShortRateProcessmodel

r:=_X

(2)

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

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

Here is the corresponding short-rate tree.

treeShortRateTreemodel,20,20

tree:=moduleend module

(3)

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

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

(4)

discountDiscountBondPricemodel,0.03,times

discount:=0.9975839096646550.9926592231662320.9850601676208590.9678601700771990.9327925652576690.8227627109835560.6538920812770460.252136624704580

(5)

term_structureDiscountCurvetimes,convertdiscount,'list'

term_structure:=moduleend module

(6)

plotterm_structure,0.1..30,thickness=2,axes=BOXED,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[VasicekModel] 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[HullWhiteModel]

Finance[OrnsteinUhlenbeckProcess]

Finance[PathGenerator]

Finance[SamplePath]

Finance[ShortRateProcess]

Finance[ShortRateTree]

 


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