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Finance[VasicekModel] - define Vasicek interest rate model
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Calling Sequence
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VasicekModel(![r[0]](/support/helpjp/helpview.aspx?si=8904/file01696/math10.png) , mu, theta, sigma)
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Parameters
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![r[0]](/support/helpjp/helpview.aspx?si=8904/file01696/math29.png)
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non-negative constant; initial interest rate
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mu
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non-negative constant; long-running mean
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theta
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non-negative constant; speed of mean reversion
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sigma
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non-negative constant; volatility parameter
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Description
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The VasicekModel command creates a Vasicek model with the specified parameters. Under this model the short-rate process  has the following dynamics with respect to the objective measure
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where  ,  ,  , and  are non-negative constants.
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Compatibility
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The Finance[VasicekModel] command was introduced in Maple 15.
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Examples
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First define a Vasicek model with parameters ![r[0] = 0.3e-1](/support/helpjp/helpview.aspx?si=8904/file01696/math114.png) ,  ,  and  .
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The following is the corresponding stochastic process.
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Here is the corresponding short-rate tree.
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![times := [0.8e-1, .24, .48, 1.0, 2.0, 5.0, 10.0, 30.0]](/support/helpjp/helpview.aspx?si=8904/file01696/math177.png)
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![times := [0.8e-1, .24, .48, 1.0, 2.0, 5.0, 10.0, 30.0]](/support/helpjp/helpview.aspx?si=8904/file01696/math180.png)
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![discount := Array([.997583909664655, .992659223166232, .985060167620859, .967860170077199, .932792565257669, .822762710983556, .653892081277046, .252136624704580])](/support/helpjp/helpview.aspx?si=8904/file01696/math187.png)
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References
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Brigo, D., Mercurio, F., Interest Rate Models: Theory and Practice, New York: Springer-Verlag, 2001.
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Glasserman, P., Monte Carlo Methods in Financial Engineering, New York: Springer-Verlag, 2004.
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Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.
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Vasicek, O.A., An Equilibrium Characterization of the Term Structure, Journal of Financial Economics, 5 (1977), pp 177-188.
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