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Discrete-Time Continuous-State Interest Rate Models


  • Michael Sullivan

    () (Florida International University)


This paper shows how to implement arbitrage-free models of the short-term interest rate in a discrete time setting that allows a continuum of rates at any particular date. Current models of the interest rate are either continuous time-continuous state models, such as the Vasicek or Cox, Ingersoll, and Ross models, or discrete time-discrete state models, such as the Hull and White model. A discrete-time process allows approximate valuation of a variety of interest-rate contingent claims that have no closed form solution -- for example, American style bond options. But binomial and trinomial models commonly employed in discrete-time settings also restrict interest rates to discrete outcomes. They have been shown in other contexts to have poor convergence properties. This paper uses numerical integration to evaluate the risk-neutral expectations that define the value of an interest-rate contingent claim. The efficiency of the technique is enhanced by summarizing information on the value of the claim at a given date in a continuous approximating function. The procedure gives a simple but flexible approach for handling arbitrage-free specifications of the short-rate process. Illustrations include the extended Vasicek model of Hull and White and the lognormal interest-rate process of Black and Karainsky.

Suggested Citation

  • Michael Sullivan, 1999. "Discrete-Time Continuous-State Interest Rate Models," Computing in Economics and Finance 1999 913, Society for Computational Economics.
  • Handle: RePEc:sce:scecf9:913

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    Cited by:

    1. Dan Pirjol, 2015. "Hogan-Weintraub singularity and explosive behaviour in the Black-Derman-Toy model," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1243-1257, July.

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