Discrete-Time Continuous-State Interest Rate Models

Michael Sullivan

No 913, Computing in Economics and Finance 1999 from Society for Computational Economics

Abstract: 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.

Date: 1999-03-01
New Economics Papers: this item is included in nep-fin
References: Add references at CitEc
Citations: View citations in EconPapers (1)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:sce:scecf9:913

Access Statistics for this paper

More papers in Computing in Economics and Finance 1999 from Society for Computational Economics CEF99, Boston College, Department of Economics, Chestnut Hill MA 02467 USA. Contact information at EDIRC.
Bibliographic data for series maintained by Christopher F. Baum ().