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Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics

Published online by Cambridge University Press:  06 April 2009

Andrew Jeffrey
Andrew Jeffrey
Affiliation:
School of Banking and Finance, The University of New South Wales, Sydney, NSW 2052, Australia.
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Abstract

This paper considers the class of Heath-Jarrow-Morton term structure models where the spot interest rate is Markov and the term structure at time t is a function of time, maturity, and the spot interest rate at time t. A representation for this class of models is derived and I show that the functional forms of the forward rate volatility structure and the initial forward rate curve cannot be arbitrarily chosen. I provide necessary and sufficient conditions indicating which combinations of these functional forms are allowable. I also derive a partial differential equation representation of the term structure dynamics that does not require explicit modeling of both the market price of risk and the drift term for the spot interest rate process. Using the analysis presented in this paper, a class of intertemporal term structure models is derived.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 30 , Issue 4 , December 1995 , pp. 619 - 642
Copyright
Copyright © School of Business Administration, University of Washington 1995

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