Discrete-time continuous-state interest rate models

We show how to implement arbitrage-free models of the short-term interest r ate in a discrete-time setting that allows a continuum of rates at any part icular date. Discrete time allows approximate pricing of interest rate cont ingent claims that cannot be valued in continuous-time models. It is usuall y associated with discrete states, with possible interest rates restricted to a limited number of outcomes, as in the lattice model of Hull and White (1994), We develop a method for approximating the prices of contingent clai ms without that restriction. We use numerical integration to evaluate the r isk-neutral expectations that define those prices, and function approximati on to efficiently summarize the information. The procedure is simple and fl exible. We illustrate its properties in the extended Vasicek model of Hull and White and show it to be an effective alternative to lattice methods. (C ) 2001 Elsevier Science B.V. All rights reserved.