Discrete-Time Continuous-State Interest Rate Models

We show how to implement arbitrage-free models of the short-term interest rate in a discretetime setting that allows a continuum of rates at any particular date. Discrete time allows approximate pricing of interest rate contingent claims that cannot be valued in continuous-time models. It is usually 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 claims without that restriction. We use numerical integration to evaluate the risk-neutral expectations that define those prices, and function approximation to efficiently summarize the information. The procedure is simple and flexible. We illustrate its properties in the extended Vasicek model of Hull and White and show it to be an effective alternative to lattice methods. JEL classification: C63; G13