Publications: Discrete-Time Continuous-State Interest Rate Models
by Michael A. Sullivan
Abstract
We show how to implement arbitrage-free models of the short-term interest rate in
discrete-time setting that allows 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 nd 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.
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do not necessarily reflect the views of the Office of the Comptroller of the Currency or the Department of the Treasury.
Any whole or partial reproduction of material in this paper should include the following citation:
Sullivan, "Discrete-Time Continuous-State Interest Rate Models,"
Office of the Comptroller of the Currency, E&PA Working Paper 2000-6, April 2000.
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