Markov Chain Approximations For Term Structure Models

We derive discrete markov chain approximations for continuous state equilibrium term structure models. The states and transition probabilities of the markov chain are chosen effciently according to a quadrature rule as in Tauchen and Hussey (1991). Quadrature provides a simple yet method which can easily incorporates complication like non- normality, heteroskedasticity, and multiple factors. We use the extended Vasicek model of the term structure as an example for this procedure and compare its pricing efficiency and accuracy to the popular trinomial tree approximation of Hull and White (1990). We further illustrate, with numerical examples, the and effciency of this procedure in pricing interest rate options when the underlying interest rate has conditional non-normality and multiple factors.