A binomial approximation for two-state Markovian HJM models

This article develops a lattice algorithm for pricing interest rate derivatives under the Heath-Jarrow-Morton (HJM) paradigm when the volatility structure of forward rates obeys the Ritchken and Sankarasubramanian condition. In such a framework, the entire term structure of the interest rate may be represented using atwo-dimensional Markov process, where one state variable is the spot rate and the other is an accrued variance statistic. Unlike in the usual approach based on the Nelson-Ramaswamy transformation, we directly discretize the heteroskedastic spot rate process by a recombining binomial tree. Further, we reduce the computational costof the pricing problem by associating with each node of the lattice a fixed number of accrued variance valuescomputed on a subset of paths reaching that node. A backward induction scheme coupled with linear interpolationis used to evaluate interest rate contingent claims.