Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics

Abstract

This paper considers the class of Heath-Jarrow-Morton term structure models where the spot interest rate is Markov and the term structure at time t is a function of time, maturity, and the spot interest rate at time t. A representation for this class of models is derived and I show that the functional forms of the forward rate volatility structure and the initial forward rate curve cannot be arbitrarily chosen. I provide necessary and sufficient conditions indicating which combinations of these functional forms are allowable. I also derive a partial differential equation representation of the term structure dynamics that does not require explicit modeling of both the market price of risk and the drift term for the spot interest rate process. Using the analysis presented in this paper, a class of intertemporal term structure models is derived.