Construction of a Single Factor Heath-Jarrow-Morton Term Structure Model

Within the single factor Heath-Jarrow-Morton framework some desirable properties of the entire term structure are proposed. From these properties necessary conditions are developed to restrict the choice of initial forward rate curve and forward rate volatility structure. An analysis of the asymptotic behavior of the term structure's evolution with the specified desirable properties indicates that : i) the dynamics of the infinitely maturing forward rate are locally deterministic in general and in some cases fully deterministic, and ii) the infinitely maturing forward rate cannot fall over time. This paper also considers some new methods, and generalizations of existing methods, for representing an entire term structure model which does notrequire the explicit characterization of the market price of risk.