Single factor models with Markovian spot interest rate: An analytical treatment (Q1397606)

This paper provides an analytic characterization of the bond prices in the class of single-factor Heath-Jarrow-Morton models in which the spot interest rate is a Markov process and the volatility structure of zero coupon bond returns is stochastic; Jeffrey's (1995) constraint is satisfied. The characterization involves a well-defined Volterra integral equation of the first kind. Under the generalized Cox-Ingersoll-Ross volatility assumption, and with an arbitrary initial term structure, it is shown that the Volterra equation can be solved by perturbation methods.