The reduction of forward rate dependent volatility HJM models to Markovian form: pricing European bond options

Ramaprasad Bhar, Carl Chiarella, Nadima El-Hassan, and Xiaosu Zheng

Abstract

ABSTRACT

The authors consider a single-factor Heath-Jarrow-Morton model with a forward rate volatility function depending upon a function of time to maturity, the instantaneous spot rate of interest, and a forward rate to a fixed maturity. With this specification, the stochastic dynamics determining the prices of interest rate derivatives may be reduced to Markovian form. Furthermore, the evolution of the forward rate curve is completely determined by the two rates specified in the volatility function and it is thus possible to obtain a closed-form expression for bond prices. The prices of bond options are determined by a partial differential equation with two spatial variables. The evaluation of European bond options in this framework using the alternating direction implicit method is discussed.