Pricing Interest Rate Derivatives With Arbitrary Skewness And Kurtosis

Term structure models employing jump-diffusion processes may be used to accommodate the observed skewness and kurtosis of interest rates. This paper extends the discrete-time, pure-diffusion version of the Heath-Jarrow-Morton model to the pricing of American bond options when the underlying term structure of interest rates follows a jump-diffusion process. The jump-diffusion process is specified using a hexanomial tree (six nodes emanating from each node), and the tree is shown to be recombining. This feature of the tree ensures path-independence. The scheme is parsimonious, accurate and convergent. A fairly general class of time-dependent volatilities preserving path independence and providing mean revision is shown to be attainable even under this enhanced jump-diffusion framework.