Discrete-Time Bond and Options Pricing for Jump-Diffusion Processes

This paper provides a methodology for pricing American type interest rate contingent claims for jump-diffusion processes. The method enhances the standard finite- differencing approach to deal with partial differential- difference equations derived in a jump-diffusion world. The numerical stability and convergence of the scheme is also proved. Numerical illustrations compare jump-diffusion and pure-diffusion models. Whereas the existence of jumps affects call options on bonds very much like those on stocks, this is not the case for puts which are affected by the asymmetric convexity of the bond pricing functions. Early exercise behavior is also analyzed.