EXACT FORMULAS FOR PRICING BONDS AND OPTIONS WHEN INTEREST RATE DIFFUSIONS CONTAIN JUMPS

I develop Heath-Jarrow-Morton extensions of the Vasicek and Jamshidian pure-diffusion models, extend these models to incorporate Poisson-Gaussian interest rate jumps, and obtain closed-form models for valuing default-free, zero-coupon bonds and European call and put options on default-free, zero-coupon bonds in a market where interest rates can experience discontinuous information shocks. The jump-diffusion pricing models value the instrument as the probability-weighted average of the pure-diffusion model prices, each conditional on a specific number of jumps occurring during the life of the instrument. I extend the models to coupon-bearing instruments by applying Jamshidian's serial-decomposition technique. 2005 The Southern Finance Association and the Southwestern Finance Association.