Exact Formulas for Pricing Bonds and Options When Interest Rate Diffusions Contain Jumps
Posted: 22 Nov 2004
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 further extend the models to coupon-bearing instruments by applying Jamshidian's serial-decomposition technique.
Keywords: Option pricing, bond pricing, diffusion, jumps
JEL Classification: G12, G13
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