Exact Solutions for Bond and Option Prices with Systematic Jump Risk

A variety of realistic economic considerations make jump- diffusion models of interest rate dynamics an appealing modeling choice to price interest rate contingent claims. However, exact closed form solutions for bond prices when interest rates follow a mixed jump-diffusion process have proved very hard to derive. This paper puts forward two new models of interest rate dynamics which combine infrequent, discrete changes in the interest rate level, modeled as a jump process, with short lived, mean reverting shocks, modeled as a diffusion process. The two models differ in the way jumps affect the central tendency of interest rates; in one case shocks are temporary, in the other shocks are permanent. We derive exact closed form solutions for the price of a discount bond, and computationally tractable schemes to price bond options