Levy processes have become cumulatively popular in Finance because they describe financial markets in a more accurate way than models based in Brownian motion. For the purpose of pricing debt value by structural model, we not only assume the interest rate is stochastic and model the dynamics of firm value return as a Levy process by the sum of a Brownian motion and compound Poisson process which is often called a jump-diffusion process. Generally speaking, the jump risk is assumed nonsystematic, and hence diversifiable. In order to describe the effect of nondiversifiable jump risk such as subprime mortgage crisis, we presume the jump risk is a systematic risk.
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