A Structural Model for Credit Risk with Markov Modulated Lévy Processes and Synchronous Jumps

This paper presents a switching regime version of the Merton's structural model for the pricing of default risk. The default event depends on the total value of the firm's asset modeled by a Markov modulated Levy process. The novelty of our approach is to consider that firm's asset jumps synchronously with a change in the regime. After a discussion of dynamics under the risk neutral measure, we present two models. In the first one, the default occurs at bond maturity if the firm's value falls below a predetermined barrier. In the second version, the company can bankrupt at multiple predetermined discrete times. The use of a Markov chain to model switches in hidden external factors makes it possible to capture the effects of changes in trends and volatilities exhibited by default probabilities. Finally, with synchronous jumps, the firm's asset and state processes are no longer uncorrelated.