Structural models of default for credit risk.
Default risk has become a predomimant driver of research in the field of credit derivatives - today the outstanding volume of traded CDS reaches $15 B, i.e. a CDS position for each daily traded corporate bond. Structural models of default follow Merton's description of the firm by specifying the default event as the first time the company's asset value falls below a threshold, thought of as the time t aggregated debt value. I will show during this presentation how to use the framework of Levy processes to describe the dynamics of the first hitting time of a lower barrier and illustrate the recent papers of Kou and Wang, as well as Madan and Schoutens. We will first recall some path properties of Levy processes and illustrate the 3 main subclasses. We will then build on the classic Black and Cox model to show how to compute the term struture of default probabilities of CDS from their underlying firm characteristics.
