A Levy model for default dependence

This dissertation proposes a structural-based model for default risk across a portfolio of defaultable securities. Under this framework, the asset value processes for each firm in the portfolio are represented by the components of a multivariate exponential Levy process. Default is declared for a particular credit when its asset value falls below a default boundary. While there are other models of this general form, the framework offered here has several key advantages. These advantages are largely attributable to the approach for defining the multivariate Levy measure. The marginal Levy measures for each individual component process are specified independently from the joint dependence properties of the multivariate Levy measure. As a result, the flexibility of the marginal Levy specification enables the model to accurately capture default risk in the single-name case, even across a portfolio with a wide range of underlying credit qualities. Most importantly, however, the structure of default dependence is not bound to the individual default characteristics of the underlying firms as is the case in many multivariate models. Furthermore, the method for defining the joint properties of the Levy measure allows for a variety of dependence structures. These features produce a mechanism for pricing both single and multi-name securities in a consistent manner; this is especially important for properly hedging risk in multi-name products such as CDO tranches. Finally, the model's fully dynamic specification provides a structure capable of pricing other derivatives that are beyond the scope of many models currently employed in practice including the factor-based Gaussian copula approach. As the markets mature and innovation continues, models with these features will become essential.