Nick Costanzino (NYU), A unified theory of default modeling

Credit risk models largely bifurcate into two classes — the structural models and the reduced form models. Attempts have been made to reconcile the two approaches by adjusting filtrations to restrict information ( for instance Cetin, Jarrow, Protter & Yldrm, Jarrow & Protter, and Giesecke) but they are technically complicated and tend to approach filtration modification in an ad-hock fashion. Here we propose a reconciliation inspired by actuarial science’s approach to survival analysis whereby we model the survival and hazard rate curves themselves as a stochastic processes. The key to the unification is extending the notion of hazard rates and survival curves to the appropriate function spaces. This puts default models in a form resembling the Heath-Jarrow-Morton (HJM) framework for interest rates and yields a unified framework for default modeling, and in particular we can talk about the hazard rate of structural models. Joint work with Albert Cohen & Harvey Stein.