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, 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. We model the survival curve and hazard rate curve as stochastic processes. This puts default models in a form resembling the HJM framework for interest rates, yielding a unified framework for default modeling.
Predictability of default appears to have a simple interpretation in this framework. The framework enables us to disentangle predictability and the distribution of the default time from calibration decisions such as whether to use market prices or balance sheet information. It supplies a formal framework for combining models, yielding a simple way to define new default models.
Harvey J. Stein is Head of the Quantitative Risk Analytics Group at Bloomberg, responsible for all quantitative aspects of Bloomberg's risk analysis products. Dr. Stein is well known in the industry, having published and lectured on mortgage backed security valuation, CVA calculations, interest rate and FX modeling, credit exposure calculations, financial regulation, and other subjects. Dr. Stein is also on the board of directors of the IAQF, an adjunct professor at Columbia University, a board member of the Rutgers University Mathematical Finance program and of the NYU Enterprise Learning program, and organizer of the IAQF/Thalesians financial seminar series. He received his BA in mathematics from WPI in 1982 and his PhD in mathematics from UC Berkeley in 1991.