
 Tail Behavior of Credit Loss Distributions for General Latent Factor Models by André Lucas of the Tinbergen Institute Amsterdam, November 8, 2002 Abstract: Using a limiting approach to portfolio credit risk, we obtain analytic expressions for the tail behavior of credit losses. To capture the comovements in defaults over time, we assume that defaults are triggered by a general, possibly nonlinear, factor model involving both systematic and idiosyncratic risk factors. The model encompasses default mechanisms in popular models of portfolio credit risk, such as CreditMetrics and CreditRisk+. We show how the tail characteristics of portfolio credit losses depend directly upon the factor model's functional form and the tail properties of the model's risk factors. In many cases the credit loss distribution has a polynomial (rather than exponential) tail. This feature is robust to changes in tail characteristics of the underlying risk factors. Finally, we show that the interaction between portfolio quality and credit loss tail behavior is strikingly different between the CreditMetrics and CreditRisk+. Finally, we comment on the applicability of Extreme Value Theory to describe the behavior of credit loss tails. JEL Classification: G21, G33, G29, C19. Keywords: portfolio credit risk, extreme value theory, tail events, tail index, factor models, economic capital, portfolio quality, secondorder expansions. Published in: Applied Mathematical Finance, Vol. 10, No. 4, (December 2003), pp. 337357. Books Referenced in this paper: (what is this?) 