Tail Behavior of Credit Loss Distributions for General Latent Factor Models

Using a limiting approach to portfolio credit risk, we obtain analytic expressions for the tail behavior of the distribution of credit losses. We show that in many cases of practical interest the distribution of these losses has polynomial ('fat') rather than exponential ('thin') tails. Our modeling framework encompasses the models available in the literature. Defaults are triggered by a general latent factor model involving systematic and idiosyncratic risk. We show explicitly how the tail behavior of the distribution of these two risk factors relates to the tail behavior of the credit loss distribution. Even if the distributions of both risk factors are thin-tailed, the credit loss distribution may have a finite tail index (polynomial tails). If idiosyncratic risk exhibits thinner tails than systematic risk, the credit loss density actually increases towards the maximum credit loss. This unconventional behaviour of the credit loss density has not been reported earlier in the literature. We also derive analytically the interaction between portfolio quality and credit loss tail behavior and find a striking difference between two well-known modeling frameworks for portfolio credit risk: CreditMetrics and CreditRisk+. <BR><BR>