Tail Behavior of Credit Loss Distributions for General Latent Factor Models

Using a limiting approach to portfolio credit risk, we obtain analyticexpressions for the tail behavior of the distribution of credit losses. We showthat in many cases of practical interest the distribution of these losses haspolynomial ('fat') rather than exponential ('thin') tails. Our modelingframework encompasses the models available in the literature. Defaults aretriggered by a general latent factor model involving systematic andidiosyncratic risk. We show explicitly how the tail behavior of the distributionof these two risk factors relates to the tail behavior of the credit lossdistribution. Even if the distributions of both risk factors are thin-tailed,the credit loss distribution may have a finite tail index (polynomial tails). Ifidiosyncratic risk exhibits thinner tails than systematic risk, the credit lossdensity actually increases towards the maximum credit loss. This unconventionalbehaviour of the credit loss density has not been reported earlier in theliterature. We also derive analytically the interaction between portfolioquality and credit loss tail behavior and find a striking difference between twowell-known modeling frameworks for portfolio credit risk: CreditMetrics andCreditRisk+.