Tail Behavior of Credit Loss Distributions for General Latent Factor Models

Andre Lucas, Pieter Klaassen, Peter Spreij and Stefan Straetmans
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Pieter Klaassen: ABN AMRO Bank NV
Peter Spreij: University of Amsterdam

No 01-023/2, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: 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+.

Keywords: portfolio credit risk; extreme value theory; tail events; tail index; factor models; economic capital; portfolio quality; second-order expansions (search for similar items in EconPapers)
Date: 2001-02-26
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Citations: View citations in EconPapers (3)

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Journal Article: Tail behaviour of credit loss distributions for general latent factor models (2003)
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Persistent link: https://EconPapers.repec.org/RePEc:tin:wpaper:20010023

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