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Tail behavior of credit loss distributions

Author

Listed:
  • Lucas, André

    (Vrije Universiteit Amsterdam, Faculteit der Economische Wetenschappen en Econometrie (Free University Amsterdam, Faculty of Economics Sciences, Business Administration and Economitrics)

  • Straetmans, Stefan
  • Klaassen, Pieter

Abstract

We derive the exact loss distribution for portfolios of bonds or cor-porate loans when the number of risks grows indefinitely. We show that in many cases this distribution lies in the maximal domain of attraction of the Weibull (Type III) limit law. Knowledge of the dis-tribution and its tail behavior is important for risk management in order not to over- or underestimate the likelihood of extreme credit losses for the portfolio as a whole. Conform to the credit risk literature, we assume that bond (or loan) defaults are triggered by a latent variable model involving two stochastic variables: systematic and idiosyncratic risk of the bond. It is shown that the tail behavior of these two variables translates into the tail behavior of the whole credit loss distribution. Surprisingly, even if both variables are thin-tailed, the credit loss distribution can have a finite tail index. Moreover, if idiosyncratic risk exhibits heavier tails than the systematic risk factor the tail index of the credit loss distribution can become extremely high, giving rise to a non-conventional shape of the credit loss distribution.

Suggested Citation

  • Lucas, André & Straetmans, Stefan & Klaassen, Pieter, 1999. "Tail behavior of credit loss distributions," Serie Research Memoranda 0060, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    • Handle: RePEc:vua:wpaper:1999-60
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    File URL: http://degree.ubvu.vu.nl/repec/vua/wpaper/pdf/19990060.pdf
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    References listed on IDEAS

    as
    1. Jón Daníelsson & Casper G. de Vries, 1998. "Beyond the Sample: Extreme Quantile and Probability Estimation," Tinbergen Institute Discussion Papers 98-016/2, Tinbergen Institute.
    2. Lucas, Andre & Klaassen, Pieter & Spreij, Peter & Straetmans, Stefan, 2001. "An analytic approach to credit risk of large corporate bond and loan portfolios," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1635-1664, September.
    3. Jon Danielsson & Casper G. De Vries, 2000. "Value-at-Risk and Extreme Returns," Annals of Economics and Statistics, GENES, issue 60, pages 239-270.
    4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
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    More about this item

    Keywords

    credit risk; value-at-risk; tail events; tail index.;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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