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The asymptotic loss distribution in a fat-tailed factor model of portfolio credit risk

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  • Marco Bee

Abstract

This paper extends the standard asymptotic results concerning the percentage loss distribution in the Vasicek uniform model to a setup where the systematic risk factor is non-normally distributed. We show that the asymptotic density in this new setup can still be obtained in closed form; in particular, we derive the return distributions, the densities and the quantile functions when the common factor follows two types of normal mixture distributions (a two-population scale mixture and a jump mixture) and the Student�s t distribution. Finally, we present a real-data application of the technique to data of the Intesa - San Paolo credit portfolio. The numerical experiments show that the asymptotic loss density is highly flexible and provides the analyst with a VaR which takes into account the event risk incorporated in the fat-tailed distribution of the common factor.

Suggested Citation

  • Marco Bee, 2007. "The asymptotic loss distribution in a fat-tailed factor model of portfolio credit risk," Department of Economics Working Papers 0701, Department of Economics, University of Trento, Italia.
    • Handle: RePEc:trn:utwpde:0701
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    References listed on IDEAS

    as
    1. Marco Bee, 2004. "Modelling credit default swap spreads by means of normal mixtures and copulas," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(2), pages 125-146.
    2. Michael S. Gibson, 2001. "Incorporating event risk into value-at-risk," Finance and Economics Discussion Series 2001-17, Board of Governors of the Federal Reserve System (U.S.).
    3. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    4. Gordy, Michael B., 2003. "A risk-factor model foundation for ratings-based bank capital rules," Journal of Financial Intermediation, Elsevier, vol. 12(3), pages 199-232, July.
    5. Subu Venkataraman, 1997. "Value at risk for a mixture of normal distributions: the use of quasi- Bayesian estimation techniques," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 21(Mar), pages 2-13.
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    Keywords

    Factor model; asymptotic loss; Value at Risk.;
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