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Tail Behavior of Credit Loss Distributions for General Latent Factor Models

Author

Listed:
  • André Lucas

    (Vrije Universiteit Amsterdam)

  • Pieter Klaassen

    (ABN AMRO Bank NV)

  • Peter Spreij

    (University of Amsterdam)

  • Stefan Straetmans

    (Maastricht University)

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+.

Suggested Citation

  • André Lucas & Pieter Klaassen & Peter Spreij & Stefan Straetmans, 2001. "Tail Behavior of Credit Loss Distributions for General Latent Factor Models," Tinbergen Institute Discussion Papers 01-023/2, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20010023
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    References listed on IDEAS

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    1. 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.
    2. Bangia, Anil & Diebold, Francis X. & Kronimus, Andre & Schagen, Christian & Schuermann, Til, 2002. "Ratings migration and the business cycle, with application to credit portfolio stress testing," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 445-474, March.
    3. Gordy, Michael B., 2000. "A comparative anatomy of credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 119-149, January.
    4. repec:bla:jfinan:v:53:y:1998:i:4:p:1363-1387 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Hsieh, Ming-Hua & Lee, Yi-Hsi & Shyu, So-De & Chiu, Yu-Fen, 2019. "Estimating multifactor portfolio credit risk: A variance reduction approach," Pacific-Basin Finance Journal, Elsevier, vol. 57(C).
    2. Caballero, Diego & Lucas, André & Schwaab, Bernd & Zhang, Xin, 2020. "Risk endogeneity at the lender/investor-of-last-resort," Journal of Monetary Economics, Elsevier, vol. 116(C), pages 283-297.
    3. Matthias Fischer & Thorsten Moser & Marius Pfeuffer, 2018. "A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations," Risks, MDPI, vol. 6(4), pages 1-28, December.
    4. André Lucas & Bernd Schwaab & Xin Zhang, 2017. "Modeling Financial Sector Joint Tail Risk in the Euro Area," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 171-191, January.
    5. Albrecht, Peter, 2005. "Kreditrisiken - Modellierung und Management: Ein Überblick," German Risk and Insurance Review (GRIR), University of Cologne, Department of Risk Management and Insurance, vol. 1(2), pages 22-152.
    6. Hayette Gatfaoui, 2003. "How Does Systematic Risk Impact US Credit Spreads? A Copula Study," Risk and Insurance 0308002, University Library of Munich, Germany.
    7. Sak Halis, 2010. "Increasing the number of inner replications of multifactor portfolio credit risk simulation in the t-copula model," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 361-377, January.
    8. Bologov , Yaroslav, 2013. "A copula-based approach to portfolio credit risk modeling," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 29(1), pages 45-66.
    9. Andre Lucas & Bernd Schwaab & Xin Zhang, 2013. "Measuring Credit Risk in a Large Banking System: Econometric Modeling and Empirics," Tinbergen Institute Discussion Papers 13-063/IV/DSF56, Tinbergen Institute, revised 13 Oct 2014.

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