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The Two Defaults Scenario for Stressing Credit Portfolio Loss Distributions

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  • Dirk Tasche

    (Bank of England, Threadneedle Street, London EC2R 8AH, UK)

Abstract

The impact of a stress scenario of default events on the loss distribution of a credit portfolio can be assessed by determining the loss distribution conditional on these events. While it is conceptually easy to estimate loss distributions conditional on default events by means of Monte Carlo simulation, it becomes impractical for two or more simultaneous defaults as then the conditioning event is extremely rare. We provide an analytical approach to the calculation of the conditional loss distribution for the CreditRisk + portfolio model with independent random loss given default distributions. The analytical solution for this case can be used to check the accuracy of an approximation to the conditional loss distribution whereby the unconditional model is run with stressed input probabilities of default (PDs). It turns out that this approximation is unbiased. Numerical examples, however, suggest that the approximation may be seriously inaccurate but that the inaccuracy leads to overestimation of tail losses and, hence, the approach errs on the conservative side.

Suggested Citation

  • Dirk Tasche, 2015. "The Two Defaults Scenario for Stressing Credit Portfolio Loss Distributions," JRFM, MDPI, vol. 9(1), pages 1-18, December.
    • Handle: RePEc:gam:jjrfmx:v:9:y:2015:i:1:p:1-:d:61528
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    References listed on IDEAS

    as
    1. Ruodu Wang & Liang Peng & Jingping Yang, 2015. "CreditRisk Model with Dependent Risk Factors," North American Actuarial Journal, Taylor & Francis Journals, vol. 19(1), pages 24-40, January.
    2. Stefan Gerhold & Uwe Schmock & Richard Warnung, 2010. "A generalization of Panjer’s recursion and numerically stable risk aggregation," Finance and Stochastics, Springer, vol. 14(1), pages 81-128, January.
    3. Bernd Engelmann & Robert Rauhmeier (ed.), 2011. "The Basel II Risk Parameters," Springer Books, Springer, number 978-3-642-16114-8, March.
    4. Paul Embrechts & Marco Frei, 2009. "Panjer recursion versus FFT for compound distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 497-508, July.
    5. Vandendorpe, Antoine & Ho, Ngoc-Diep & Vanduffel, Steven & Van Dooren, Paul, 2008. "On the parameterization of the CreditRisk + model for estimating credit portfolio risk," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 736-745, April.
    6. Norbert Jobst & Dirk Tasche, 2010. "Capital allocation for credit portfolios under normal and stressed market conditions," Papers 1009.5401, arXiv.org, revised Mar 2012.
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