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Value-at-Risk and expected shortfall for rare events

Author

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  • Mittnik, Stefan
  • Yener, Tina

Abstract

We show that the use of correlations for modeling dependencies may lead to counterintuitive behavior of risk measures, such as Value-at-Risk (VaR) and Expected Short- fall (ES), when the risk of very rare events is assessed via Monte-Carlo techniques. The phenomenon is demonstrated for mixture models adapted from credit risk analysis as well as for common Poisson-shock models used in reliability theory. An obvious implication of this finding pertains to the analysis of operational risk. The alleged incentive suggested by the New Basel Capital Accord (Basel II), amely decreasing minimum capital requirements by allowing for less than perfect correlation, may not necessarily be attainable.

Suggested Citation

  • Mittnik, Stefan & Yener, Tina, 2008. "Value-at-Risk and expected shortfall for rare events," CFS Working Paper Series 2008/14, Center for Financial Studies (CFS).
    • Handle: RePEc:zbw:cfswop:200814
    as

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    File URL: https://www.econstor.eu/bitstream/10419/25549/1/577548247.PDF
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    References listed on IDEAS

    as
    1. Lindskog, Filip & McNeil, Alexander J., 2003. "Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling," ASTIN Bulletin, Cambridge University Press, vol. 33(2), pages 209-238, November.
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    More about this item

    Keywords

    Operational Risk; Latent Variables; Correlated Events;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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