IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-01317391.html
   My bibliography  Save this paper

Measuring risks in the extreme tail: The extreme VaR and its confidence interval

Author

Listed:
  • Dominique Guegan

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Bertrand Hassani

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Kehan Li

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

Contrary to the current regulatory trend concerning extreme risks, the purpose of this paper is to emphasize the necessity of considering the Value-at-Risk (VaR) with extreme confidence levels like 99.9%, as an alternative way to measure risks in the "extreme tail". Although the mathematical definition of the extreme VaR is trivial, its computation is challenging in practice, because the uncertainty of the extreme VaR may not be negligible for a finite amount of data. We begin to build confidence intervals around the unknown VaR. We build them using two different approaches, the first using Smirnov's result (Smirnov, 1949 [24]) and the second Zhu and Zhou's result (Zhu and Zhou, 2009 [25]), showing that this last one is robust when we use finite samples. We compare our approach with other methodologies which are based on bootstrapping techniques, Christoffersen et al. (2005) [7], focusing on the estimation of the extreme quantiles of a distribution. Finally, we apply these confidence intervals to perform a stress testing exercice with historical stock returns during financial crisis, for identifying potential violations of the VaR during turmoil periods on financial markets.

Suggested Citation

  • Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Measuring risks in the extreme tail: The extreme VaR and its confidence interval," Post-Print halshs-01317391, HAL.
  • Handle: RePEc:hal:journl:halshs-01317391
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01317391v3
    as

    Download full text from publisher

    File URL: https://halshs.archives-ouvertes.fr/halshs-01317391v3/document
    Download Restriction: no

    References listed on IDEAS

    as
    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Gao, Feng & Song, Fengming, 2008. "ESTIMATION RISK IN GARCH VaR AND ES ESTIMATES," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1404-1424, October.
    3. McAleer, Michael & Jimenez-Martin, Juan-Angel & Perez-Amaral, Teodosio, 2013. "Has the Basel Accord improved risk management during the global financial crisis?," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 250-265.
    4. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    5. Pérignon, Christophe & Smith, Daniel R., 2010. "The level and quality of Value-at-Risk disclosure by commercial banks," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 362-377, February.
    6. Kellner, Ralf & Rösch, Daniel, 2016. "Quantifying market risk with Value-at-Risk or Expected Shortfall? – Consequences for capital requirements and model risk," Journal of Economic Dynamics and Control, Elsevier, vol. 68(C), pages 45-63.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 137(2), pages 556-576, April.
    9. Koch-Medina, Pablo & Munari, Cosimo, 2016. "Unexpected shortfalls of Expected Shortfall: Extreme default profiles and regulatory arbitrage," Journal of Banking & Finance, Elsevier, vol. 62(C), pages 141-151.
    10. Matthew Pritsker, 1997. "Evaluating Value at Risk Methodologies: Accuracy versus Computational Time," Journal of Financial Services Research, Springer;Western Finance Association, vol. 12(2), pages 201-242, October.
    11. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    12. Halbleib, Roxana & Pohlmeier, Winfried, 2012. "Improving the value at risk forecasts: Theory and evidence from the financial crisis," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1212-1228.
    13. Ivo Francioni & Florian Herzog, 2012. "Probability-unbiased Value-at-Risk estimators," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 755-768, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:halshs-01317391. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.