IDEAS home Printed from https://ideas.repec.org/a/wly/jmoncb/v39y2007i7p1613-1649.html
   My bibliography  Save this article

A Generalized Extreme Value Approach to Financial Risk Measurement

Author

Listed:
  • TURAN G. BALI

Abstract

This paper develops an unconditional and conditional extreme value approach to calculating value at risk (VaR), and shows that the maximum likely loss of financial institutions can be more accurately estimated using the statistical theory of extremes. The new approach is based on the distribution of extreme returns instead of the distribution of all returns and provides good predictions of catastrophic market risks. Both the in‐sample and out‐of‐sample performance results indicate that the Box–Cox generalized extreme value distribution introduced in the paper performs surprisingly well in capturing both the rate of occurrence and the extent of extreme events in financial markets. The new approach yields more precise VaR estimates than the normal and skewed t distributions.

Suggested Citation

  • Turan G. Bali, 2007. "A Generalized Extreme Value Approach to Financial Risk Measurement," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1613-1649, October.
    • Handle: RePEc:wly:jmoncb:v:39:y:2007:i:7:p:1613-1649
    DOI: 10.1111/j.1538-4616.2007.00081.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1538-4616.2007.00081.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1538-4616.2007.00081.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Francis X. Diebold & Til Schuermann & John D. Stroughair, 2000. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 1(2), pages 30-35, January.
    2. Jeremy Berkowitz & James O'Brien, 2002. "How Accurate Are Value‐at‐Risk Models at Commercial Banks?," Journal of Finance, American Finance Association, vol. 57(3), pages 1093-1111, June.
    3. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    4. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    5. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    6. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    7. Turan G. Bali, 2003. "An Extreme Value Approach to Estimating Volatility and Value at Risk," The Journal of Business, University of Chicago Press, vol. 76(1), pages 83-108, January.
    8. Peter F. Christoffersen & Francis X. Diebold, 2000. "How Relevant is Volatility Forecasting for Financial Risk Management?," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 12-22, February.
    9. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    10. Bali, Turan G. & Weinbaum, David, 2007. "A conditional extreme value volatility estimator based on high-frequency returns," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 361-397, February.
    11. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    12. 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.
    13. Bali, Turan G. & Neftci, Salih N., 2003. "Disturbing extremal behavior of spot rate dynamics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 455-477, September.
    14. Loistl, Otto, 1976. "The Erroneous Approximation of Expected Utility by Means of a Taylor's Series Expansion: Analytic and Computational Results," American Economic Review, American Economic Association, vol. 66(5), pages 904-910, December.
    15. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    16. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    17. Scott, Robert C & Horvath, Philip A, 1980. "On the Direction of Preference for Moments of Higher Order Than the Variance," Journal of Finance, American Finance Association, vol. 35(4), pages 915-919, September.
    18. Black, Fischer, 1972. "Capital Market Equilibrium with Restricted Borrowing," The Journal of Business, University of Chicago Press, vol. 45(3), pages 444-455, July.
    19. Longin, Francois M., 2000. "From value at risk to stress testing: The extreme value approach," Journal of Banking & Finance, Elsevier, vol. 24(7), pages 1097-1130, July.
    20. Arzac, Enrique R. & Bawa, Vijay S., 1977. "Portfolio choice and equilibrium in capital markets with safety-first investors," Journal of Financial Economics, Elsevier, vol. 4(3), pages 277-288, May.
    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. Farkas, Walter & Fringuellotti, Fulvia & Tunaru, Radu, 2020. "A cost-benefit analysis of capital requirements adjusted for model risk," Journal of Corporate Finance, Elsevier, vol. 65(C).
    2. Julia S. Mehlitz & Benjamin R. Auer, 2021. "Time‐varying dynamics of expected shortfall in commodity futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(6), pages 895-925, June.
    3. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    4. Madhusudan Karmakar, 2013. "Estimation of tail‐related risk measures in the Indian stock market: An extreme value approach," Review of Financial Economics, John Wiley & Sons, vol. 22(3), pages 79-85, September.
    5. Rizwan, Muhammad Suhail & Ahmad, Ghufran & Ashraf, Dawood, 2020. "Systemic risk: The impact of COVID-19," Finance Research Letters, Elsevier, vol. 36(C).
    6. Aranit Muja, 2018. "Extreme Value of Intraday Returns," Academic Journal of Interdisciplinary Studies, Richtmann Publishing Ltd, vol. 7, November.
    7. Sahibzada, Irfan Ullah & Rizwan, Muhammad Suhail & Qureshi, Anum, 2022. "Impact of sovereign credit ratings on systemic risk and the moderating role of regulatory reforms: An international investigation," Journal of Banking & Finance, Elsevier, vol. 145(C).
    8. Hamid Mohtadi & Bryan S. Weber, 2021. "Catastrophe And Rational Policy: Case Of National Security," Economic Inquiry, Western Economic Association International, vol. 59(1), pages 140-161, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Benjamin R. Auer & Benjamin Mögel, 2016. "How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?," CESifo Working Paper Series 6288, CESifo.
    2. Benjamin Mögel & Benjamin R. Auer, 2018. "How accurate are modern Value-at-Risk estimators derived from extreme value theory?," Review of Quantitative Finance and Accounting, Springer, vol. 50(4), pages 979-1030, May.
    3. Turan Bali & Panayiotis Theodossiou, 2007. "A conditional-SGT-VaR approach with alternative GARCH models," Annals of Operations Research, Springer, vol. 151(1), pages 241-267, April.
    4. Bali, Turan G. & Mo, Hengyong & Tang, Yi, 2008. "The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 269-282, February.
    5. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    6. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    7. Chebbi, Ali & Hedhli, Amel, 2022. "Revisiting the accuracy of standard VaR methods for risk assessment: Using the Copula–EVT multidimensional approach for stock markets in the MENA region," The Quarterly Review of Economics and Finance, Elsevier, vol. 84(C), pages 430-445.
    8. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    9. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    10. Bali, Turan G. & Weinbaum, David, 2007. "A conditional extreme value volatility estimator based on high-frequency returns," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 361-397, February.
    11. Gordy, Michael B. & McNeil, Alexander J., 2020. "Spectral backtests of forecast distributions with application to risk management," Journal of Banking & Finance, Elsevier, vol. 116(C).
    12. Allen, Linda & Bali, Turan G., 2007. "Cyclicality in catastrophic and operational risk measurements," Journal of Banking & Finance, Elsevier, vol. 31(4), pages 1191-1235, April.
    13. DAVID G. McMILLAN & ALAN E. H. SPEIGHT, 2007. "Value‐at‐Risk in Emerging Equity Markets: Comparative Evidence for Symmetric, Asymmetric, and Long‐Memory GARCH Models," International Review of Finance, International Review of Finance Ltd., vol. 7(1‐2), pages 1-19, March.
    14. Wong, Woon K., 2010. "Backtesting value-at-risk based on tail losses," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 526-538, June.
    15. Ibrahim Ergen, 2015. "Two-step methods in VaR prediction and the importance of fat tails," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 1013-1030, June.
    16. Manel Youssef & Lotfi Belkacem & Khaled Mokni, 2015. "Extreme Value Theory and long-memory-GARCH Framework: Application to Stock Market," International Journal of Economics and Empirical Research (IJEER), The Economics and Social Development Organization (TESDO), vol. 3(8), pages 371-388, August.
    17. Chen, Qian & Gerlach, Richard & Lu, Zudi, 2012. "Bayesian Value-at-Risk and expected shortfall forecasting via the asymmetric Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3498-3516.
    18. Li, Longqing, 2017. "A Comparative Study of GARCH and EVT Model in Modeling Value-at-Risk," MPRA Paper 85645, University Library of Munich, Germany.
    19. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-544, National Bureau of Economic Research, Inc.
    20. Lazar, Emese & Zhang, Ning, 2019. "Model risk of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 74-93.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jmoncb:v:39:y:2007:i:7:p:1613-1649. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0022-2879 .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.