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A Generalized Extreme Value Approach to Financial Risk Measurement

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  • 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. Copyright 2007 The Ohio State University.

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:mcb:jmoncb:v:39:y:2007:i:7:p:1613-1649
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    Cited by:

    1. Karmakar, Madhusudan, 2013. "Estimation of tail-related risk measures in the Indian stock market: An extreme value approach," Review of Financial Economics, Elsevier, vol. 22(3), pages 79-85.
    2. 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).
    3. Chun-Pin Hsu & Chin-Wen Huang & Wan-Jiun Chiou, 2012. "Effectiveness of copula-extreme value theory in estimating value-at-risk: empirical evidence from Asian emerging markets," Review of Quantitative Finance and Accounting, Springer, vol. 39(4), pages 447-468, November.
    4. 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.
    5. 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.
    6. Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Mitov, Ivan & Fabozzi, Frank J., 2011. "Time series analysis for financial market meltdowns," Journal of Banking & Finance, Elsevier, vol. 35(8), pages 1879-1891, August.
    7. Hussain, Saiful Izzuan & Li, Steven, 2018. "The dependence structure between Chinese and other major stock markets using extreme values and copulas," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 421-437.
    8. 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.
    9. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    10. 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.
    11. Rizwan, Muhammad Suhail & Ahmad, Ghufran & Ashraf, Dawood, 2020. "Systemic risk: The impact of COVID-19," Finance Research Letters, Elsevier, vol. 36(C).
    12. Gatfaoui, Hayette, 2015. "Pricing the (European) option to switch between two energy sources: An application to crude oil and natural gas," Energy Policy, Elsevier, vol. 87(C), pages 270-283.
    13. Tolikas, Konstantinos, 2014. "Unexpected tails in risk measurement: Some international evidence," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 476-493.
    14. Aranit Muja, 2018. "Extreme Value of Intraday Returns," Academic Journal of Interdisciplinary Studies, Richtmann Publishing Ltd, vol. 7, November.
    15. 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.
    16. Li, Longqing, 2017. "A Comparative Study of GARCH and EVT Model in Modeling Value-at-Risk," MPRA Paper 85645, University Library of Munich, Germany.
    17. 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).
    18. 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.
    19. Samet Gunay & Audil Rashid Khaki, 2018. "Best Fitting Fat Tail Distribution for the Volatilities of Energy Futures: Gev, Gat and Stable Distributions in GARCH and APARCH Models," JRFM, MDPI, vol. 11(2), pages 1-19, June.
    20. Basu, Sanjay, 2011. "Comparing simulation models for market risk stress testing," European Journal of Operational Research, Elsevier, vol. 213(1), pages 329-339, August.
    21. Katarina Valaskova & Tomas Kliestik & Lucia Svabova & Peter Adamko, 2018. "Financial Risk Measurement and Prediction Modelling for Sustainable Development of Business Entities Using Regression Analysis," Sustainability, MDPI, vol. 10(7), pages 1-15, June.
    22. Brée, David S. & Joseph, Nathan Lael, 2013. "Testing for financial crashes using the Log Periodic Power Law model," International Review of Financial Analysis, Elsevier, vol. 30(C), pages 287-297.
    23. Hassan A. Fallahgoul & Young S. Kim & Frank J. Fabozzi, 2016. "Elliptical tempered stable distribution," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1069-1087, July.
    24. Lang, Korbinian & Auer, Benjamin R., 2020. "The economic and financial properties of crude oil: A review," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    25. 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.

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