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A Comparative Study of GARCH and EVT Model in Modeling Value-at-Risk

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  • Li, Longqing

Abstract

The paper addresses an inefficiency of the traditional approach in modeling the tail risk, particularly the 1-day ahead forecast of Value-at-Risk (VaR), using Extreme Value Theory (EVT) and GARCH model. Specifically, I apply both models onto major countries stock markets daily loss, including U.S., U.K., China and Hong Kong between 2006 and 2015, and compare the relative forecasting performance. The paper differs from other studies in two important ways. First, it incorporates an asymmetric shock of volatility in the financial time series. Second, it applies a skewed fat-tailed return distribution using the Generalized Error Distribution (GED). The back-testing result shows that, on one hand, the conditional EVT performs equally well relative to GARCH model under the Generalized Error Distribution. On the other hand, the Exponential GARCH based model is the best performing one in Value-at-Risk forecasting, because it not only correctly identifies the future extreme loss, but more importantly, its occurrence is independent.

Suggested Citation

  • Li, Longqing, 2017. "A Comparative Study of GARCH and EVT Model in Modeling Value-at-Risk," MPRA Paper 85645, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:85645
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    References listed on IDEAS

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    1. Giot, Pierre & Laurent, Sebastien, 2004. "Modelling daily Value-at-Risk using realized volatility and ARCH type models," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 379-398, June.
    2. Marimoutou, Velayoudoum & Raggad, Bechir & Trabelsi, Abdelwahed, 2009. "Extreme Value Theory and Value at Risk: Application to oil market," Energy Economics, Elsevier, vol. 31(4), pages 519-530, July.
    3. 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.
    4. Panayiotis Theodossiou, 2015. "Skewed Generalized Error Distribution of Financial Assets and Option Pricing," Multinational Finance Journal, Multinational Finance Journal, vol. 19(4), pages 223-266, December.
    5. 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.
    6. 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.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Angelidis, Timotheos & Benos, Alexandros & Degiannakis, Stavros, 2004. "The Use of GARCH Models in VaR Estimation," MPRA Paper 96332, University Library of Munich, Germany.
    9. Manfred Gilli & Evis këllezi, 2006. "An Application of Extreme Value Theory for Measuring Financial Risk," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 207-228, May.
    10. Karmakar, Madhusudan & Shukla, Girja K., 2015. "Managing extreme risk in some major stock markets: An extreme value approach," International Review of Economics & Finance, Elsevier, vol. 35(C), pages 1-25.
    11. Kittiakarasakun, Jullavut & Tse, Yiuman, 2011. "Modeling the fat tails in Asian stock markets," International Review of Economics & Finance, Elsevier, vol. 20(3), pages 430-440, June.
    12. Chu-Hsiung Lin & Shan-Shan Shen, 2006. "Can the student-t distribution provide accurate value at risk?," Journal of Risk Finance, Emerald Group Publishing, vol. 7(3), pages 292-300, May.
    13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    14. Allen, David E. & Singh, Abhay K. & Powell, Robert J., 2013. "EVT and tail-risk modelling: Evidence from market indices and volatility series," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 355-369.
    15. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    16. 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.).
    17. Hatice Gaye Gencer & Sercan Demiralay, 2016. "Volatility Modeling and Value-at-Risk (VaR) Forecasting of Emerging Stock Markets in the Presence of Long Memory, Asymmetry, and Skewed Heavy Tails," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 52(3), pages 639-657, March.
    18. 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.
    19. repec:adr:anecst:y:2000:i:60:p:10 is not listed on IDEAS
    20. Jon Danielsson & Casper G. De Vries, 2000. "Value-at-Risk and Extreme Returns," Annals of Economics and Statistics, GENES, issue 60, pages 239-270.
    21. 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.
    22. Bekiros, Stelios D. & Georgoutsos, Dimitris A., 2005. "Estimation of Value-at-Risk by extreme value and conventional methods: a comparative evaluation of their predictive performance," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 15(3), pages 209-228, July.
    23. Fernandez, Viviana, 2005. "Risk management under extreme events," International Review of Financial Analysis, Elsevier, vol. 14(2), pages 113-148.
    24. Paul Embrechts & Sidney Resnick & Gennady Samorodnitsky, 1999. "Extreme Value Theory as a Risk Management Tool," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 30-41.
    25. 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.
    26. Ahmed Ghorbel & Abdelwahed Trabelsi, 2008. "Predictive performance of conditional Extreme Value Theory in Value-at-Risk estimation," International Journal of Monetary Economics and Finance, Inderscience Enterprises Ltd, vol. 1(2), pages 121-148.
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    Cited by:

    1. Krzysztof Echaust & Małgorzata Just, 2020. "Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
    2. Krzysztof Echaust & Małgorzata Just, 2021. "Tail Dependence between Crude Oil Volatility Index and WTI Oil Price Movements during the COVID-19 Pandemic," Energies, MDPI, vol. 14(14), pages 1-21, July.
    3. Amiri , Hossein & Najafi Nejad , Mahmood & Mousavi , Seyede Mohadese, 2021. "Estimation of Value at Risk (VaR) Based On Lévy-GARCH Models: Evidence from Tehran Stock Exchange," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 16(2), pages 165-186, June.

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    More about this item

    Keywords

    Value-at-Risk; Extreme Value Theory; Backtesting; Risk Forecasting;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • 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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