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EVT and tail-risk modelling: Evidence from market indices and volatility series

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  • Allen, David E.
  • Singh, Abhay K.
  • Powell, Robert J.
Abstract
Value-at-Risk (VaR) has become the universally accepted risk metric adopted internationally under the Basel Accords for banking industry internal control, capital adequacy and regulatory reporting. The recent extreme financial market events such as the Global Financial Crisis (GFC) commencing in 2007 and the following developments in European markets mean that there is a great deal of attention paid to risk measurement and risk hedging. In particular, to risk indices and attached derivatives as hedges for equity market risk. The techniques used to model tail risk such as VaR have attracted criticism for their inability to model extreme market conditions. In this paper we discuss tail specific distribution based Extreme Value Theory (EVT) and evaluate different methods that may be used to calculate VaR ranging from well known econometrics models of GARCH and its variants to EVT based models which focus specifically on the tails of the distribution. We apply Univariate Extreme Value Theory to model extreme market risk for the FTSE100 UK Index and S&P-500 US markets indices plus their volatility indices. We show with empirical evidence that EVT can be successfully applied to financial market return series for predicting static VaR, CVaR or Expected Shortfall (ES) and also daily VaR and ES using a GARCH(1,1) and EVT based dynamic approach to these various indices. The behaviour of these indices in their tails have implications for hedging strategies in extreme market conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecofin:v:26:y:2013:i:c:p:355-369
    DOI: 10.1016/j.najef.2013.02.010
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    3. Sharif Mozumder & Arafatur Rahman, 2016. "Market Risk Of Investment In Us Subprime Crisis: Comparison Of A Pure Diffusion And A Pure Jump Model," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 1-17, September.
    4. Candia, Claudio & Herrera, Rodrigo, 2024. "An empirical review of dynamic extreme value models for forecasting value at risk, expected shortfall and expectile," Journal of Empirical Finance, Elsevier, vol. 77(C).
    5. Aloui, Chaker & Hamida, Hela ben, 2014. "Modelling and forecasting value at risk and expected shortfall for GCC stock markets: Do long memory, structural breaks, asymmetry, and fat-tails matter?," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 349-380.
    6. Chia-Lin Chang & Allen, David & McAleer, Michael, 2013. "Recent developments in financial economics and econometrics: An overview," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 217-226.
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    8. Roni Bhowmik & Wu Chao & Jewel Roy Kumar & Wang Shouyang, 2017. "A Study on the Volatility of the Bangladesh Stock Market — Based on GARCH Type Models," Journal of Systems Science and Information, De Gruyter, vol. 5(3), pages 193-215, June.
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    10. Su, Jung-Bin, 2014. "Empirical analysis of long memory, leverage, and distribution effects for stock market risk estimates," The North American Journal of Economics and Finance, Elsevier, vol. 30(C), pages 1-39.
    11. Srilakshminarayana Gali, 2021. "The Behavior of Extreme and Cumulative Stock Price Random Variables during the Crisis Periods-A Study of Nifty 50 Stocks," Economic Research Guardian, Weissberg Publishing, vol. 11(1), pages 103-129, June.
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    13. Santanu Dutta & Tushar Kanti Powdel, 2023. "Modeling Long Term Return Distribution and Nonparametric Market Risk Estimation," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 257-289, May.
    14. Ahmed, Rizwan & Chaudhry, Sajid M. & Kumpamool, Chamaiporn & Benjasak, Chonlakan, 2022. "Tail risk, systemic risk and spillover risk of crude oil and precious metals," Energy Economics, Elsevier, vol. 112(C).
    15. Feria-Domínguez, José Manuel & Jiménez-Rodríguez, Enrique & Sholarin, Ola, 2015. "Tackling the over-dispersion of operational risk: Implications on capital adequacy requirements," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 206-221.
    16. Liu, Yanxin & Li, Johnny Siu-Hang & Ng, Andrew Cheuk-Yin, 2015. "Option pricing under GARCH models with Hansen's skewed-t distributed innovations," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 108-125.

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    Keywords

    VaR; EVT; CVaR; ES;
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