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Extreme value theory versus traditional GARCH approaches applied to financial data: a comparative evaluation

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  • Dolores Furió
  • Francisco J. Climent

Abstract

Although stock prices fluctuate, the variations are relatively small and are frequently assumed to be normally distributed on a large time scale. But sometimes these fluctuations can become determinant, especially when unforeseen large drops in asset prices are observed that could result in huge losses or even in market crashes. The evidence shows that these events happen far more often than would be expected under the generalised assumption of normally distributed financial returns. Thus it is crucial to model distribution tails properly so as to be able to predict the frequency and magnitude of extreme stock price returns. In this paper we follow the approach suggested by McNeil and Frey in 2000 and combine GARCH-type models with the extreme value theory to estimate the tails of three financial index returns -- S&P 500, FTSE 100 and NIKKEI 225 -- representing three important financial areas in the world. Our results indicate that EVT-based conditional quantile estimates are more accurate than those from conventional GARCH models assuming normal or Student's t distribution innovations when doing not only in-sample but also out-of-sample estimation. Moreover, these results are robust to alternative GARCH model specifications. The findings of this paper should be useful to investors in general, since their goal is to be able to forecast unforeseen price movements and take advantage of them by positioning themselves in the market according to these predictions.

Suggested Citation

  • Dolores Furió & Francisco J. Climent, 2013. "Extreme value theory versus traditional GARCH approaches applied to financial data: a comparative evaluation," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 45-63, January.
  • Handle: RePEc:taf:quantf:v:13:y:2013:i:1:p:45-63
    DOI: 10.1080/14697688.2012.696679
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    References listed on IDEAS

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    1. Danielsson, Jon & Morimoto, Yuji, 2000. "Forecasting Extreme Financial Risk: A Critical Analysis of Practical Methods for the Japanese Market," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 18(2), pages 25-48, December.
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    Cited by:

    1. H. Kaibuchi & Y. Kawasaki & G. Stupfler, 2022. "GARCH-UGH: a bias-reduced approach for dynamic extreme Value-at-Risk estimation in financial time series," Quantitative Finance, Taylor & Francis Journals, vol. 22(7), pages 1277-1294, July.
    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. Seyfi, Seyed Mohammad Sina & Sharifi, Azin & Arian, Hamidreza, 2021. "Portfolio Value-at-Risk and expected-shortfall using an efficient simulation approach based on Gaussian Mixture Model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1056-1079.
    4. Robert J. Powell & Duc H. Vo & Thach N. Pham, 2018. "Do Nonparametric Measures of Extreme Equity Risk Change the Parametric Ordinal Ranking? Evidence from Asia," Risks, MDPI, vol. 6(4), pages 1-22, October.
    5. Seyed Mohammad Sina Seyfi & Azin Sharifi & Hamidreza Arian, 2020. "Portfolio Risk Measurement Using a Mixture Simulation Approach," Papers 2011.07994, arXiv.org.
    6. Viviane Naimy & José-María Montero & Rim El Khoury & Nisrine Maalouf, 2020. "Market Volatility of the Three Most Powerful Military Countries during Their Intervention in the Syrian War," Mathematics, MDPI, vol. 8(5), pages 1-21, May.
    7. Hamidreza Arian & Hossein Poorvasei & Azin Sharifi & Shiva Zamani, 2020. "The Uncertain Shape of Grey Swans: Extreme Value Theory with Uncertain Threshold," Papers 2011.06693, arXiv.org.
    8. 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.
    9. Ra l de Jes s-Guti rrez & Roberto J. Santill n-Salgado, 2019. "Conditional Extreme Values Theory and Tail-related Risk Measures: Evidence from Latin American Stock Markets," International Journal of Economics and Financial Issues, Econjournals, vol. 9(3), pages 127-141.

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