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Fat Tails and Asymmetry in Financial Volatility Models

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  • Peter Verhoeven

    (School of Economics and Finance, Curtin University of Technology)

  • Michael McAleer

    (Department of Economics, University of Western Australia)

Abstract

Although the GARCH model has been quite successful in capturing important empirical aspects of financial data, particularly for the symmetric effects of volatility, it has had far less success in capturing the effects of extreme observations, outliers and skewness in returns. This paper examines the GARCH model under various non-normal error distributions in order to evaluate skewness and leptokurtosis. The empirical results show that GARCH models estimated using asymmetric leptokurtic distributions are superior to their counterparts estimated under normality, in terms of: (i) capturing skewness and leptokurtosis; (ii) the maximized log-likelihood values; and (iii) isolating the ARCH and GARCH parameter estimates from the adverse effects of outliers. Overall, the flexible asymmetric Student-t distribution performs best in terms of capturing the non-normal aspects of the data.

Suggested Citation

  • Peter Verhoeven & Michael McAleer, 2003. "Fat Tails and Asymmetry in Financial Volatility Models," CIRJE F-Series CIRJE-F-211, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2003cf211
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    3. Yuichi Nagahara, 2011. "Using Nonnormal Distributions to Analyze the Relationship Between Stock Returns in Japan and the US," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(4), pages 429-443, November.
    4. Sylvia J. Soltyk & Felix Chan, 2023. "Modeling time‐varying higher‐order conditional moments: A survey," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 33-57, February.
    5. F. Pizzutilo, 2012. "The behaviour of the distributions of stock returns: an analysis of the European market using the Pearson system of continuous probability distributions," Applied Financial Economics, Taylor & Francis Journals, vol. 22(20), pages 1743-1752, October.
    6. Hayette Gatfaoui, 2010. "Investigating the dependence structure between credit default swap spreads and the U.S. financial market," Annals of Finance, Springer, vol. 6(4), pages 511-535, October.
    7. Javed Farrukh & Podgórski Krzysztof, 2014. "Leverage Effect for Volatility with Generalized Laplace Error," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 157-166, December.
    8. Gamini Premaratne & Prabhath Jayasinghe, 2005. "Exchange rate exposure of stock returns at firm level," International Finance 0503004, University Library of Munich, Germany.
    9. Fulvio Corsi & Stefan Mittnik & Christian Pigorsch & Uta Pigorsch, 2008. "The Volatility of Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 46-78.
    10. Andrés Mora-Valencia & Trino-Manuel Ñíguez & Javier Perote, 2017. "Multivariate approximations to portfolio return distribution," Computational and Mathematical Organization Theory, Springer, vol. 23(3), pages 347-361, September.
    11. Gatfaoui, Hayette, 2017. "Equity market information and credit risk signaling: A quantile cointegrating regression approach," Economic Modelling, Elsevier, vol. 64(C), pages 48-59.
    12. Yuichi Nagahara, 2008. "A Method of Calculating the Downside Risk by Multivariate Nonnormal Distributions," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 15(3), pages 175-184, December.
    13. Amélie Charles, 2008. "Forecasting volatility with outliers in GARCH models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(7), pages 551-565.
    14. Meade, Nigel, 2010. "Oil prices -- Brownian motion or mean reversion? A study using a one year ahead density forecast criterion," Energy Economics, Elsevier, vol. 32(6), pages 1485-1498, November.
    15. Zhu, Ke & Li, Wai Keung, 2013. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52344, University Library of Munich, Germany.
    16. McAleer, Michael & Chan, Felix & Marinova, Dora, 2007. "An econometric analysis of asymmetric volatility: Theory and application to patents," Journal of Econometrics, Elsevier, vol. 139(2), pages 259-284, August.
    17. Hayette Gatfaoui, 2010. "Capital Asset Pricing Model," Post-Print hal-00589904, HAL.
    18. Del Brio, Esther B. & Perote, Javier, 2012. "Gram–Charlier densities: Maximum likelihood versus the method of moments," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 531-537.
    19. Park, Jeong-Soo, 2005. "A simulation-based hyperparameter selection for quantile estimation of the generalized extreme value distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(4), pages 227-234.
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    21. Gatfaoui, Hayette, 2013. "Translating financial integration into correlation risk: A weekly reporting's viewpoint for the volatility behavior of stock markets," Economic Modelling, Elsevier, vol. 30(C), pages 776-791.

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