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GARCH processes with skewed and leptokurtic innovations: Revisiting the Johnson Su case

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  • Simonato, Jean-Guy

Abstract

We revisit the specification of GARCH processes with Johnson Su innovations examined in Choi and Nam [2008. Journal of Empirical Finance 15, 41–63]. This model, allowing for skewed and leptokurtic innovations, has many advantages over well known alternatives. We examine a simpler version of their specification which does not require the introduction of a location parameter. The likelihood function is derived and the model is estimated with the daily returns of six international stock indexes. The results show that the model provides an accurate fit using the past ten years of index returns which include the recent turbulent periods of the sub-prime and European sovereign debt crisis.

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  • Simonato, Jean-Guy, 2012. "GARCH processes with skewed and leptokurtic innovations: Revisiting the Johnson Su case," Finance Research Letters, Elsevier, vol. 9(4), pages 213-219.
    • Handle: RePEc:eee:finlet:v:9:y:2012:i:4:p:213-219
    DOI: 10.1016/j.frl.2012.06.002
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    References listed on IDEAS

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    1. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    2. Choi, Pilsun & Nam, Kiseok, 2008. "Asymmetric and leptokurtic distribution for heteroscedastic asset returns: The SU-normal distribution," Journal of Empirical Finance, Elsevier, vol. 15(1), pages 41-63, January.
    3. Hsieh, David A, 1989. "Modeling Heteroscedasticity in Daily Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 307-317, July.
    4. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    5. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    6. Jen S. Shang & Pandu R. Tadikamalla, 2004. "Modeling Financial Series Distributions: A Versatile Data Fitting Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 231-251.
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    Cited by:

    1. Jean-Guy Simonato & Lars Stentoft, 2015. "Which pricing approach for options under GARCH with non-normal innovations?," CREATES Research Papers 2015-32, Department of Economics and Business Economics, Aarhus University.
    2. Brenda Castillo-Brais & Ángel León & Juan Mora, 2022. "Estimating Value-at-Risk and Expected Shortfall: Do Polynomial Expansions Outperform Parametric Densities?," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    3. Patra, Saswat, 2021. "Revisiting value-at-risk and expected shortfall in oil markets under structural breaks: The role of fat-tailed distributions," Energy Economics, Elsevier, vol. 101(C).
    4. Simon Lalancette & Jean†Guy Simonato, 2017. "The Role of the Conditional Skewness and Kurtosis in VIX Index Valuation," European Financial Management, European Financial Management Association, vol. 23(2), pages 325-354, March.
    5. Peter Bossaerts & Shijie Huang & Nitin Yadav, 2020. "Exploiting Distributional Temporal Difference Learning to Deal with Tail Risk," Risks, MDPI, vol. 8(4), pages 1-20, October.

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    More about this item

    Keywords

    GARCH; Johnson distributions; Skewness; Kurtosis;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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