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Autoregressive Conditional Volatility, Skewness And Kurtosis

Author

Listed:
  • Ángel León

    (Universidad de Alicante)

  • Gonzalo Rubio

    (Universidad del País Vasco)

  • Gregorio Serna

    (Universidad de Castilla-La Mancha)

Abstract

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram-Charlier series expansion of the normal density function for the error term, which is easier to estimate than the non-central t distribution proposed by Harvey and Siddique (1999). Moreover, this approach accounts for time-varying skewness and kurtosis while the approach by Harvey and Siddique (1999) only accounts for nonnormal skewness. We apply this method to daily returns of a variety of stock indices and exchange rates. Our results indicate a significant presence of conditional skewness and kurtosis. It is also found that specifications allowing for time-varying skewness and kurtosis outperform specifications with constant third and fourth moments.

Suggested Citation

  • Ángel León & Gonzalo Rubio & Gregorio Serna, 2004. "Autoregressive Conditional Volatility, Skewness And Kurtosis," Working Papers. Serie AD 2004-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    • Handle: RePEc:ivi:wpasad:2004-13
    as

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    File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2004-13.pdf
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    References listed on IDEAS

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    4. ROCKINGER, Michael & JONDEAU, Eric, 2000. "Conditional Volatility, Skewness, and Kurtosis : Existence and Persistence," HEC Research Papers Series 710, HEC Paris.
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    8. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Trino-Manuel Niguez & Javier Perote, 2004. "Forecasting the density of asset returns," STICERD - Econometrics Paper Series 479, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Krishnakumar, Jaya & Kabili, Andi & Roko, Ilir, 2012. "Estimation of SEM with GARCH errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3153-3181.
    3. Mantalos, Panagiotis & Karagrigoriou, Alex, 2012. "Testing For Skewness In Ar Conditional Volatility Models For Financial Return Series," Working Papers 2012:4, Örebro University, School of Business.
    4. Mouna Abbes, 2013. "Does Overconfidence Bias Explain Volatility During the Global Financial Crisis?," Transition Studies Review, Springer;Central Eastern European University Network (CEEUN), vol. 19(3), pages 291-312, February.
    5. Gurjeet Dhesi & Bilal Shakeel & Marcel Ausloos, 2021. "Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach," Annals of Operations Research, Springer, vol. 299(1), pages 1397-1410, April.

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    More about this item

    Keywords

    Conditional volatility; skewness and kurtosis; Gram-Charlier series expansion; Stock indices.;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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