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The Equity Index Skew, Market Crashes and Asymmetric Normal Mixture GARCH

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Author Info

  • Carol Alexandra

    ()
    (ICMA Centre, University of Reading)

  • Emese Lazar

    ()
    (ICMA Centre, University of Reading)

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    Abstract

    The skewness in physical distributions of equity index returns and the implied volatility skew in the risk-neutral measure are subjects of extensive academic research. Much attention is now being focused on models that are able to capture time-varying conditional skewness and kurtosis. For this reason normal mixture GARCH(1,1) models have become very popular in financial econometrics. We introduce further asymmetries into this class of models by modifying the GARCH(1,1) variance processes to skewed variance processes with leverage effects. These asymmetric normal mixture GARCH models can differentiate between two different sources of asymmetry: a persistent asymmetry due to the different means in the conditional normal mixture distributions, and a dynamic asymmetry (the leverage effect) due to the skewed GARCH processes. Empirical results on five major equity indices first employ many statistical criteria to determine whether asymmetric (GJR and AGARCH) normal mixture GARCH models can improve on asymmetric normal and Student’s-t GARCH specifications. These models were also used to simulate implied volatility smiles for the S&P index, and we find that much the most realistic skews are obtained from a GARCH model with a mixture of two GJR variance components.

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    File URL: http://www.icmacentre.ac.uk/pdf/discussion/DP2004-14.pdf
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    Bibliographic Info

    Paper provided by Henley Business School, Reading University in its series ICMA Centre Discussion Papers in Finance with number icma-dp2004-13.

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    Length: 31 pages
    Date of creation: Oct 2004
    Date of revision:
    Handle: RePEc:rdg:icmadp:icma-dp2004-13

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    Related research

    Keywords: GARCH process; normal misture; equity skew; market crash; skew persistence; leverage effect;

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    Cited by:
    1. Giannikis, D. & Vrontos, I.D. & Dellaportas, P., 2008. "Modelling nonlinearities and heavy tails via threshold normal mixture GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1549-1571, January.

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