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


  • Carol Alexandra

    () (ICMA Centre, University of Reading)

  • Emese Lazar

    () (ICMA Centre, University of Reading)


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.

Suggested Citation

  • Carol Alexandra & Emese Lazar, 2004. "The Equity Index Skew, Market Crashes and Asymmetric Normal Mixture GARCH," ICMA Centre Discussion Papers in Finance icma-dp2004-13, Henley Business School, Reading University.
  • Handle: RePEc:rdg:icmadp:icma-dp2004-13

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    Cited by:

    1. Xi, Yanhui & Peng, Hui & Qin, Yemei & Xie, Wenbiao & Chen, Xiaohong, 2015. "Bayesian analysis of heavy-tailed market microstructure model and its application in stock markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 141-153.
    2. 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.

    More about this item


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

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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