IDEAS home Printed from https://ideas.repec.org/p/rdg/icmadp/icma-dp2004-13.html
   My bibliography  Save this paper

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

Author

Listed:
  • Carol Alexandra

    () (ICMA Centre, University of Reading)

  • Emese Lazar

    () (ICMA Centre, University of Reading)

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.

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
    as

    Download full text from publisher

    File URL: http://www.icmacentre.ac.uk/pdf/discussion/DP2004-14.pdf
    Download Restriction: no

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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

    Keywords

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:rdg:icmadp:icma-dp2004-13. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marie Pearson). General contact details of provider: http://edirc.repec.org/data/bsrdguk.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.