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A Comparison of VaR Estimation Procedures for Leptokurtic Equity Index Returns


  • Bhattacharyya, Malay
  • Madhav R, Siddarth


The paper presents and tests Dynamic Value at Risk (VaR) estimation procedures for equity index returns. Volatility clustering and leptokurtosis are well-documented characteristics of such time series. An ARMA (1, 1)-GARCH (1, 1) ap- proach models the inherent autocorrelation and dynamic volatility. Fat-tailed behavior is modeled in two ways. In the first approach, the ARMA-GARCH process is run assuming alternatively that the standardized residuals are distributed with Pearson Type IV, Johnson SU, Manly’s exponential transformation, normal and t-distributions. In the second ap- proach, the ARMA-GARCH process is run with the pseudo-normal assumption, the parameters calculated with the pseudo maximum likelihood procedure, and the standardized residuals are later alternatively modeled with Mixture of Normal distributions, Extreme Value Theory and other power transformations such as John-Draper, Bickel-Doksum, Manly, Yeo-Johnson and certain combinations of the above. The first approach yields five models, and the second ap- proach yields nine. These are tested with six equity index return time series using rolling windows. These models are compared by computing the 99%, 97.5% and 95% VaR violations and contrasting them with the expected number of violations.

Suggested Citation

  • Bhattacharyya, Malay & Madhav R, Siddarth, 2012. "A Comparison of VaR Estimation Procedures for Leptokurtic Equity Index Returns," MPRA Paper 54189, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:54189

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    References listed on IDEAS

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    4. Bhattacharyya, Malay & Chaudhary, Abhishek & Yadav, Gaurav, 2008. "Conditional VaR estimation using Pearson's type IV distribution," European Journal of Operational Research, Elsevier, vol. 191(2), pages 386-397, December.
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    12. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Luiz Vitiello & Ser-Huang Poon, 2014. "Non-monotonic pricing kernel and an extended class of mixture of distributions for option pricing," Review of Derivatives Research, Springer, vol. 17(2), pages 241-259, July.

    More about this item


    Dynamic VaR; GARCH; EVT; Johnson SU; Pearson Type IV; Mixture of Normal Distributions; Manly; John Draper; Yeo-Johnson Transformations;

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics


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