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A Comparison of VaR Estimation Procedures for Leptokurtic Equity Index Returns

Listed author(s):
  • Bhattacharyya, Malay
  • Madhav R, Siddarth
Registered author(s):

    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.

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    File URL: https://mpra.ub.uni-muenchen.de/54189/1/MPRA_paper_54189.pdf
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    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 54189.

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    Date of creation: 2012
    Publication status: Published in Journal of Mathematical Finance 1.2(2012): pp. 13-30
    Handle: RePEc:pra:mprapa:54189
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    1. Kon, Stanley J, 1984. " Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-165, March.
    2. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
    3. Bhattacharyya, Malay & Ritolia, Gopal, 2008. "Conditional VaR using EVT - Towards a planned margin scheme," International Review of Financial Analysis, Elsevier, vol. 17(2), pages 382-395.
    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.
    5. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    6. Ball, Clifford A. & Torous, Walter N., 1983. "A Simplified Jump Process for Common Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(01), pages 53-65, March.
    7. Tucker, Alan L, 1992. "A Reexamination of Finite- and Infinite-Variance Distributions as Models of Daily Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(1), pages 73-81, January.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    10. Malay Bhattacharyya & Nityanand Misra & Bharat Kodase, 2009. "MaxVaR for non-normal and heteroskedastic returns," Quantitative Finance, Taylor & Francis Journals, vol. 9(8), pages 925-935.
    11. Hamilton, James D, 1991. "A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 27-39, January.
    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..
    13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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