A Comparison of VaR Estimation Procedures for Leptokurtic Equity Index Returns

Malay Bhattacharyya and Siddarth Madhav R

MPRA Paper from University Library of Munich, Germany

Abstract: 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.

Keywords: Dynamic VaR; GARCH; EVT; Johnson SU; Pearson Type IV; Mixture of Normal Distributions; Manly; John Draper; Yeo-Johnson Transformations (search for similar items in EconPapers)
JEL-codes: C58 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Published in Journal of Mathematical Finance 1.2(2012): pp. 13-30

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