Value at Risk Estimation in the Mexican Stock Exchange: A Comparison of Empirical Distributions
Value at Risk Estimation in the Mexican Stock Exchange: A Comparison of Empirical Distributions

Summary/Abstract: The objective of this paper is to address the issue of VaR model selection for the Mexican equity market. To this end, we consider the family of stable distributions in VaR modeling as an alternative in the Mexican financial market and its performance is compared with the normal, NIG, GLD and GST estimations. We directed a statistical analysis to compare the suitability of these five distributions on the equity stock returns during a period of high volatility. The approaches are based on the maximum likelihood estimation of the parameters of a distribution. The estimation of the conditional variance of returns is based on the GARGH model with the innovation of α-stable, GST, GLD and NIG distributions to describe returns. In addition, the predictive power of the heteroscedasticity in VaR models is tested using the so called back testing and the Kupiec likelihood ratio test. The statistical results showed evidence that the α-stable model provides superior fit in modeling VaR at high confidence levels. In contrast, stable modeling is not satisfactory at low confidence level.

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