A conditional heteroscedastic VaR approach with alternative distributions

Abstract

Objective: The purpose of this paper is to explore different distributions in conditional Value at Risk (VaR) modeling as an option in the Mexican market. Methodology: We estimate a GARCH model under the Gaussian, Normal Inverse Gaussian, Skew Generalized t and the Stable distribution assumption, then we implement the model in predicting one-day ahead VaR, and finally we examine the performance among the four VaR models during a period of high volatility. Results: The backtesting result confirms that the stable-VaR approach outperforms the other models in the VaR's prediction at a 99% confidence level. Limitations: Although the VaR is a widely used risk measure, it is not a coherent risk measure, for this reason, a natural extension of our work should be to estimate the expected shortfall and this may produce different insights. Conclusions: Our findings reveal that models that consider some empirical characteristics of financial returns such as leptokurtic, volatility clustering and asymmetry improve the VaR predicting capacity. This finding is important in the search for more robust approaches for VaR estimates.