Value at Risk using an α-Stable Conditional Heterocedastic Model

Abstract

The aim of this research is to describe and compare the estimation of Value at Risk (VaR), considering a univariate GARCH model with the innovation of the a-stable distribution. The statistical results suggest that the a-stable VaR model provides more accurate VaR estimations than the traditional Gaussian model, which significantly underestimates VaR in periods of high volatility. In contrast, in the post-crisis period, VaR at 95% under the Gaussian hypothesis shows acceptable results, and that obtained under the a-stable model is below the admissible range. The main contribution of this research is that it proposes an alternative conditional distribution for asset price yields in the Mexican financial market, considering a GARCH model with the innovation of the a-stable distribution. Finally, this research provides evidence that the a-stable VaR model satisfactorily estimates the VaR for high levels of confidence even in periods of high volatility. In contrast, in periods of relative financial tranquility for low confidence levels, this model overestimates potential losses.