Non-Extensive Value-at-Risk Estimation During Times of Crisis

Value-at-risk is one of the important subjects that extensively used by researchers and practitioners for measuring and managing uncertainty in financial markets. Although value-at-risk is a common risk control instrument, but there are criticisms about its performance. One of these cases, which has been studied in this research, is the value-at-risk underestimation during times of crisis. In these periods, the non-Gaussian behavior of markets intensifies and the estimated value-at-risks by normal models are lower than the real values. In fact, during times of crisis, the probability density of extreme values in financial return series increases and this heavy-tailed behavior of return series reduces the accuracy of the normal value-at-risk estimation models. A potential approach that can be used to describe non-Gaussian behavior of return series, is Tsallis entropy framework and non-extensive statistical methods. In this paper, we have used non-extensive value at risk model for analyzing the behavior of financial markets during times of crisis. By applying q-Gaussian probability density function, we can see a better value-at-risk estimation in comparison with the normal models, especially during times of crisis. We showed that q-Gaussian model estimates value-at-risk better than normal model. Also we saw in the mature markets, it is obvious that the difference of value-at-risk between normal condition and non-extensive approach increase more than one standard deviation during times of crisis, but in the emerging markets we cannot see a specific pattern.