Risk model validation for BRICS countries: a value-at-risk, expected shortfall and extreme value theory approach

In this paper, we employ value-at-risk (VaR) and expected shortfall (ES) as risk measures to assess the competency of several volatility models, based on the stock indexes of the BRICS countries (Brazil, Russia, India, China and South Africa) after the financial crisis. The aim is to determine the most appropriate model for each country and identify a set of common models for the BRICS countries. A family of generalized autoregressive conditional heteroscedasticity (GARCH) models, extreme value theory (EVT) and a dynamic bivariate technique are considered to demonstrate different volatility dynamics. Some models are ruled out under the presented back-testing operations, while the nonrejected models are ranked using two loss functions. In spite of returns displaying large kurtosis, the models with normal innovation generally prove to have better estimates of VaR and ES. GARCH and fractionally integrated GARCH are preferred by Brazil and Russia, while India favors dual models and the Student t distribution. The Glosten, Jagannathan and Runkle GARCH-N is the best model for South Africa, which is the only country that rejects the stationary EVT approach. Despite these contrasting results, we find that it is possible to obtain more than one model that can be used to model all of the BRICS countries: these are the integrated GARCH-N and exponential GARCH-EVT approaches.