Extreme value theory and Value-at-Risk: Relative performance in emerging markets

In this paper, we investigate the relative performance of Value-at-Risk (VaR) models with the daily stock market returns of nine different emerging markets. In addition to well-known modeling approaches, such as variance–covariance method and historical simulation, we study the extreme value theory (EVT) to generate VaR estimates and provide the tail forecasts of daily returns at the 0.999 percentile along with 95% confidence intervals for stress testing purposes. The results indicate that EVT-based VaR estimates are more accurate at higher quantiles. According to estimated Generalized Pareto Distribution parameters, certain moments of the return distribution do not exist in some countries. In addition, the daily return distributions have different moment properties at their right and left tails. Therefore, risk and reward are not equally likely in these economies.