Managing extreme risk in some major stock markets: An extreme value approach

The study investigates the relative performance of Value-at-Risk (VaR) models using daily share price index data from six different countries across Asia, Europe and the United States for a period of 10 years from January 01, 2000 to December 31, 2009. The main emphasis of the study has been given to Extreme Value Theory (EVT) and to evaluate how well Conditional EVT model performs in modeling tails of distributions and in estimating and forecasting VaR measures. We have followed McNeil and Frey's (2000) two stage approach called Conditional EVT to estimate dynamic VaR. In stage 1, we model the conditional volatility of each series using an appropriate asymmetric GARCH model which serves to filter the return series such that the asymmetric GARCH residuals are closer to iid than the raw return series. In stage 2, we apply EVT to model the fat tails of the asymmetric GARCH residuals. We have compared the accuracy of Conditional EVT approach to VaR estimation with other competing models. The best performing model is found to be the Conditional EVT for the entire sample. To confirm whether the Conditional EVT would still be the best for a sub-period, we have compared the forecasting accuracy for the sub-sample of bull market. Here too the Conditional EVT maintains its superiority even more precisely. Since the Conditional EVT approach clearly dominates other competing models in terms of VaR forecasting, we would advocate the use of the model when managing tail related market risk in such equity markets.