Forecasting value at risk and expected shortfall using high-frequency data of domestic and international stock markets

This paper first proposes the generalized autoregressive score (GAS) factor X model for predicting Value-at-Risk (VaR) and expected shortfall (ES). This model is flexible for adding explanatory variables (X) that are informative for forecasting extreme risks and thus can improve forecast accuracy of the traditional GAS factor model. Then, to investigate whether high-frequency data of domestic and international stock market are predictive of the extreme risk of Chinese stock market, X is set to be the corresponding realized volatility (RV) of these markets. Empirical studies based on 13 stock markets show that lagged RVs of domestic and influential international markets have prediction ability of extreme risks in Chinese stock market. The RV of the domestic market is more informative than that of international markets, among which the RVs of Asian and US markets are more predictive than European markets. We have also investigated compound information of the RVs of all markets, the results of which show that the mean of RVs is more informative than the first principle component; however, it is less informative than the individual RV of some markets. Additionally, there is no gain in forecast accuracy of the GAS factor RV models by forecast combination.