The various tools for risk measurement and management, especially for value-at-risk (VaR), are compared, with special emphasis on Japanese market data. Traditional Generalized Autoregressive Conditional Heteroskedasticity (GARCH) -type methods are compared to extreme value theory (EVT). The distribution of extremes, asymmetry, clustering, and the dynamic structure of VaR all count as criteria for comparison of the various methods. We find that the GARCH class of models is not suitable for VaR forecasting for the sample data, due to both the inaccuracy and the high volatility of the VaR forecasts. In contrast, EVT forecasting of VaR resulted in much better VaR estimates, and more importantly, the EVT forecasts were considerably more stable, enhancing their practical applicability for Japanese market risk forecasts.
Keywords: Risk; Regulation; Extreme value theory; Volatility; Value-at-risk
Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.