Interval Estimation of Value-at-Risk Based on GARCH Models with Heavy Tailed Innovations

ARCH and GARCH models are widely used to model financial market volatilities in risk management applications. Considering a GARCH model with heavy-tailed in-novations, we characterize the limiting distribution of an estimator of the conditional Value-at-Risk (VaR), which corresponds to the extremal quantile of the conditional dis-tribution of the GARCH process. We propose two methods, the normal approximation method and the data tilting method, for constructing confidence intervals for the condi-tional VaR estimator and assess their accuracies by simulation studies. Finally, we apply the proposed approach to an energy market data set