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 innovations, we characterize the limiting distribution of an estimator of the conditional Value-at-Risk (VaR), which corresponds to the extremal quantile of the conditional distribution of the GARCH process. We propose two methods, the normal approximation method and the data tilting method, for constructing confidence intervals for the conditional VaR estimator and assess their accuracies by simulation studies. Finally, we apply the proposed approach to an energy market data set.