The Best of Two Worlds—Combining Conditional Volatility Models with Extreme Value Theory to Calculate Value at Risk

Abstract: We compare Value at Risk estimates from an AR(1)-GARCH(1,1) model with t- or normally distributed innovations, to estimates from an AR(1)-GARCH(1,1) model where the Peak-Over-Threshold method is applied to the tails of the innovations. Using the Christoffersen backtest, we find that the performance of the second type of model is superior to the first, particularly at high confidence levels for the VaR estimate.