heteroskedasticity (GARCH) models capture extreme events in stock market returns. We estimate Hill's tail indexes for individual S&P 500 … stock market returns ranging from 1995-2014 and compare these to the tail indexes produced by simulating GARCH models. Our … results suggest that actual and simulated values differ greatly for GARCH models with normal conditional distributions, which …

influential for Value at Risk (VaR) performance than the conditional volatility specification. We also show that some recently … proposed asymmetric probability distributions and the APARCH and FGARCH volatility specifications beat more standard … alternatives for VaR forecasting, and they should be preferred when estimating tail risk. The flexibility of the free power …