We perform a large simulation study to examine the extent to which various generalized autoregressive conditional 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...

We argue against the view that it is mostly the peaks of the empirical densities of stock returns (and of other risky returns as well) that set such data aside from ‘normal’ variables. We show that peaks depend on sample size and on the way returns are standardized, and that for given data...