Several models with conditional heterosckedasticity have been studied in financial econometrics, with the simple GARCH(1,1) with Gaussian innovation representing the standard benchmark. There is evidence of asymmetry in some daily data and more flexible models, which take such an asymmetry into account, have become recently popular. Understanding the extremal behaviour of asymmetric processes becomes very important to build proper inference about extremal events. For processes satisfying mild mixing conditions the clustering of extreme values is characterzied by a single key-parameter, known as the extremal index, which represents the average clusters size of values which exceed a high-level threshold. An approach extending results for the GARCH(1,1) is presented, with skew-t innovation
