Diagnosing and treating the fat tails in financial returns data

We address an open and important question regarding the nature of the fat tails found in financial-return data, which has been raised by Ghose and Kroner [Journal of Empirical Finance, 2 (1995) 225]. These authors find that two classes of models used for modeling financial returns, namely the independent and identically distributed (iid) stable Paretian and the GARCH assumption, have several features in common, with the latter being preferred. We advocate models that combine the two allegedly disjoint paradigms, i.e., GARCH processes driven by stable Paretian innovations, and investigate some of their theoretical and small-sample properties. Finally, we demonstrate the plausibility of the new models for several exchange-rate series involved in the Asian crisis.