The most extreme events, such as economic crises, are rare but often have a great impact. It is difficult to precisely determine the likelihood of such events because the sample is small.
Worst-case analysis is used among financial regulators in the wake of the recent financial crisis to gauge the tail risk. We provide insight into worst-case analysis and provide guidance on how to estimate it. We derive the bias for the non-parametric heavy-tailed order statistics and contrast it with the semi-parametric extreme value theory (EVT) approach.