Small-Samples and EVT Estimators for Computing Risk Measures : Simulation and Empirical Evidences

Extreme Value Theory (EVT) deals with the analysis of rare events and it has been recently used in finance to predict the occurrence of such events, or, at least, to build more robust models for unexpected extreme events. Particularly, EVT has been used to model the loss severities in Operational Risk management, while the use of GARCH-EVT models has gained popularity when computing the Value at Risk (or other risk measures) in Market Risk management. To date, little attention has been devoted to the analysis of the small-sample properties of EVT estimators and their effects on the computation of financial risk measures. In this work we present and discuss the results of a Monte Carlo study of the small sample properties of these estimators in an Operational Risk setting, together with an empirical analysis dealing with Market Risk management