Tail index and quantile estimation with very high frequency data

Abstract

A precise estimation of the tail shape of forex returns is of critical importance for proper risk assessment. We improve upon the efficiency of conventional estimators that rely on a first order expansion of the tail shape, by using the second order expansion. Here we advocate a moments estimator for the second term. The paper uses both Monte Carlo simulations and the high frequency foreign exchange recordings collected by the Olsen corporation to illustrate the technique. © 1997 Elsevier Science B.V.