On Tail Index Estimation and Financial Risk Management Implications

Estimation bias is a critical issue when drawing inferences about the tails of the return distribution of risky assets. Risk management applications which rely on methods of extreme value theory must consider the statistical properties of the tail index estimator used; see for example recent simulation studies by Gomes and Oliveira (2001), Matthys and Beirlant (2000), and Wagner and Marsh (2000). The present contribution outlines potential effects of bias on quantile estimation thereby considering error sensitivities within the widespread Value-at-Riskapproach. The results show that particularly inference far out in the distribution tails is sensitive to bias. The paper further gives an overview of recent literature documenting small sample bias in tail index estimation and points out some new approaches aiming at its reduction.