On Adaptive Tail Index Estimation for Financial Return Models

Niklas Wagner and Terry Marsh

Research Program in Finance, Working Paper Series from Research Program in Finance, Institute for Business and Economic Research, UC Berkeley

Abstract: Estimation of the tail index of stationary, fat-tailed return distributions is non-trivial since the well-known Hill estimator is optimal only under iid draws from an exact Pareto model. We provide a small sample simulation study of recently suggested adaptive estimators under ARCH-type dependence. The Hill estimator's performance is found to be dominated by a ratio estimator. Dependence increases estimation error which can remain substantial even in larger data sets. As small sample bias is related to the magnitude of the tail index, recent standard applications may have overestimated (underestimated) the risk of assets with low (high) degrees of fat-tailedness.

Keywords: fat-tails; tail index of stationary marginal distributions; Hill estimator; minimal AMSE (search for similar items in EconPapers)
Date: 2000-11-01
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Citations: View citations in EconPapers (5)

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