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On Adaptive Tail Index Estimation for Financial Return Models

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Author Info
Niklas Wagner (University of California, Berkeley)
Terry Marsh (Haas School of Business, University of California, Berkeley)

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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.

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File URL: http://repositories.cdlib.org/cgi/viewcontent.cgi?article=1000&context=iber/finance
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Publisher Info
Paper provided by Research Program in Finance, Institute for Business and Economic Research, UC Berkeley in its series Research Program in Finance, Working Paper Series with number 1000.

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Date of creation: 01 Nov 2000
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Handle: RePEc:cdl:rpfina:1000

Note: oai:cdlib1:iber/finance-1000
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Related research
Keywords: fat-tails tail index of stationary marginal distributions Hill estimator minimal AMSE

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References listed on IDEAS
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  1. ROCKINGER, Michael & JONDEAU, Eric, 1999. "The Tail Behavior of Stock Returns: Emerging versus Mature Markets," Les Cahiers de Recherche 668, Groupe HEC. [Downloadable!]
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  2. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May. [Downloadable!] (restricted)
  3. Vries, Caspar de & Danielsson, Jon, 1996. "Tail Index and Quantile Estimation with Very High Frequency Data," CESifo Working Paper Series CESifo Working Paper No. , CESifo GmbH.
  4. Jon Danielsson & Casper G. de Vries, 1998. "Beyond the Sample: Extreme Quantile and Probability Estimation," FMG Discussion Papers dp298, Financial Markets Group. [Downloadable!] (restricted)
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  5. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," Journal of Business, University of Chicago Press, vol. 47(2), pages 244-80, April. [Downloadable!] (restricted)
  6. Michel M. Dacorogna, & Ulrich A. Muller & Olivier V. Pictet & Casper De Vries,, . "The Distribution of Extremal Foreign Exchange Rate Returns in Extremely Large Data Sets," Working Papers 1992-10-22, Olsen and Associates. [Downloadable!]
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