Monte Carlo-Based Tail Exponent Estimator

Jozef Baruník and Lukas Vacha

No 2010/06, Working Papers IES from Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies

Abstract: In this paper we study the finite sample behavior of the Hill estimator under α-stable distributions. Using large Monte Carlo simulations we show that the Hill estimator overestimates the true tail exponent and can hardly be used on samples with small length. Utilizing our results, we introduce a Monte Carlo-based method of estimation for the tail exponent. Our method is not sensitive to the choice of k and works well also on small samples. The new estimator gives unbiased results with symmetrical con_dence intervals. Finally, we demonstrate the power of our estimator on the main world stock market indices. On the two separate periods of 2002-2005 and 2006-2009 we estimate the tail exponent.

Keywords: Hill estimator; α-stable distributions; tail exponent estimation (search for similar items in EconPapers)
JEL-codes: C1 C13 C15 G0 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2010-04, Revised 2010-04
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (2)

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Related works:
Working Paper: Monte Carlo-based tail exponent estimator (2012)
Journal Article: Monte Carlo-based tail exponent estimator (2010)
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