Monte Carlo-Based Tail Exponent Estimator

0342493 - ÚTIA 2011 CZ eng J - Journal Article
Baruník, Jozef - Vácha, Lukáš
Monte Carlo-Based Tail Exponent Estimator.
IES Working Paper. Roč. 2010, č. 6 (2010), s. 1-26
R&D Projects: GA ČR GA402/09/0965; GA ČR GD402/09/H045; GA ČR GP402/08/P207
Institutional research plan: CEZ:AV0Z10750506
Keywords : Hill estimator * α-stable distributions * tail exponent estimation
Subject RIV: AH - Economics
http://library.utia.cas.cz/separaty/2010/E/barunik-0342493.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0185214