Barunik J., Vacha L.: Monte Carlo-based tail exponent estimator
| Author(s): | doc. PhDr. Jozef Baruník Ph.D., Mgr. Lukáš Vácha Ph.D., |
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| Type: | Articles in journals with impact factor |
| Year: | 2010 |
| Number: | 21 |
| ISSN / ISBN: | |
| Published in: | Physica A, 389 (21), pp.4863-4874 PDF |
| Publishing place: | |
| Keywords: | Hill estimator, α-stable distributions, Tail exponent estimation |
| JEL codes: | |
| Suggested Citation: | Barunik J., Vacha L. (2010): Monte Carlo-based tail exponent estimator, Physica A: Statistical Mechanics and its Applications, 389 (21), pp. 4863-4874 |
| Grants: | 402/09/0965: New Approaches for monitoring and prediction of capital markets 402/09/H045 - Nelineární dynamika v peněžní ekonomii a financích. Teorie a empirické modely IES Research Framework Institutional task (2005-2011) Integration of the Czech economy into European union and its development |
| Abstract: | In this paper we propose a new approach to estimation of the tail exponent in financial stock markets. We begin the study with 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 proposed method is not sensitive to the choice of tail size and works well also on small data samples. The new estimator also gives unbiased results with symmetrical confidence intervals. Finally, we demonstrate the power of our estimator on the international world stock market indices. On the two separate periods of 2002–2005 and 2006–2009, we estimate the tail exponent. |
