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Monte Carlo-based tail exponent estimator

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  • Barunik, Jozef
  • Vacha, Lukas

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.

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Bibliographic Info

Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 389 (2010)
Issue (Month): 21 ()
Pages: 4863-4874

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Handle: RePEc:eee:phsmap:v:389:y:2010:i:21:p:4863-4874

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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

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Keywords: Hill estimator; α-stable distributions; Tail exponent estimation;

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References

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  1. Mantegna, Rosario N & Palágyi, Zoltán & Stanley, H.Eugene, 1999. "Applications of statistical mechanics to finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 216-221.
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  5. Niklas Wagner & Terry Marsh, 2004. "Tail index estimation in small smaples Simulation results for independent and ARCH-type financial return models," Statistical Papers, Springer, vol. 45(4), pages 545-561, October.
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  7. Xavier Gabaix & Rustam Ibragimov, 2007. "Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents," NBER Technical Working Papers 0342, National Bureau of Economic Research, Inc.
  8. Szymon Borak & Wolfgang Härdle & Rafal Weron, 2005. "Stable Distributions," SFB 649 Discussion Papers SFB649DP2005-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  9. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  10. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
  11. Plerou, V & Gopikrishnan, P & Rosenow, B & Amaral, L.A.N & Stanley, H.E, 2000. "A random matrix theory approach to financial cross-correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 374-382.
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Cited by:
  1. Barunik, Jozef & Aste, Tomaso & Di Matteo, T. & Liu, Ruipeng, 2012. "Understanding the source of multifractality in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(17), pages 4234-4251.

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