Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime

Details Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime

2001-03-12

arxiv.org/abs/cond-mat/0103256v1

Int. J. Modern Physics C, Vol. 12, No. 2 (2001) 209-223

Physics

Condensed Matter

To be published in Int. J. Modern Physics C (2001) vol. 12 no. 2

Scientific paper

Power-law tail behavior and the summation scheme of Levy-stable distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset returns exhibit tail exponents well above the Levy-stable regime ($0<\alpha\le 2$). In this paper we illustrate that widely used tail index estimates (log-log linear regression and Hill) can give exponents well above the asymptotic limit for $\alpha$ close to 2, resulting in overestimation of the tail exponent in finite samples. The reported value of the tail exponent $\alpha$ around 3 may very well indicate a Levy-stable distribution with $\alpha\approx 1.8$.

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