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

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