Article,
Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime
International Journal of Modern Physics C, (2001)
Abstract
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
<= 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 ==
1.8.
