30 research outputs found
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 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 (). 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 close to 2, resulting in overestimation of the tail exponent in
finite samples. The reported value of the tail exponent around 3 may
very well indicate a Levy-stable distribution with .Comment: To be published in Int. J. Modern Physics C (2001) vol. 12 no.
Models for Heavy-tailed Asset Returns
Many of the concepts in theoretical and empirical finance developed over the past decades – including the classical portfolio theory, the Black-Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR – rest upon the assumption that asset returns follow a normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat
tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model – the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the so-called truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples