Return Distributions and Bootstrap Goodness-of-fit Tests

Abstract

It is seen as a “stylised fact” that marginal distributions of stock returns have thick tails, are skewed and leptocurtic (see for example Campbell et al. 1997, Eijgenhuijsen and Buckley 1999, Cont 2001 and Behr and Poetter 2007). Therefore, the simple normal distribution is inappropriate to describe empirical return distributions. In response to these “stylised fact” several flexible parametric distributions of returns have been proposed in the literature. The generalised hyperbolic distribution has obtained a fair amount of interest. This five parameter family includes skew leptocurtic densities with thicker tails than the normal while still having moments of all orders (Barndorff Nielsen 1977, Eberlein and Keller 1995 and Kchler et al. 1999)