A General Distribution for Describing Security Price Returns

Abstract

This paper introduces a generalized distribution, called the GB2 distribution, for describing security returns. The distribution is extremely flexible, containing a large number of well-known distributions, such as the lognormal, log-t, and log-Cauchy distribu tions, as special or limiting cases and allowing large, even infinite, higher moments. This flexibility allows a direct representation of different degrees of fat tails in the distribution. The properties of the GB2 make it useful in empirical estimation of security returns and in facilitating the development of option-pricing models and other models that depend on the specification and mathematical manipulation of distributions. Copyright 1987 by the University of Chicago.