The Distribution of Security Price Changes: A Test of a Volume-Mixture Model with Cauchy Disturbances

Abstract

This paper considers a time-series model for changes in security prices from one transaction to the next, in which they are viewed as depending on previous price changes, on transaction volume, and on a random disturbance. The dependence on transaction volume implies that the marginal distribution of price changes is a mixture of distributions, the form of which is determined by the behaviors of volume and the disturbance. Even when the disturbance follows a finite-variance distribution, such as the normal, the volume-mixture model implies a marginal distribution for price changes with the characteristic thick tails that are observed in practice. An alternative hypothesis, however, is that volume plays no role and that the disturbance itself is appropriately described by an infinite-variance probability law. Parametric tests of these two hypotheses are conducted by estimating the volume parameter in the mixture model under the alternative assumptions that the disturbance follows Gaussian and Cauchy laws.