Scaling of Levy-Student processes

Student's t-distributions are Widely used in financial studies as heavy-tailed alternatives to normal distributions. As these distributions are not closed under Convolution, there exist no Levy processes with Student's t-marginals at all points in time. In this article we show that a Student's t-approximation of these marginals is still suitable, while nor exact. Using this approximation, we are able to describe the scaling behavior of Such Levy-Student processes and the parameters of its marginal distributions by a simple analytical scaling law. This scaling law drastically simplifies the use of Levy-Student processes as a general diffusion process in various interdisciplinary applications. We explicitly provide an application in the context of modelling high-frequency price returns. (C) 2009 Elsevier B.V. All rights reserved.