Scaling of Lévy–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 Lévy 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 not exact. Using this approximation, we are able to describe the scaling behavior of such Lévy–Student processes and the parameters of its marginal distributions by a simple analytical scaling law. This scaling law drastically simplifies the use of Lévy–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.