Simulation of Student–Lévy processes using series representations

Abstract

Levy processes have become very popular in many applications in finance, physics and beyond. The Student–Levy process is one interesting special case where increments are heavy-tailed and, for 1-increments, Student t distributed. Although theoretically available, there is a lack of path simulation techniques in the literature due to its complicated form. In this paper we address this issue using series representations with the inverse Levy measure method and the rejection method and prove upper bounds for the mean squared approximation error. In the numerical section we discuss a numerical inversion scheme to find the inverse Levy measure efficiently. We extend the existing numerical inverse Levy measure method to incorporate explosive Levy tail measures. Monte Carlo studies verify the error bounds and the effectiveness of the simulation routine. As a side result we obtain series representations of the so called inverse gamma subordinator which are used to generate paths in this model.