On Approximation of Some Lévy Processes

Abstract

 In this paper, we extend the Asmussen-Rosinski approach for the approximation of Levy processes. To simulate the value of the process at time t, we introduce a time-dependent truncation of the Levy measure, which we refer to as dynamic cutting, followed by the simulation of the large-jump component. We provide the sufficient condition under which the compensated small-jump part can be replaced by a Gaussian approximation. We also derive weak approximation rates for both approaches. Finally, we run numerical simulations and compare the performance of our method with the Asmussen-Rosinski approach.