Multilevel Monte Carlo Implementation for SDEs Driven by Truncated Stable Processes

In this article we present an implementation of a multilevel Monte Carlo scheme for Levy-driven SDEs introduced and analysed in (Dereich and Li, Multilevel Monte Carlo for Levy-driven SDEs: central limit theorems for adaptive Euler schemes, Ann. Appl. Probab. 26, No. 1, 136-185, 2016 [12]). The scheme is based on direct simulation of Levy increments. We give an efficient implementation of the algorithm. In particular, we explain direct simulation techniques for Levy increments. Further, we optimise over the involved parameters and, in particular, the refinement multiplier. This article complements the theoretical considerations of the above reference. We stress that we focus on the case where the frequency of small jumps is particularly high, meaning that the Blumenthal-Getoor index is larger than one.