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Monte Carlo and Quasi-Monte Carlo Methods pp 3–27Cite as

Multilevel Monte Carlo Implementation for SDEs Driven by Truncated Stable Processes

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 163))

Abstract

In this article we present an implementation of a multilevel Monte Carlo scheme for Lévy-driven SDEs introduced and analysed in (Dereich and Li, Multilevel Monte Carlo for Lévy-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 Lévy increments. We give an efficient implementation of the algorithm. In particular, we explain direct simulation techniques for Lévy 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.

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Author information

Authors and Affiliations

  1. Institut Für Mathematische Statistik, Westfälische Wilhelms-Universität Münster, Orléans-Ring 10, 48149, Münster, Germany

    Steffen Dereich & Sangmeng Li

Authors
  1. Steffen Dereich
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  2. Sangmeng Li
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Correspondence to Steffen Dereich .

Editor information

Editors and Affiliations

  1. Department of Computer Science, KU Leuven, Heverlee, Belgium

    Ronald Cools

  2. Department of Computer Science, KU Leuven, Heverlee, Belgium

    Dirk Nuyens

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Dereich, S., Li, S. (2016). Multilevel Monte Carlo Implementation for SDEs Driven by Truncated Stable Processes. In: Cools, R., Nuyens, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods. Springer Proceedings in Mathematics & Statistics, vol 163. Springer, Cham. https://doi.org/10.1007/978-3-319-33507-0_1

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