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The Multilevel Monte Carlo method used on a Lévy driven SDE
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Henning Marxen
Published/Copyright:
July 12, 2010
Abstract
In this paper the Multilevel Monte Carlo method introduced by Giles [Operations Research 56: 607–617, 2008] is refined by the extended complexity theorem and applied to Lévy process driven SDEs. The restricted approximate Euler scheme is used to simulate the SDEs. Recent results about the convergence by Fournier [ArXiv e-prints: 2009] and by Jacod, Kurtz, Máléard and Protter [Annales de l'Institut Henri Poincare (B) Probability and Statistics 41: 523–558, 2005] are used. The theoretical results are illustrated by numerical simulations.
Keywords.: Lévy processes; stochastic differential equations; Monte Carlo; Multilevel Monte Carlo; complexity theorem; Euler scheme; Blumenthal–Getoor index
Received: 2009-12-11
Revised: 2010-05-18
Published Online: 2010-07-12
Published in Print: 2010-July
© de Gruyter 2010
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- Approximate formulas for expectations of functionals of solutions to stochastic differential equations
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Keywords for this article
Lévy processes;
stochastic differential equations;
Monte Carlo;
Multilevel Monte Carlo;
complexity theorem;
Euler scheme;
Blumenthal–Getoor index
Articles in the same Issue
- Approximate formulas for expectations of functionals of solutions to stochastic differential equations
- Simulation of binary random fields with Gaussian numerical models
- A spectral-based Monte Carlo algorithm for generating samples of nonstationary Gaussian processes
- The Multilevel Monte Carlo method used on a Lévy driven SDE
- Erratum. Exact retrospective Monte Carlo computation of arithmetic average Asian options
