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Numerical analysis of multilevel Monte Carlo path simulation using the Milstein discretisation

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  • Michael Giles
  • Kristian Debrabant
  • Andreas R\"o{\ss}ler
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    Abstract

    The multilevel Monte Carlo path simulation method introduced by Giles (Operations Research, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. Previous research has analysed its efficiency when using the Euler-Maruyama discretisation, and also demonstrated its improved efficiency using the Milstein discretisation with its improved strong convergence. In this paper we analyse its efficiency for scalar SDEs using the Milstein discretisation, bounding the order of convergence of the variance of the multilevel estimator, and hence determining the computational complexity of the method.

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    File URL: http://arxiv.org/pdf/1302.4676
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    Paper provided by arXiv.org in its series Papers with number 1302.4676.

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    Date of creation: Feb 2013
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    Handle: RePEc:arx:papers:1302.4676

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    1. Rainer Avikainen, 2009. "On irregular functionals of SDEs and the Euler scheme," Finance and Stochastics, Springer, vol. 13(3), pages 381-401, September.
    2. Michael Giles & Desmond Higham & Xuerong Mao, 2009. "Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff," Finance and Stochastics, Springer, vol. 13(3), pages 403-413, September.
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