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


  • Michael Giles
  • Kristian Debrabant
  • Andreas Ro{ss}ler


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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  • Michael Giles & Kristian Debrabant & Andreas Ro{ss}ler, 2013. "Numerical analysis of multilevel Monte Carlo path simulation using the Milstein discretisation," Papers 1302.4676,
  • Handle: RePEc:arx:papers:1302.4676

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    References listed on IDEAS

    1. 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.
    2. Rainer Avikainen, 2009. "On irregular functionals of SDEs and the Euler scheme," Finance and Stochastics, Springer, vol. 13(3), pages 381-401, September.
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