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Improved multilevel Monte Carlo convergence using the Milstein scheme

Abstract:
In this paper we show that the Milstein scheme can be used to improve the convergence of the multilevel Monte Carlo method for scalar stochastic differential equations, so that the computational cost to achieve a root-mean-square error of $\epsilon$ is reduced to $O(\epsilon^{-2})$. Numerical results are presented for Asian, lookback, barrier and digital options.

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Publication date:
2006-12-05
URN:
uuid:a2696159-d43a-4cc0-bfb1-dd6a786aab4d
Local pid:
oai:eprints.maths.ox.ac.uk:1102

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