Monte Carlo and Quasi-Monte Carlo Methods 2006

pp 343-358

Improved Multilevel Monte Carlo Convergence using the Milstein Scheme

  • Mike GilesAffiliated withOxford University Computing Laboratory

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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. Numerical results for Asian, lookback, barrier and digital options demonstrate that the computational cost to achieve a root-mean-square error of ε is reduced to O(ε -2). This is achieved through a careful construction of the multilevel estimator which computes the difference in expected payoff when using different numbers of timesteps.