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We introduce three related but distinct improvements to multilevel MonteCarlo (MLMC) methods for the solution of systems of stochastic differentialequations (SDEs). Firstly, we show that when the payoff function is twicecontinuously differentiable, the computational cost of the scheme can bedramatically reduced using a technique we call `Ito linearization'. Secondly,by again using Ito's lemma, we introduce an alternative to the antitheticmethod of Giles et. al [M.B. Giles, L. Szpruch. arXiv preprint arXiv:1202.6283,2012] that uses an approximate version of the Milstein discretization requiringno Levy area simulation to obtain the theoretically optimal cost-to-errorscaling. Thirdly, we generalize the antithetic method of Giles to arbitraryrefinement factors. We present numerical results and compare the relativestrengths of various MLMC-type methods, including each of those presented here.

Three Improvements to Multi-Level Monte Carlo Simulation of SDE Systems