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In this paper we introduce a new multilevel Monte Carlo (MLMC) estimator formulti-dimensional SDEs driven by Brownian motions. Giles has previously shownthat if we combine a numerical approximation with strong order of convergence$O(\Delta t)$ with MLMC we can reduce the computational complexity to estimateexpected values of functionals of SDE solutions with a root-mean-square errorof $\epsilon$ from $O(\epsilon^{-3})$ to $O(\epsilon^{-2})$. However, ingeneral, to obtain a rate of strong convergence higher than $O(\Delta t^{1/2})$requires simulation, or approximation, of L\'{e}vy areas. In this paper,through the construction of a suitable antithetic multilevel correctionestimator, we are able to avoid the simulation of L\'{e}vy areas and stillachieve an $O(\Delta t^2)$ multilevel correction variance for smooth payoffs,and almost an $O(\Delta t^{3/2})$ variance for piecewise smooth payoffs, eventhough there is only $O(\Delta t^{1/2})$ strong convergence. This results in an$O(\epsilon^{-2})$ complexity for estimating the value of European and Asianput and call options.

Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without L\'{e}vy area simulation