A higher order weak approximation scheme of multidimensional stochastic differential equations using Malliavin weights

We show a new higher order weak approximation with Malliavin weights for multidimensional stochastic differential equations by extending the method in Takahashi and Yamada (2016). The estimate of global error of the discretization is based on a sharp small time expansion using a Malliavin calculus approach. We give explicit Malliavin weights for second order discretization as polynomials of Brownian motions. The effectiveness is illustrated through an example in option pricing.