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We provide the first generic exact simulation algorithm for multivariatediffusions. Current exact sampling algorithms for diffusions require theexistence of a transformation which can be used to reduce the sampling problemto the case of a constant diffusion matrix and a drift which is the gradient ofsome function. Such transformation, called Lamperti transformation, can beapplied in general only in one dimension. So, completely different ideas arerequired for exact sampling of generic multivariate diffusions. The developmentof these ideas is the main contribution of this paper. Our strategy combinestechniques borrowed from the theory of rough paths, on one hand, and multilevelMonte Carlo on the other.

Exact Simulation for Multivariate It\^o Diffusions