Exact Simulation for Multivariate Itô Diffusions

Abstract

We provide the first generic exact simulation algorithm for multivariate diffusions. Current exact sampling algorithms for diffusions require the existence of a transformation which can be used to reduce the sampling problem to the case of a constant diffusion matrix and a drift which is the gradient of some function. Such transformation, called Lamperti transformation, can be applied in general only in one dimension. So, completely different ideas are required for exact sampling of generic multivariate diffusions. The development of these ideas is the main contribution of this paper. Our strategy combines techniques borrowed from the theory of rough paths, on one hand, and multilevel Monte Carlo on the other.

28 pages; Accepted for publication by the Applied Probability Trust (http://www.appliedprobability.org) in 52.4 (December 2020)

References in corpus (5)

• Exact simulation of diffusions
• Fast simulation of new coins from old
• Closed-form likelihood expansions for multivariate diffusions
• Lower bounds for the density of locally elliptic Itô processes
• $\epsilon$-Strong Simulation for Multidimensional Stochastic Differential Equations via Rough Path Analysis

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