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This work deals with the simulation of Wishart processes and affinediffusions on positive semidefinite matrices. To do so, we focus on thesplitting of the infinitesimal generator, in order to use compositiontechniques as Ninomiya and Victoir or Alfonsi. Doing so, we have found aremarkable splitting for Wishart processes that enables us to sample exactlyWishart distributions, without any restriction on the parameters. It is relatedbut extends existing exact simulation methods based on Bartlett'sdecomposition. Moreover, we can construct high-order discretization schemes forWishart processes and second-order schemes for general affine diffusions. Theseschemes are in practice faster than the exact simulation to sample entirepaths. Numerical results on their convergence are given.

Exact and high order discretization schemes for Wishart processes and their affine extensions