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

TL;DR

This paper introduces exact and high-order discretization schemes for Wishart processes and affine diffusions, enabling efficient and accurate simulation without parameter restrictions, extending existing methods with novel splitting techniques.

Contribution

It presents a new splitting approach that allows exact sampling of Wishart distributions and constructs high-order schemes for Wishart and affine diffusions, improving simulation efficiency.

Findings

Exact sampling of Wishart distributions achieved without parameter restrictions

High-order discretization schemes outperform exact simulation in speed

Numerical results confirm convergence and efficiency of the proposed methods

Abstract

This work deals with the simulation of Wishart processes and affine diffusions on positive semidefinite matrices. To do so, we focus on the splitting of the infinitesimal generator, in order to use composition techniques as Ninomiya and Victoir or Alfonsi. Doing so, we have found a remarkable splitting for Wishart processes that enables us to sample exactly Wishart distributions, without any restriction on the parameters. It is related but extends existing exact simulation methods based on Bartlett's decomposition. Moreover, we can construct high-order discretization schemes for Wishart processes and second-order schemes for general affine diffusions. These schemes are in practice faster than the exact simulation to sample entire paths. Numerical results on their convergence are given.