# Exact Simulation for Multivariate It\^o Diffusions

## TL;DR

This paper introduces the first generic exact simulation algorithm for multivariate Itô diffusions, overcoming the limitations of Lamperti transformations which are only applicable in one dimension.

## Contribution

It develops a novel exact sampling method for multivariate diffusions by combining rough path theory and multilevel Monte Carlo techniques.

## Key findings

- First generic exact simulation algorithm for multivariate diffusions
- Successfully overcomes Lamperti transformation limitations in higher dimensions
- Demonstrates practical applicability of combined rough path and Monte Carlo methods

## 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.