Computing Functionals of Multidimensional Diffusions via Monte Carlo Methods

TL;DR

This paper develops Monte Carlo methods for computing functionals of multidimensional diffusion processes relevant to finance, including exact simulation schemes and multilevel algorithms within the benchmark approach.

Contribution

It introduces new exact simulation schemes for certain diffusion processes and integrates them into multilevel Monte Carlo methods using the benchmark approach.

Findings

Exact simulation schemes for multidimensional diffusions

Multilevel Monte Carlo integration within the benchmark approach

Enhanced computational efficiency for finance-related functionals

Abstract

We discuss suitable classes of diffusion processes, for which functionals relevant to finance can be computed via Monte Carlo methods. In particular, we construct exact simulation schemes for processes from this class. However, should the finance problem under consideration require e.g. continuous monitoring of the processes, the simulation algorithm can easily be embedded in a multilevel Monte Carlo scheme. We choose to introduce the finance problems under the benchmark approach, and find that this approach allows us to exploit conveniently the analytical tractability of these diffusion processes.