An Introduction to Multilevel Monte Carlo for Option Valuation

TL;DR

This paper introduces multilevel Monte Carlo, a significant improvement over standard Monte Carlo methods, enabling faster and more efficient option valuation through a novel multilevel approach that reduces computational complexity.

Contribution

The paper provides an accessible introduction to multilevel Monte Carlo and summarizes recent advancements in its application to option valuation.

Findings

Multilevel Monte Carlo achieves a speed-up proportional to 1/epsilon.

The method allows computations to be 100 times faster for two-digit accuracy.

Recent results demonstrate practical efficiency in option evaluation.

Abstract

Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation. In 2008, Giles proposed a remarkable improvement to the approach of discretizing with a numerical method and applying standard Monte Carlo. His multilevel Monte Carlo method offers an order of speed up given by the inverse of epsilon, where epsilon is the required accuracy. So computations can run 100 times more quickly when two digits of accuracy are required. The multilevel philosophy has since been adopted by a range of researchers and a wealth of practically significant results has arisen, most of which have yet to make their way into the expository literature. In this work, we give a brief, accessible, introduction to multilevel Monte Carlo and summarize recent results applicable to the task of option evaluation.