《An introduction to multilevel Monte Carlo for option valuation》

此篇论文发表在2015年《International Journal of Computer Mathematics 》上，作者在此文中介绍了多级蒙特卡罗方法 并总结了近期用此方法使用在期权评估的结果。

简介

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 a speed up of
O(ϵ−1)
, where ε 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.