Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff

被引：0
|
作者：
Michael B. Giles
Desmond J. Higham
Xuerong Mao
机构：
[1] University of Oxford,Mathematical Institute and Oxford
[2] University of Strathclyde,Man Institute of Quantitative Finance
[3] University of Strathclyde,Department of Mathematics
来源：
Finance and Stochastics | 2009年 / 13卷
关键词：
Barrier option; Complexity; Digital option; Euler–Maruyama; Lookback option; Path-dependent option; Statistical error; Strong error; Weak error; 65C05; 60H10; C15; C63;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Giles (Oper. Res. 56:607–617, 2008) introduced a multi-level Monte Carlo method for approximating the expected value of a function of a stochastic differential equation solution. A key application is to compute the expected payoff of a financial option. This new method improves on the computational complexity of standard Monte Carlo. Giles analysed globally Lipschitz payoffs, but also found good performance in practice for non-globally Lipschitz cases. In this work, we show that the multi-level Monte Carlo method can be rigorously justified for non-globally Lipschitz payoffs. In particular, we consider digital, lookback and barrier options. This requires non-standard strong convergence analysis of the Euler–Maruyama method.
引用
收藏
页码：403 / 413
页数：10
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