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

被引：51

作者：

Giles, Michael B. ^{[2
,3
]}

Higham, Desmond J. ^{[1
]}

Mao, Xuerong ^{[4
]}

机构：

[1] Univ Strathclyde, Dept Math, Glasgow G1 1XH, Lanark, Scotland

[2] Univ Oxford, Math Inst, Oxford OX1 3LB, England

[3] Univ Oxford, Oxford Man Inst Quantitat Finance, Oxford OX1 3LB, England

[4] Univ Strathclyde, Dept Stat & Modelling Sci, Glasgow G1 1XH, Lanark, Scotland

来源：

FINANCE AND STOCHASTICS | 2009年 / 13卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Barrier option; Complexity; Digital option; Euler-Maruyama; Lookback option; Path-dependent option; Statistical error; Strong error; Weak error;

D O I：

10.1007/s00780-009-0092-1

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

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

页码：403 / 413

页数：11

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