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

被引：52

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

共 11 条

[1]

[Anonymous], 2007, STOCHASTIC DIFFERENT

[2] On irregular functionals of SDEs and the Euler scheme [J].

Avikainen, Rainer .

FINANCE AND STOCHASTICS, 2009, 13 (03) :381-401

[3] The law of the Euler scheme for stochastic differential equations .1. Convergence rate of the distribution function [J].

Bally, V ;

Talay, D .

PROBABILITY THEORY AND RELATED FIELDS, 1996, 104 (01) :43-60

[4] BLACK'S CONSOL RATE CONJECTURE [J].

Duffie, Darrell ;

Ma, Jin ;

Yong, Jiongmin .

ANNALS OF APPLIED PROBABILITY, 1995, 5 (02) :356-382

[5] Multilevel Monte Carlo path simulation [J].

Giles, Michael B. .

OPERATIONS RESEARCH, 2008, 56 (03) :607-617

[6]

Glasserman P, 2004, Monte Carlo Methods in Financial Engineering

[7]

Gobet E, 2007, LECT NOTES MATH, V1899, P355

[8]

Higham Desmond., 2004, INTRO FINANCIAL OPTI, DOI [10.1017/CBO9780511800948, DOI 10.1017/CBO9780511800948]

[9]

Hull J. C., 2014, Options, Futures, and Other Derivatives

[10]

Kloeden P. E., 1999, NUMERICAL SOLUION ST, DOI DOI 10.1007/978-3-662-12616-5

← 1 2 →