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

共 50 条

[31] Linear implicit approximations of invariant measures of semi-linear SDEs with non-globally Lipschitz coefficients
Pang, Chenxu
Wang, Xiaojie
Wu, Yue
JOURNAL OF COMPLEXITY, 2024, 83
[32] Convergence Rates of Split-Step Theta Methods for SDEs with Non-Globally Lipschitz Diffusion Coefficients
Wu, Xiaojuan
Gan, Siqing
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2023, 13 (01) : 59 - 75
[33] Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients
Andrea Barth
Christoph Schwab
Nathaniel Zollinger
Numerische Mathematik, 2011, 119 : 123 - 161
[34] Multi-level Monte Carlo methods for the approximation of invariant measures of stochastic differential equations
Michael B. Giles
Mateusz B. Majka
Lukasz Szpruch
Sebastian J. Vollmer
Konstantinos C. Zygalakis
Statistics and Computing, 2020, 30 : 507 - 524
[35] Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients
Barth, Andrea
Schwab, Christoph
Zollinger, Nathaniel
NUMERISCHE MATHEMATIK, 2011, 119 (01) : 123 - 161
[36] Multi-level Monte Carlo computation of the hadronic vacuum polarization contribution to (gμ-2)
Dalla Brida, Mattia
Giusti, Leonardo
Harris, Tim
Pepe, Michele
PHYSICS LETTERS B, 2021, 816
[37] Multi-level Monte Carlo methods for the approximation of invariant measures of stochastic differential equations
Giles, Michael B.
Majka, Mateusz B.
Szpruch, Lukasz
Vollmer, Sebastian J.
Zygalakis, Konstantinos C.
STATISTICS AND COMPUTING, 2020, 30 (03) : 507 - 524
[38] Strong Convergence of a Fully Discrete Scheme for Multiplicative Noise Driving SPDEs with Non-Globally Lipschitz Continuous Coefficients
Yang, Xu
Zhao, Weidong
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2021, 14 (04): : 1085 - 1109
[39] Robustly simulating biochemical reaction kinetics using multi-level Monte Carlo approaches
Lester, Christopher
Yates, Christian A.
Baker, Ruth E.
JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 375 : 1401 - 1423
[40] TAMED STOCHASTIC RUNGE-KUTTA-CHEBYSHEV METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-GLOBALLY LIPSCHITZ COEFFICIENTS*
Yu, Yanyan
Xiao, Aiguo
Tang, Xiao
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2024,

← 1 2 3 4 5 →