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

Journal article

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. © Springer-Verlag 2009.

Authors: Giles, M; Higham, D; Mao, X

• Publication status: Published
• Journal: FINANCE AND STOCHASTICS
• Volume: 13
• Issue: 3
• Pages: 403-413
• Publication date: 2009-09-01
• DOI: 10.1007/s00780-009-0092-1
• EISSN: 1432-1122
• ISSN: 0949-2984
• Language: English
• Keywords: Statistical error; Path-dependent option; Euler-Maruyama; Complexity; Strong error; Barrier option; Weak error; Digital option; Lookback option