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

Michael B. Giles, Desmond J. Higham, Xuerong Mao

Research output: Contribution to journalArticle

45 Citations (Scopus)
182 Downloads (Pure)

Abstract

Giles (Multilevel Monte Carlo path simulation Operations Research, 2008; 56:607-617) 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 payff 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 justifed 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.
Original languageEnglish
Pages (from-to)403-413
Number of pages10
JournalFinance and Stochastics
Volume13
Issue number3
DOIs
Publication statusPublished - Sep 2009

Keywords

  • barrier option
  • complexity
  • digital option
  • Euler-Maruyama
  • lookback option
  • path
  • dependent option
  • statistical error
  • strong error
  • weak error

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