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

Giles, Michael B. and Higham, Desmond J. and Mao, Xuerong (2009) Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff. Finance and Stochastics, 13 (3). pp. 403-413. ISSN 0949-2984

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    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.

    Item type: Article
    ID code: 14025
    Keywords: barrier option, complexity, digital option, Euler-Maruyama, lookback option, path, dependent option, statistical error, strong error, weak error, Mathematics
    Subjects: Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
      Depositing user: Mrs Carolynne Westwood
      Date Deposited: 11 Dec 2009 11:47
      Last modified: 13 Mar 2012 00:56
      URI: http://strathprints.strath.ac.uk/id/eprint/14025

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