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

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Abstract

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.

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Authors and Affiliations

  1. Mathematical Institute and Oxford-Man Institute of Quantitative Finance, University of Oxford, Oxford, OX1 3LB, UK

    Michael B. Giles

  2. Department of Mathematics, University of Strathclyde, Glasgow, G1 1XH, UK

    Desmond J. Higham

  3. Department of Statistics and Modelling Science, University of Strathclyde, Glasgow, G1 1XH, UK

    Xuerong Mao

Authors
  1. Michael B. Giles
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  2. Desmond J. Higham
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  3. Xuerong Mao
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Correspondence to Desmond J. Higham.

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Giles, M.B., Higham, D.J. & Mao, X. Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff. Finance Stoch 13, 403–413 (2009). https://doi.org/10.1007/s00780-009-0092-1

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  • DOI: https://doi.org/10.1007/s00780-009-0092-1

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