Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff |
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| Authors: | Michael B Giles Desmond J Higham Xuerong Mao |
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| Institution: | (1) Mathematical Institute and Oxford-Man Institute of Quantitative Finance, University of Oxford, Oxford, OX1 3LB, UK;(2) Department of Mathematics, University of Strathclyde, Glasgow, G1 1XH, UK;(3) Department of Statistics and Modelling Science, University of Strathclyde, Glasgow, G1 1XH, UK |
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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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| Keywords: | Barrier option Complexity Digital option Euler– Maruyama Lookback option Path-dependent option Statistical error Strong error Weak error |
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