Giles, Michael B. and Higham, Desmond J. and Mao, Xuerong (2009) Analysing multilevel Monte Carlo for options with nonglobally Lipschitz payoff. Finance and Stochastics, 13 (3). pp. 403413. ISSN 09492984

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Abstract
Giles (Multilevel Monte Carlo path simulation Operations Research, 2008; 56:607617) introduced a multilevel 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 nonglobally Lipschitz cases. In this work, we show that the multilevel Monte Carlo method can be rigorously justifed for nonglobally Lipschitz payoffs. In particular, we consider digital, lookback and barrier options. This requires nonstandard strong convergence analysis of the EulerMaruyama method.
Item type:  Article 

ID code:  14025 
Keywords:  barrier option, complexity, digital option, EulerMaruyama, lookback option, path, dependent option, statistical error, strong error, weak error, Mathematics, Finance, Statistics and Probability, Statistics, Probability and Uncertainty 
Subjects:  Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Mrs Carolynne Westwood 
Date Deposited:  11 Dec 2009 11:47 
Last modified:  15 Apr 2015 11:02 
URI:  http://strathprints.strath.ac.uk/id/eprint/14025 
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