Multilevel Monte Carlo Path Simulation

Michael B. Giles ()
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Michael B. Giles: Oxford University Mathematical Institute, and Oxford---Man Institute of Quantitative Finance, Oxford OX1 3LB, United Kingdom

Operations Research, 2008, vol. 56, issue 3, 607-617

Abstract: We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretisation, the computational cost to achieve an accuracy of O ((epsilon)) is reduced from O ((epsilon) -3 ) to O ((epsilon) -2 (log (epsilon)) 2 ). The analysis is supported by numerical results showing significant computational savings.

Keywords: analysis of algorithms; computational complexity; finance; simulation; efficiency (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (138)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:56:y:2008:i:3:p:607-617

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