Multilevel Monte Carlo Path Simulation

Michael B. Giles

doi:10.1287/opre.1070.0496

Multilevel Monte Carlo Path Simulation

Oxford University Mathematical Institute, and Oxford—Man Institute of Quantitative Finance, Oxford OX1 3LB, United Kingdom

Operations Research 2008

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(ϵ) is reduced from O(ϵ−3) to O(ϵ−2 (log ϵ)2). The analysis is supported by numerical results showing significant computational savings.

DOI: 10.1287/opre.1070.0496
Volume: 56 (3)
Pages: 607-617
Language: en
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