Multilevel Monte Carlo Path Simulation

Authors:
Michael B. Giles
Affiliations:
Oxford University Mathematical Institute, and Oxford---Man Institute of Quantitative Finance, Oxford OX1 3LB, United Kingdom
Venue:
Operations Research
Year:
2008

Citing 0
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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(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.