Multilevel Monte Carlo Path Simulation
Operations Research · 2008 · Volume 56 · Issue 3
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.
Keywords
analysis of algorithms, computational complexity, finance, simulation, efficiency
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