Multilevel Monte Carlo Path Simulation

@article{Giles2008MultilevelMC,
  title={Multilevel Monte Carlo Path Simulation},
  author={Michael B. Giles},
  journal={Operations Research},
  year={2008},
  volume={56},
  pages={607-617}
}
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 an Euler discretisation, the computational cost to achieve an accuracy of O( ) is reduced from O( −3) to O( −2(log )2). The analysis is supported by numerical results showing significant computational savings. 
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