Multi-level Monte Carlo path simulation - Giles, M (Unspecified, 2006)
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 $O(ε)$ is reduced from $O(ε^{-3})$ to $O(ε^{-2} (\log ε)^2)$. The analysis is supported by numerical results showing significant computational savings.