Multilevel Monte Carlo path simulation

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