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(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.