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 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.