Summary: 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 \(O(\varepsilon)\) is reduced from \(O(\varepsilon)^{-3})\) to \(O(\varepsilon)^{-2} (\log \varepsilon)^{2})\). The analysis is supported by numerical results showing significant computational savings.