We will see how multigrid ideas can be used to reduce the computational complexity (computational cost) of estimating an expected value arising from the solution of a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretization, the computational cost to achieve an accuracy of O(e) is reduced from O(e^-3) to O(e^-2 * (log e)^2). A brief overview of related concepts will be provided before discussing the main details of the paper. (e = \epsilon)
*Reference: *Giles, M.B., Multilevel Monte Carlo Path Simulation, Operations Research, 2008.