Multilevel Monte Carlo Path Simulation

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.