Multilevel Monte Carlo Path Simulation - Giles, Michael B (Operations research, 2008)
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 ( ) is reduced from O ( –3 ) to O ( –2 (log ) 2 ). The analysis is supported by numerical results showing significant computational savings.