General Multilevel Monte Carlo Methods for Pricing Discretely Monitored Asian Options

We describe general multilevel Monte Carlo methods that estimate the price of an Asian option monitored at m fixed dates. For a variety of processes that can be simulated exactly, we prove that, for the same computational cost, our method yields an unbiased estimator with variance lower than the variance of the standard Monte Carlo estimator by a factor of order m. We show how to combine our approach with the Milstein scheme for processes driven by scalar stochastic differential equations, and with the Euler scheme for processes driven by multidimensional stochastic differential equations. Numerical experiments confirm that our method outperforms the conventional Monte Carlo algorithm by a factor proportional to m