  We describe general multilevel Monte Carlo methods that estimate the price of
an Asian option monitored at $m$ fixed dates. Our approach yields unbiased
estimators with standard deviation $O(\epsilon)$ in $O(m + (1/\epsilon)^{2})$
expected time for a variety of processes including the Black-Scholes model,
Merton's jump-diffusion model, the Square-Root diffusion model, Kou's double
exponential jump-diffusion model, the variance gamma and NIG exponential Levy
processes and, via the Milstein scheme, processes driven by scalar stochastic
differential equations. Using the Euler scheme, our approach estimates the
Asian option price with root mean square error $O(\epsilon)$ in
$O(m+(\ln(\epsilon)/\epsilon)^{2})$ expected time for processes driven by
multidimensional stochastic differential equations. Numerical experiments
confirm that our approach outperforms the conventional Monte Carlo method by a
factor of order $m$.
