  In this article we propose a novel approach to reduce the computational
complexity of various approximation methods for pricing discrete time American
options. Given a sequence of continuation values estimates corresponding to
different levels of spatial approximation and time discretization, we propose a
multi-level low biased estimate for the price of an American option. It turns
out that the resulting complexity gain can be rather high and can even reach
the order (\varepsilon^{-1}) with (\varepsilon) denoting the desired precision.
The performance of the proposed multilevel algorithm is illustrated by a
numerical example of pricing Bermudan max-call options.
