Multilevel Monte Carlo for basket options

The multilevel Monte Carlo method has been previously introduced for the efficient pricing of options based on a single underlying quantity. In this paper we show that the method is easily extended to basket options based on a weighted average of several underlying quantities. Numerical results for Asian, lookback, barrier and digital basket options demonstrate that the computational cost to achieve a root-mean-square error of ¿ is O(¿^-2). This is achieved through a careful construction of the multilevel estimator which computes the difference in expected payoff when using different numbers of timesteps.