Pricing American options on assets with dividends by a Brownian bridge simulation method

This paper presents a Brownian bridge backward simulation method for pricing American options on assets with discrete dividends. In the traditional Monte Carlo methods, in order to determine when to exercise, we have to store the simulated asset prices at all time steps on all paths. If N time steps and M paths are used, then the storage requirement is O(M N). To overcome this disadvantage, backward simulation methods have been given, but the additional cost in the methods is needed. In this paper, we use Brownian bridge to generate paths backwardly and improve original backward simulation methods to price American options. And in the new method, the additional is not needed, and the number of storage required only grows like O(M).