Quasirandom tree method for pricing American style derivatives

Pricing American options is a difficult task due to the early exercise opportunities, and the higher the dimension, i.e. the number of underlying assets, is, the more complicated the problem is. Broadie and Glasserman proposed a Monte Carlo method for pricing American style options by using random trees. Their method has a merit that its computational complexity is linear in the dimension of the problem, but it often shows a slow convergence. In this paper, we propose a method making use of low-discrepancy sequences instead of random numbers to construct trees, based on which we obtain the estimate of the option price. We will present the detail of our ‘quasirandom tree method’, and compare the random tree method with our method in pricing some American style options of high dimensionality. Our numerical experiments show a rapid convergence of our quasirandom tree method.