Mathematics and Computers in Simulation 62 (2003) 315–322 An improved simulation method for pricing high-dimensional American derivatives Phelim P. Boyle a , Adam W. Kolkiewicz b , Ken Seng Tan b,∗ a Centre for Advanced Studies in Finance, University of Waterloo, Waterloo, Ont., Canada N2L 3G1 b Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ont., Canada N2L 3G1 Abstract In this paper, we propose an estimator for pricing high-dimensional American-style options and show that asymp- totically its upper bias converges to zero. An advantage of the proposed estimator is that when combined with low discrepancy sequences, it exhibits a superior rate of convergence. Numerical examples are conducted to demonstrate its efficiency. © 2003 IMACS. Published by Elsevier Science B.V. All rights reserved. MSC: 91B28; 11K45; 65C05 Keywords: American options; Monte Carlo; Quasi-Monte Carlo; Dynamic programming 1. Introduction In this paper, we consider the pricing of high-dimensional American options. While Monte Carlo methods are particularly useful in high-dimensional applications, the valuation of American options by simulation still remains a challenging problem. The main difficulty in applying this method stems from the early exercise feature embedded in these contracts. A variety of approaches have been used to handle the early exercise feature by simulation. Typically they involve techniques for approximating the early exercise boundary or approximating the transition density. This problem can also be set up in a dynamic programming framework where we solve the optimization problem by working backwards through time. A strong advantage of this method over other methods is that it does not require any initial knowledge of the shape of the exercise region, which in a high-dimensional problem can be very complex (see [11]). The papers [4,5] have made important contributions to this problem. They show [4] that for a large class of instruments the simulation estimator is biased and develop a simulated tree approach that produces biased high and biased low estimates. Unfortunately, this algorithm becomes computational burdensome ∗ Corresponding author. Tel.: +1-519-888-4567; fax: +1-519-746-1875. E-mail address: kstan@uwaterloo.ca (K.S. Tan). 0378-4754/03/$ – see front matter © 2003 IMACS. Published by Elsevier Science B.V. All rights reserved. PII:S0378-4754(02)00248-3