Pricing American Derivatives using Simulation: A Biased-Low Approach - Proceedings AFIR 2001 - Toronto, Canada

In Boyle et al. (2000) we propose a simulation method for pricing high-dimensional American style derivatives. The method exploits the uniformity property of the low discrepancy sequences so that the resulting biased high estimator can achieve higher rate of convergence of quasi-Monte Carlo method. In this paper, we extend this work by proposing another estimator that is biased low. It has the computational advantage that it can be obtained concurrently with the high-biased estimator using a recursive valuation approach. Some numerical examples are conducted to demonstrate its efficiency. We also show that further enhancement to the proposed estimator is possible by incorporating the standard variance reduction technique such as the use of control variates. Acknowledgments: Phelim P. Boyle thanks the Social Science and Humanities Research Council of Canada for research support. Adam Kolkiewicz and Ken Seng Tan acknowledge research support from the Natural Sciences and Engineering Research Council of Canada. Phelim P. Boyle and Ken Seng Tan are also grateful to the Committee for Knowledge Extension and Research of the Society of Actuaries for financial support.