Pricing Bermudan options using low-discrepancy mesh methods

<title>Abstract</title> This paper proposes a new simulation method for pricing Bermudan derivatives that is applicable to problems where the transition density of the underlying asset price process is known analytically. We assume that the owner can exercise the option at a finite, although possibly large, number of exercise dates. The method is computationally efficient for high-dimensional problems and is easy to apply. Its efficiency stems from our use of quasi-Monte Carlo techniques, which have proven effective in the case of European derivatives. The valuation of a Bermudan derivative hinges on the optimal exercise strategy. The optimal exercise decision can be reduced to the evaluation of a series of conditional expectations with respect to different distributions. These expectations can be approximated by sampling from just a single distribution at each exercise point. We provide a theoretical basis for the selection of this distribution and develop a simple approximation that has good convergence properties. We describe how to implement the method and confirm its efficiency using numerical examples involving Bermudan options written on multiple assets and options on a foreign asset with a stochastic interest rate.