Comparison of low discrepancy mesh methods for pricing Bermudan options under a Lévy process

Abstract

This paper discusses simulation methods for pricing Bermudan options under an exponential Lévy process. We investigate an efficient simulation approach that can generate sample trajectories from an explicitly known density function under an exponential Lévy process. The paper examines the impact of the choice of mesh density for sampling trajectories on the efficiency of both the low discrepancy and stochastic mesh methods. Three mesh densities are introduced and compared, that is, average, marginal and squared average. Numerical experiments show that the squared average density is the best choice for the mesh density function in pricing Bermudan put options under an exponential normal inverse Gaussian Lévy process. The low discrepancy mesh method using the squared average density can provide unbiased estimates with a smaller number of mesh points. Furthermore, it can provide estimates with the smallest standard error.