Adaptive (quasi-)Monte Carlo methods for pricing path-dependent options

Abstract

We study a recently developed adaptive path-integration technique for pricing financial derivatives. The method is based on the rearrangement and splitting of path-integral variables to apply a combination of bridge sampling, adaptive methods of numerical integration, and the quasi-Monte Carlo method. We study the subregion adaptive Vegas-type method Suave from the CUBA library and propose a new variance reduction method with a multivariate piecewise constant sampling density. Two models of asset pricing are considered: The constant elasticity of variance diffusion model and the variance gamma Ĺevy model. Numerical tests are done for Asian-type options. © Springer-Verlag Berlin Heidelberg 2009.