Lévy modeled GMWB: Pricing with wavelets

Abstract

In this paper we propose the study of the problem of the guaranteed minimum withdraw benefit (or GMWB for short) rider pricing by the means of American option pricing in the Lévy setting with a new method. Using wavelet discretization we reduce the problem to a matrix linear complementary problem giving the value function in the log price domain. Our approach with wavelets seems to be helpful in allowing practitioners to decide in advance how accurate a result they want and decide on the way whether to refine the mesh or stop the iteration procedure.