Pricing bermudan options in ĺevy process models

This paper presents a Hilbert transform method for pricing Bermudan options in ĺevy process models. The corresponding optimal stopping problem can be solved using a backward induction, where a sequence of inverse Fourier and Hilbert transforms needs to be evaluated. Using results from a sinc expansion-based approximation theory for analytic functions, the inverse Fourier and Hilbert transforms can be approximated using very simple rules. The approximation errors decay exponentially with the number of terms used to evaluate the transforms for many popular ĺevy process models. The resulting discrete approximations can be efficiently implemented using the fast Fourier transform. The early exercise boundary is obtained at the same time as the price. Accurate American option prices can be obtained by using Richardson extrapolation.