Pricing Bermudan Options in Lévy Models

This paper presents a Hilbert transform method for pricing Bermudan options in Lévy models. The corresponding optimal stopping problem is reduced to a backward induction in the Fourier space that involves taking Hilbert transforms of certain analytic functions or integrating such functions. The Hilbert transforms and integrals can be discretized using very simple schemes. The resulting discrete approximation can be efficiently implemented using the fast Fourier transform. The computational cost is linear in the number of monitoring times, and O(M log(M)) in the number of points used to approximate the Hilbert transforms and integrals. The method is remarkably accurate. The pricing error decays exponentially in terms of the computational cost M for a wide class of Lévy process models. The early exercise boundary is obtained as a by-product. American options can be priced by increasing the number of monitoring times and using extrapolation when applicable.