Pricing Bermudan Options in Lévy Process Models

SIAM Journal on Financial Mathematics, 4(1), pp. 474-493, 2013

20 Pages Posted: 6 Aug 2013

See all articles by Liming Feng

Liming Feng

University of Illinois at Urbana-Champaign - Department of Industrial and Enterprise Systems Engineering

Xiong Lin

University of Illinois at Urbana-Champaign, Department of Mathematics

Date Written: March 5, 2013

Abstract

This paper presents a Hilbert transform method for pricing Bermudan options in Lévy process models. The corresponding optimal stopping problem can be solved using a backward induction, where a sequence of inverse Fourier and Hilbert transforms need 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 Lévy 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.

Keywords: Lévy process, Bermudan option, early exercise boundary, optimal stopping, Fourier transform, Hilbert transform, sinc methods, fast Fourier transform, analytic characteristic function

JEL Classification: C10, G13

Suggested Citation

Feng, Liming and Lin, Xiong, Pricing Bermudan Options in Lévy Process Models (March 5, 2013). SIAM Journal on Financial Mathematics, 4(1), pp. 474-493, 2013, Available at SSRN: https://ssrn.com/abstract=2306566

Liming Feng (Contact Author)

University of Illinois at Urbana-Champaign - Department of Industrial and Enterprise Systems Engineering ( email )

104 S. Mathews Avenue
Urbana, IL 61801
United States

Xiong Lin

University of Illinois at Urbana-Champaign, Department of Mathematics ( email )

104 S. Mathews Avenue
Urbana, IL 61801
United States

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