On Modified Mellin Transforms, Gauss-Laguerre Quadrature and the Valuation of American Call Options

Journal of Computational and Applied Mathematics

30 Pages Posted: 19 Feb 2009 Last revised: 16 Sep 2010

See all articles by Robert Frontczak

Robert Frontczak

Landesbank Baden-Württemberg (LBBW)

Rainer Schoebel

University of Tuebingen - Faculty of Economics and Social Sciences

Date Written: 2010

Abstract

We extend a framework based on Mellin transform techniques and show how the approach can be modified to value American call options on dividend paying stocks. We derive a new integral equation to determine the price of an American call option and its free boundary using modified Mellin transforms. We show how the new framework can be used to derive the valuation formula for perpetual American call options and use the new integral characterization to recover a result due to Kim (1990) regarding the optimal exercise price of American call options at expiry. Finally, we apply Gauss-Laguerre quadrature for the purpose of an efficient and accurate American call option valuation.

Keywords: American call option, Mellin transform, Integral representation

JEL Classification: G13

Suggested Citation

Frontczak, Robert and Schoebel, Rainer, On Modified Mellin Transforms, Gauss-Laguerre Quadrature and the Valuation of American Call Options (2010). Journal of Computational and Applied Mathematics . Available at SSRN: https://ssrn.com/abstract=1341044

Robert Frontczak

Landesbank Baden-Württemberg (LBBW) ( email )

Kleiner SchloBplatz 11
D-70173 Stuttgart, 70174
Germany

Rainer Schoebel (Contact Author)

University of Tuebingen - Faculty of Economics and Social Sciences ( email )

Mohlstrasse 36
D-72074 Tuebingen
Germany
+49 7071 2977088 (Phone)

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