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

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

Frontczak, Robert; Schöbel, Rainer
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URI: http://nbn-resolving.de/urn:nbn:de:bsz:21-opus-39215
http://hdl.handle.net/10900/47621
Dokumentart: WorkingPaper
Date: 2009
Source: Tübinger Diskussionsbeiträge der Wirtschaftswissenschaftlichen Fakultät ; 320
Language: English
Faculty: 6 Wirtschafts- und Sozialwissenschaftliche Fakultät
Department: Wirtschaftswissenschaften
DDC Classifikation: 330 - Economics
Keywords: Mellin-Transformation
Other Keywords:
Modified Mellin transform , American call option , Integral representation
License: http://tobias-lib.uni-tuebingen.de/doku/lic_ohne_pod.php?la=de http://tobias-lib.uni-tuebingen.de/doku/lic_ohne_pod.php?la=en
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Abstract:

We extend a framework based on Mellin transforms and show how to modify the approach to value American call options on dividend paying stocks. We present a new integral equation to determine the price of an American call option and its free boundary using modied Mellin transforms. We also show how to derive the pricing formula for perpetual American call options using the new framework. A recovery of a result due to Kim (1990) regarding the optimal exercise price at expiry is also presented. Finally, we apply Gauss-Laguerre quadrature for the purpose of an efficient and accurate numerical valuation.

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