Pricing American Options with Mellin Transforms

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URI: http://nbn-resolving.de/urn:nbn:de:bsz:21-opus-37353
http://hdl.handle.net/10900/47603
Dokumentart: ResearchPaper
Date: 2008
Source: Tübinger Diskussionsbeiträge der Wirtschaftswissenschaftlichen Fakultät ; 319
Language: English
Faculty: 6 Wirtschafts- und Sozialwissenschaftliche Fakultät
Department: Wirtschaftswissenschaften
DDC Classifikation: 330 - Economics
Keywords: Mellin-Transformation
Other Keywords:
Mellin transform , Power option , American put option , Free boundary , Integral representation
License: Publishing license excluding print on demand
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Abstract:

Mellin transforms in option pricing theory were introduced by Panini and Srivastav (2004). In this contribution, we generalize their results to European power options. We derive Black-Scholes-Merton-like valuation formulas for European power put options using Mellin transforms. Thereafter, we restrict our attention to plain vanilla options on dividend-paying stocks and derive the integral equations to determine the free boundary and the price of American put options using Mellin transforms. We recover a result found by Kim (1990) regarding the optimal exercise price of American put options at expiry and prove the equivalence of integral representations herein, the representation derived by Kim (1990), Jacka (1991), and by Carr et al. (1992). Finally, we extend the results obtained in Panini and Srivastav (2005) and show how the Mellin transform approach can be used to derive the valuation formula for perpetual American put options on dividend-paying stocks.

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