Pricing American options with Mellin transforms

Robert Frontczak and Rainer Schöbel

No 319, Tübinger Diskussionsbeiträge from University of Tübingen, School of Business and Economics

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.

Keywords: Mellin transform; Power option; American put option; Free boundary; Integral representation (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:zbw:tuedps:319

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