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Morse Potential, Contour Integrals, and Asian Options

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  • Peng Zhang

Abstract

Completeness of the eigenfunctions of a quantum mechanical system is crucial for its probability interpretation. By using the method of contour integral we give properly normalized eigenfunctions for both discrete and continuum spectrum of the Morse potential, and explicitly prove the completeness relation. As an application we use our spectral decomposition formula to study the problem of the pricing of an Asian option traded in financial markets.

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  • Peng Zhang, 2010. "Morse Potential, Contour Integrals, and Asian Options," Papers 1010.3820, arXiv.org, revised Nov 2010.
    • Handle: RePEc:arx:papers:1010.3820
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    References listed on IDEAS

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    1. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    2. Vadim Linetsky, 2004. "Spectral Expansions for Asian (Average Price) Options," Operations Research, INFORMS, vol. 52(6), pages 856-867, December.
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