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Multi-Asset Option Pricing with Exponential L\'evy Processes and the Mellin Transform

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  • D. J. Manuge

Abstract

Exponential L\'evy processes have been used for modelling financial derivatives because of their ability to exhibit many empirical features of markets. Using their multidimensional analogue, a general analytic pricing formula is obtained, allowing for the direct valuation of multi-asset options on $n \in \z^+$ risky assets. By providing alternate expressions for multi-asset option payoffs, the general pricing formula can reduce to many popular cases, including American basket options which are considered herein. This work extends previous results of basket options to dimensions $n \geq 3$ and more generally, to payoff functions that satisfy Lipschitz continuity.

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  • D. J. Manuge, 2013. "Multi-Asset Option Pricing with Exponential L\'evy Processes and the Mellin Transform," Papers 1309.3035, arXiv.org.
    • Handle: RePEc:arx:papers:1309.3035
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    References listed on IDEAS

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    1. Kim, In Joon, 1990. "The Analytic Valuation of American Options," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
    2. Peter Carr & Robert Jarrow & Ravi Myneni, 2008. "Alternative Characterizations Of American Put Options," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Jean-Philippe Aguilar & Cyril Coste & Hagen Kleinert & Jan Korbel, 2016. "Distributional Mellin calculus in $\mathbb{C}^n$, with applications to option pricing," Papers 1611.03239, arXiv.org, revised Nov 2016.
    2. Leila Khodayari & Mojtaba Ranjbar, 2017. "A Numerical Method to Approximate Multi-Asset Option Pricing Under Exponential Lévy Model," Computational Economics, Springer;Society for Computational Economics, vol. 50(2), pages 189-205, August.

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