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A moment expansion approach to option pricing

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  • Marco Airoldi

Abstract

In this paper we present a new methodology for option pricing. The main idea consists of representing a generic probability distribution function (PDF) by an expansion around a given, simpler, PDF (typically a Gaussian function) by matching moments of increasing order. Because, as shown in the literature, the pricing of path-dependent European options can often be reduced to recursive (or nested) one-dimensional integral calculations, the moment expansion (ME) approach leads very quickly to excellent numerical solutions. In this paper, we present the basic ideas of the method and the relative applications to a variety of contracts, mainly: Asian, reverse cliquet and barrier options. A comparison with other numerical techniques is also presented.

Suggested Citation

  • Marco Airoldi, 2005. "A moment expansion approach to option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 5(1), pages 89-104.
    • Handle: RePEc:taf:quantf:v:5:y:2005:i:1:p:89-104
    DOI: 10.1080/14697680500117641
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    Cited by:

    1. Jarno Talponen, 2018. "Matching distributions: Recovery of implied physical densities from option prices," Papers 1803.03996, arXiv.org.
    2. Aprahamian, Hrayer & Maddah, Bacel, 2015. "Pricing Asian options via compound gamma and orthogonal polynomials," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 21-43.
    3. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    4. Schlögl, Erik, 2013. "Option pricing where the underlying assets follow a Gram/Charlier density of arbitrary order," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 611-632.

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