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Pricing discretely monitored Asian options under Levy processes

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  • Fusai, Gianluca
  • Meucci, Attilio
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    Abstract

    We present methodologies to price discretely monitored Asian options when the underlying evolves according to a generic Levy process. For geometric Asian options we provide closed-form solutions in terms of the Fourier transform and we study in particular these formulas in the Levy-stable case. For arithmetic Asian options we solve the valuation problem by recursive integration and derive a recursive theoretical formula for the moments to check the accuracy of the results. We compare the implementation of our method to Monte Carlo simulation implemented with control variates and using different parametric Levy processes. We also discuss model risk issues.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Banking & Finance.

    Volume (Year): 32 (2008)
    Issue (Month): 10 (October)
    Pages: 2076-2088

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    Handle: RePEc:eee:jbfina:v:32:y:2008:i:10:p:2076-2088

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    Web page: http://www.elsevier.com/locate/jbf

    Related research

    Keywords: Asian options Discrete monitoring Quadrature Levy processes Stable processes Model risk;

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    Cited by:
    1. Friedrich Hubalek & Martin Keller-Ressel & Carlo Sgarra, 2014. "Geometric Asian Option Pricing in General Affine Stochastic Volatility Models with Jumps," Papers 1407.2514, arXiv.org.
    2. Fajardo, José & Farias, Aquiles, 2010. "Derivative pricing using multivariate affine generalized hyperbolic distributions," Journal of Banking & Finance, Elsevier, vol. 34(7), pages 1607-1617, July.
    3. Alexander Novikov & Nino Kordzakhia, 2013. "On lower and upper bounds for Asian-type options: a unified approach," Papers 1309.2383, arXiv.org.
    4. Fabozzi, Frank J. & Leccadito, Arturo & Tunaru, Radu S., 2014. "Extracting market information from equity options with exponential Lévy processes," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 125-141.
    5. Dingeç, Kemal Dinçer & Hörmann, Wolfgang, 2012. "A general control variate method for option pricing under Lévy processes," European Journal of Operational Research, Elsevier, vol. 221(2), pages 368-377.
    6. Lemmens, D. & Liang, L.Z.J. & Tempere, J. & De Schepper, A., 2010. "Pricing bounds for discrete arithmetic Asian options under Lévy models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5193-5207.
    7. Akira Yamazaki, 2014. "Pricing average options under time-changed Lévy processes," Review of Derivatives Research, Springer, vol. 17(1), pages 79-111, April.

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