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Option Pricing with a Pentanomial Lattice Model that Incorporates Skewness and Kurtosis


  • James Primbs
  • Muruhan Rathinam
  • Yuji Yamada


This paper analyzes a pentanomial lattice model for option pricing that incorporates skewness and kurtosis of the underlying asset. The lattice is constructed using a moment matching procedure, and explicit positivity conditions for branch probabilities are provided in terms of skewness and kurtosis. We also explore the limiting distribution of this lattice, which is compound Poisson, and give a Fourier transform based formula that can be used to more efficiently price European call and put options. An example illustrates some of the features of this model in capturing volatility smiles and smirks.

Suggested Citation

  • James Primbs & Muruhan Rathinam & Yuji Yamada, 2007. "Option Pricing with a Pentanomial Lattice Model that Incorporates Skewness and Kurtosis," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 1-17.
  • Handle: RePEc:taf:apmtfi:v:14:y:2007:i:1:p:1-17 DOI: 10.1080/13504860600659172

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    References listed on IDEAS

    1. Windcliff, H. & Forsyth, P.A. & Vetzal, K.R., 2006. "Pricing methods and hedging strategies for volatility derivatives," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 409-431, February.
    2. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    4. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    6. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 117-133.
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    Cited by:

    1. Bowei Chen & Jun Wang, 2014. "A lattice framework for pricing display advertisement options with the stochastic volatility underlying model," Papers 1409.0697,, revised Dec 2015.

    More about this item


    Lattice; volatility smile; option pricing;


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