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Johnson binomial trees

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  • Jean-Guy Simonato

Abstract

Rubinstein developed a binomial lattice technique for pricing European and American derivatives in the context of skewed and leptokurtic asset return distributions. A drawback of this approach is the limited set of skewness and kurtosis pairs for which valid stock return distributions are possible. A solution to this problem is proposed here by extending Rubinstein's Edgeworth tree idea to the case of the Johnson system of distributions which is capable of accommodating all possible skewness and kurtosis pairs. Numerical examples showing the performance of the Johnson tree to approximate the prices of European and American options in Merton's jump diffusion framework and Duan's GARCH framework are examined.

Suggested Citation

  • Jean-Guy Simonato, 2011. "Johnson binomial trees," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1165-1176.
    • Handle: RePEc:taf:quantf:v:11:y:2011:i:8:p:1165-1176
    DOI: 10.1080/14697680902950821
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    References listed on IDEAS

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    Cited by:

    1. Arturo Leccadito & Pietro Toscano & Radu S. Tunaru, 2012. "Hermite Binomial Trees: A Novel Technique For Derivatives Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-36.
    2. Marcellino Gaudenzi & Alice Spangaro & Patrizia Stucchi, 2017. "Efficient European and American option pricing under a jump-diffusion process," Papers 1712.08137, arXiv.org.
    3. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2023. "Option pricing using a skew random walk pricing tree," Papers 2303.17014, arXiv.org.

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