Johnson Binomial Trees

32 Pages Posted: 19 Feb 2009

Date Written: November 20, 2008

Abstract

Rubinstein (1998) 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 (1998) Edgeworth tree idea to the case of the Johnson (1949) 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 (1976) jump diffusion framework and Duan's (1995) GARCH framework are examined.

Keywords: Binomial tree, skewness, kurtosis, Johnson distribution, American option, Jump diffusion, GARCH

Suggested Citation

Simonato, Jean-Guy, Johnson Binomial Trees (November 20, 2008). Available at SSRN: https://ssrn.com/abstract=1346110 or http://dx.doi.org/10.2139/ssrn.1346110

Jean-Guy Simonato (Contact Author)

HEC Montréal ( email )

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Service de l'enseignement de la finance
Montreal, Quebec H3T 2A7
Canada
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