Johnson Binomial Trees

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