The binomial options pricing models are widely used after it was first introduced by Cox, Ross and Rubinstein (1979) and Rendleman and Bartter (1979) independently. The model is constructed through a binomial tree. The values of the underlying asset is found by calculating nodal prices backwards recursively. Rubinstein made numerous contributions to make the model more realistic with his works on Implied Binomial Trees (1994) and Edgeworth Binomial Trees (1998). The Edgeworth expansion is used to have a valid stock return distributions with prespecified skewness and kurtosis pairs. Later Simonato applied the Johnson model of distributions to get the return distributions with arbitrary skewness and kurtosis pairs. A comparison made in the last chapters between these approaches, the Edgeworth and Johnson trees.