A quadrinomial lattice model that incorporates skewness and kurtosis

Primbs et al. (2007) proposed an option pricing method using a pentanomial lattice that incorporated mean, volatility, skewness and kurtosis. This approach is very useful when the return of the underlying asset follows a lognormal distribution. However, Primbs et al. (2007) claimed that "with four moments, one could conceivably use a quadrinomial lattice (i.e., four branches); however, the recombination conditions along with the requirement of non-negative probabilities are quite limiting in terms of the range of skewness and kurtosis that can be captured". In this research, as a refutation, a quadrinomial lattice model has been developed incorporating mean, volatility, skewness, and kurtosis; and it has been shown that the conditions for the non-negative probabilities are the same as the conditions obtained for the pentanomial lattice in Primbs et al. (2007). Several numerical examples are presented to compare the result obtained from the quadrinomial lattice with that of the pentanomial lattice.