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Option Pricing with a Pentanomial Lattice Model that Incorporates Skewness and Kurtosis

This paper analyzes a pentanomial lattice model for option pricing that incorporates skewness and kurtosis of the underlying asset. The lattice is constructed using a moment matching procedure, and explicit positivity conditions for branch probabilities are provided in terms of skewness and kurtosis. We also explore the limiting distribution of this lattice, which is compound Poisson, and give a Fourier transform based formula that can be used to more efficiently price European call and put options. An example illustrates some of the features of this model in capturing volatility smiles and smirks.