A relaxed lattice option pricing model: implied skewness and kurtosis

Purpose – The purpose of this paper is to develop an option pricing model applicable to US options. The lognormality assumption that has typically been imposed with past binomial and trinomial option pricing models is relaxed. The relaxed lattice model is then used to determine skewness and kurtosis of distributions of futures prices implied from option prices. Design/methodology/approach – The relaxed lattice is based on Gaussian quadrature. The markets studied include corn, soybeans, and wheat. Skewness and kurtosis are implied by minimizing the squared deviations of actual option premia from predicted premia. Findings – Positive skewness is the major source of nonnormality, but both skewness and kurtosis are important as the trinomial model that considers kurtosis has greater accuracy than the binomial model. The out-of-sample forecasting accuracy of the relaxed lattice models is better than the Black-Scholes model in most, but not all cases. Research limitations/implications – The model might benefit from using option prices from more than one day. The implied skewness and kurtosis were quite variable and using more data might reduce this variability. Practical implications – Empirical results mostly show positive implied skewness, which suggests extreme price rises were more likely than extreme price decreases. Originality/value – The relaxed lattice is a new model and the results about implied higher moments are new for these commodities. There are competing models available that should be able to get similar accuracy, so one key advantage of the new approach is its simplicity and ease of use.