Alternative option pricing models incorporating higher moments and non-restrictive distributions - Ang, Kian Ping (2008)
A new method of inferring moments of risk-neutral probability density function that is consistent with the traded option prices is developed. Incorporating the market inferred moments of the risk-neutral probability density function is a practical way to overcome the need for using different volatility inputs into "Black-Scholes" types of models for option differing in strike and maturity. The new method utilized Gram-Charlier expansion series to account for the higher moments of the asset's return probability density, and Rubinstein's (1994) optimization method to infer the moments of the risk-neutral probabilities. This moment pricing method contains Black-Scholes model as a special case- when the third and higher moments are set to zero.