Option pricing with maximum entropy densities: The inclusion of higher-order moments

Entropy pricing applies notions of information theory to derive the theoretical value of options. This paper employs the maximum entropy (ME) formulation of option pricing, given risk-neutral moment constraints computed directly from the observed prices. First, higher-order moments are used to generate option prices. Then a generalization of Shannon entropy, known as Renyi entropy, is studied to account for extreme events. This ME problem provides a class of heavy-tailed distributions. Examples and Monte Carlo simulations are provided to examine the effects of moment constraints on option prices. The call option values are then constructed using daily Standard and Poor's 500 index options. The findings suggest that entropy pricing with higher-order moment constraints provides higher forecasting accuracy.