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

Abstract

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.

Information Theory and the Pricing of Contingent Claims: An Alternative Derivation of the Black–Scholes–Merton Formula

“…Furthermore, the Black-Scholes equation is derived with only two assumptions: that a forward contract is traded in the market, and that the probability distribution used has some measure of dispersion and, importantly, a guarantee that no other information has been used. A recent paper extends the analysis in this paper by using the maximum entropy formulation and all available option prices to infer higher moments of the distribution Ardakani (2022).…”