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

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  • Omid M. Ardakani

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.

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  • Omid M. Ardakani, 2022. "Option pricing with maximum entropy densities: The inclusion of higher‐order moments," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(10), pages 1821-1836, October.
    • Handle: RePEc:wly:jfutmk:v:42:y:2022:i:10:p:1821-1836
    DOI: 10.1002/fut.22361
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    Cited by:

    1. Thomas P. Davis, 2023. "Information Theory and the Pricing of Contingent Claims: An Alternative Derivation of the Black–Scholes–Merton Formula," JRFM, MDPI, vol. 16(12), pages 1-7, December.
    2. Ardakani, Omid M., 2023. "Capturing information in extreme events," Economics Letters, Elsevier, vol. 231(C).
    3. Ardakani, Omid M., 2023. "Coherent measure of portfolio risk," Finance Research Letters, Elsevier, vol. 57(C).
    4. Harshit Mishra & Parama Barai, 2024. "Entropy Augmented Asset Pricing Model: Study on Indian Stock Market," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 31(1), pages 81-99, March.

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