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The Entropy Theory Of Stock Option Pricing

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  • LES GULKO

    (287 Hamilton Avenue, #3C, Stamford, CT 06902, USA)

Abstract

An informationally efficient price keeps investors as a group in the state of maximum uncertainty about the next price change. The Entropy Pricing Theory (EPT) captures this intuition and suggests that, in informationally efficient markets, perfectly uncertain market beliefs must prevail. When the entropy functional is used to index the market uncertainty, then the entropy-maximizing market beliefs must prevail. The EPT resolves the ambiguity of asset valuation in incomplete markets, notably, the valuation of derivative securities. We use the EPT to derive a new stock option pricing model that is similar to Black–Scholes' with the lognormal distribution replaced by a gamma distribution. Unlike the Black–Scholes model, the gamma model does not restrict the dynamics of the stock price or the short-term interest rate. Option replication based on the gamma model accounts for random changes in the stock price, price volatility and interest rates.

Suggested Citation

  • Les Gulko, 1999. "The Entropy Theory Of Stock Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(03), pages 331-355.
    • Handle: RePEc:wsi:ijtafx:v:02:y:1999:i:03:n:s0219024999000182
    DOI: 10.1142/S0219024999000182
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    Citations

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    Cited by:

    1. 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.
    2. Paul McCloud, 2020. "Expectation and Price in Incomplete Markets," Papers 2006.16703, arXiv.org.
    3. Malhotra, Gifty & Srivastava, R. & Taneja, H.C., 2019. "Calibration of the risk-neutral density function by maximization of a two-parameter entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 45-54.
    4. Luckshay Batra & Harish Chander Taneja, 2022. "Comparison between Information Theoretic Measures to Assess Financial Markets," FinTech, MDPI, vol. 1(2), pages 1-18, May.
    5. Sylvia Gottschalk, 2016. "Entropy and credit risk in highly correlated markets," Papers 1604.07042, arXiv.org.
    6. Będowska-Sójka, Barbara & Kliber, Agata, 2021. "Information content of liquidity and volatility measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    7. Batra, Luckshay & Taneja, H.C., 2021. "Approximate-Analytical solution to the information measure’s based quanto option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    8. José L. Vilar-Zanón & Barbara Rogo, 2024. "Pricing and Hedging Contingent Claims by Entropy Segmentation and Fenchel Duality," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-20, December.
    9. Colin Beardsley & John R. O'Brien, 2005. "The Financial Services Reform Act 2001: Impact on Systemic risk in Australia," ICMA Centre Discussion Papers in Finance icma-dp2005-12, Henley Business School, University of Reading.
    10. Kai Schindelhauer & Chen Zhou, 2018. "Value-at-Risk prediction using option-implied risk measures," DNB Working Papers 613, Netherlands Central Bank, Research Department.
    11. Grilli, Luca & Santoro, Domenico, 2020. "Boltzmann Entropy in Cryptocurrencies: A Statistical Ensemble Based Approach," MPRA Paper 99591, University Library of Munich, Germany.
    12. Minzhi Wu & Emili Tortosa-Ausina, 2020. "Bank Diversification and Focus in Disruptive Times: China, 2007–2018," Working Papers 2020/21, Economics Department, Universitat Jaume I, Castellón (Spain).
    13. Muhammad Sheraz & Imran Nasir, 2021. "Information-Theoretic Measures and Modeling Stock Market Volatility: A Comparative Approach," Risks, MDPI, vol. 9(5), pages 1-20, May.
    14. John A. Buzacott, 2016. "Capital allocation to alternatives with a multivariate ladder gamma return distribution," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 235-258, November.
    15. Gottschalk, Sylvia, 2017. "Entropy measure of credit risk in highly correlated markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 11-19.

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