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The Entropy Theory Of Bond Option Pricing

Author

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  • LES GULKO

    (Paloma Partners, Two American Lane, Greenwich, CT 06836-2571, 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 collective market uncertainty, then the entropy-maximizing consensus beliefs must prevail. The EPT resolves the ambiguity of arbitrage-free valuation in incomplete markets. The EPT produces a new bond option model that is similar to Black–Scholes' with the lognormal distribution replaced by a beta distribution. Unlike alternative models, the beta model is valid for arbitrary term structure dynamics and for arbitrary credit risk of the underlying bonds. Option replication and hedging under the beta model accounts for random changes in the underlying bond price, price volatility and short-term interest rates.

Suggested Citation

  • Les Gulko, 2002. "The Entropy Theory Of Bond Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 355-383.
    • Handle: RePEc:wsi:ijtafx:v:05:y:2002:i:04:n:s021902490200147x
    DOI: 10.1142/S021902490200147X
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    Citations

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    Cited by:

    1. 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.
    2. Sylvia Gottschalk, 2016. "Entropy and credit risk in highly correlated markets," Papers 1604.07042, arXiv.org.
    3. Cassio Neri & Lorenz Schneider, 2011. "A Family of Maximum Entropy Densities Matching Call Option Prices," Papers 1102.0224, arXiv.org.
    4. Będowska-Sójka, Barbara & Kliber, Agata, 2021. "Information content of liquidity and volatility measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    5. Cassio Neri & Lorenz Schneider, 2012. "Maximum entropy distributions inferred from option portfolios on an asset," Finance and Stochastics, Springer, vol. 16(2), pages 293-318, April.
    6. 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.
    7. Kai Schindelhauer & Chen Zhou, 2018. "Value-at-Risk prediction using option-implied risk measures," DNB Working Papers 613, Netherlands Central Bank, Research Department.

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