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Subjective probability distributions of nonlinear payoffs: Recovering option payoff, agent’s utility, and pricing kernel distributions

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  • Yamazaki, Akira

Abstract

This paper proposes a general method to recover the subjective probability distributions of nonlinear payoffs from option prices. We show that the characteristic function of the distribution is represented as the present value of a static option portfolio with complex-valued portfolio weights. By applying Fourier inversion, we derive the subjective distribution from the characteristic function. Using the recovery method with the S&P 500 index option data, we examine the historical behaviors of subjective distributions for agent’s utility and pricing kernels. Additionally, we elucidate the theoretical relation between expected option returns and pricing kernels, offering enhanced insights compared to previous studies.

Suggested Citation

  • Yamazaki, Akira, 2025. "Subjective probability distributions of nonlinear payoffs: Recovering option payoff, agent’s utility, and pricing kernel distributions," The North American Journal of Economics and Finance, Elsevier, vol. 76(C).
    • Handle: RePEc:eee:ecofin:v:76:y:2025:i:c:s1062940825000026
    DOI: 10.1016/j.najef.2025.102362
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    References listed on IDEAS

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    1. Ranadeb Chaudhuri & Mark Schroder, 2015. "Monotonicity of the Stochastic Discount Factor and Expected Option Returns," The Review of Financial Studies, Society for Financial Studies, vol. 28(5), pages 1462-1505.
    2. Ian W. R. Martin & Christian Wagner, 2019. "What Is the Expected Return on a Stock?," Journal of Finance, American Finance Association, vol. 74(4), pages 1887-1929, August.
    3. Peter Christoffersen & Steven Heston & Kris Jacobs, 2013. "Capturing Option Anomalies with a Variance-Dependent Pricing Kernel," The Review of Financial Studies, Society for Financial Studies, vol. 26(8), pages 1963-2006.
    4. Jason Fink, 2003. "An examination of the effectiveness of static hedging in the presence of stochastic volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(9), pages 859-890, September.
    5. Polkovnichenko, Valery & Zhao, Feng, 2013. "Probability weighting functions implied in options prices," Journal of Financial Economics, Elsevier, vol. 107(3), pages 580-609.
    6. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    7. Joshua D. Coval & Tyler Shumway, 2001. "Expected Option Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 983-1009, June.
    8. repec:bla:jfinan:v:53:y:1998:i:3:p:1165-1190 is not listed on IDEAS
    9. Ian Martin, 2017. "What is the Expected Return on the Market?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(1), pages 367-433.
    10. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    11. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    12. Whitney Newey & Kenneth West, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    13. Morten Nalholm & Rolf Poulsen, 2006. "Static hedging and model risk for barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(5), pages 449-463, May.
    14. Akihiko Takahashi & Akira Yamazaki, 2009. "A new scheme for static hedging of European derivatives under stochastic volatility models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(5), pages 397-413, May.
    15. repec:bla:jfinan:v:59:y:2004:i:1:p:407-446 is not listed on IDEAS
    16. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    17. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    18. Steve Ross, 2015. "The Recovery Theorem," Journal of Finance, American Finance Association, vol. 70(2), pages 615-648, April.
    19. Akira Yamazaki, 2022. "Recovering subjective probability distributions," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1234-1263, July.
    20. Oleg Bondarenko, 2014. "Why Are Put Options So Expensive?," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 1-50.
    21. Akihiko Takahashi & Akira Yamazaki, 2009. "Efficient static replication of European options under exponential Lévy models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(1), pages 1-15, January.
    22. Shuichi Ohsaki & Akira Yamazaki, 2011. "Static Hedging Of Defaultable Contingent Claims: A Simple Hedging Scheme Across Equity And Credit Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 239-264.
    23. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    24. Akihiko Takahashi & Yukihiro Tsuzuki & Akira Yamazaki, 2011. "Hedging European Derivatives With The Polynomial Variance Swap Under Uncertain Volatility Environments," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 485-505.
    25. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
    26. Bakshi, Gurdip & Gao, Xiaohui & Xue, Jinming, 2023. "Recovery with Applications to Forecasting Equity Disaster Probability and Testing the Spanning Hypothesis in the Treasury Market," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 58(4), pages 1808-1842, June.
    27. Akira Yamazaki, 2020. "Probability weighting and default risk: a possible explanation for distressed stock puzzles," Quantitative Finance, Taylor & Francis Journals, vol. 20(5), pages 745-767, May.
    28. Chabi-Yo, Fousseni & Loudis, Johnathan, 2020. "The conditional expected market return," Journal of Financial Economics, Elsevier, vol. 137(3), pages 752-786.
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    More about this item

    Keywords

    Subjective probability distribution; Option payoff; Utility function; Pricing kernel; Static replication;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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