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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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    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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