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A Closed-Form Solution for Options with Ambiguity about Stochastic Volatility

Author

Listed:
  • Gonçalo Faria

    (RGEA, Universidad de Vigo)

  • João Correia-da-Silva

    (CEF.UP and Faculdade de Economia, Universidade do Porto)

Abstract

We derive a closed-form solution for the price of a European call option in the presence of ambiguity about the stochastic process that determines the variance of the underlying asset's return. The option pricing formula of Heston (1993) is a particular case of ours, corresponding to the case in which there is no ambiguity (uncertainty is exclusively risk). In the presence of ambiguity, the variance uncertainty price becomes either a convex or a concave function of the instantaneous variance, depending on whether the variance ambiguity price is negative or positive. We find that if the variance ambiguity price is positive, the option price is decreasing in the level of ambiguity (across all moneyness levels). The opposite happens if the variance ambiguity price is negative. Consistently, in the former (and more natural) scenario, ambiguity aversion decreases the option's implied volatility, which helps to explain the variance premium puzzle.

Suggested Citation

  • Gonçalo Faria & João Correia-da-Silva, 2011. "A Closed-Form Solution for Options with Ambiguity about Stochastic Volatility," FEP Working Papers 414, Universidade do Porto, Faculdade de Economia do Porto.
    • Handle: RePEc:por:fepwps:414
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    Citations

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    Cited by:

    1. Ben-Zhang Yang & Xiaoping Lu & Guiyuan Ma & Song-Ping Zhu, 2020. "Robust Portfolio Optimization with Multi-Factor Stochastic Volatility," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 264-298, July.
    2. repec:osf:socarx:ud7yw_v1 is not listed on IDEAS
    3. Zghal, Imen & Ben Hamad, Salah & Eleuch, Hichem & Nobanee, Haitham, 2020. "The effect of market sentiment and information asymmetry on option pricing," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    4. Ben-Zhang Yang & Xiaoping Lu & Guiyuan Ma & Song-Ping Zhu, 2019. "Robust portfolio optimization with multi-factor stochastic volatility," Papers 1910.06872, arXiv.org, revised Jun 2020.
    5. Chen, Qiang & Han, Yu, 2023. "Options market ambiguity and its information content," Journal of Financial Markets, Elsevier, vol. 64(C).
    6. Yanchu Liu & Chen Liu & Yiyao Chen & Xianming Sun, 2024. "Option‐Implied Ambiguity and Equity Return Predictability," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(9), pages 1556-1577, September.
    7. Ben-Rephael, Azi & Cookson, J. Anthony & izhakian, yehuda, 2022. "Trading, Ambiguity and Information in the Options Market," SocArXiv ewunv, Center for Open Science.
    8. Izhakian, Yehuda, 2020. "A theoretical foundation of ambiguity measurement," Journal of Economic Theory, Elsevier, vol. 187(C).
    9. Tarik Driouchi & Lenos Trigeorgis & Raymond H. Y. So, 2018. "Option implied ambiguity and its information content: Evidence from the subprime crisis," Annals of Operations Research, Springer, vol. 262(2), pages 463-491, March.
    10. repec:osf:socarx:ewunv_v1 is not listed on IDEAS
    11. Hu, Duni & Wang, Hailong, 2024. "Heterogeneous beliefs with preference interdependence and asset pricing," International Review of Economics & Finance, Elsevier, vol. 93(PA), pages 1-37.
    12. Nihad Aliyev, 2019. "Financial Markets with Multidimensional Uncertainty," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2019, January-A.
    13. Yehuda Izhakian & David Yermack & Jaime F. Zender, 2022. "Ambiguity and the Tradeoff Theory of Capital Structure," Management Science, INFORMS, vol. 68(6), pages 4090-4111, June.
    14. Gonçalo Faria & João Correia-da-Silva, 2012. "The price of risk and ambiguity in an intertemporal general equilibrium model of asset prices," Annals of Finance, Springer, vol. 8(4), pages 507-531, November.
    15. Brenner, Menachem & Izhakian, Yehuda, 2018. "Asset pricing and ambiguity: Empirical evidence⁎," Journal of Financial Economics, Elsevier, vol. 130(3), pages 503-531.
    16. Ben-Rephael, Azi & Cookson, J. Anthony & izhakian, yehuda, 2022. "Do I Really Want to Hear The News? Public Information Arrival and Investor Beliefs," SocArXiv ud7yw, Center for Open Science.
    17. Chunpeng Yang & Bin Gao & Jianlei Yang, 2016. "Option pricing model with sentiment," Review of Derivatives Research, Springer, vol. 19(2), pages 147-164, July.

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    Keywords

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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