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Risk premium and rough volatility

Author

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  • Ofelia Bonesini
  • Antoine Jacquier
  • Aitor Muguruza

Abstract

One the one hand, rough volatility has been shown to provide a consistent framework to capture the properties of stock price dynamics both under the historical measure and for pricing purposes. On the other hand, market price of volatility risk is a well-studied object in Financial Economics, and empirical estimates show it to be stochastic rather than deterministic. Starting from a rough volatility model under the historical measure, we take up this challenge and provide an analysis of the impact of such a non-deterministic risk for pricing purposes.

Suggested Citation

  • Ofelia Bonesini & Antoine Jacquier & Aitor Muguruza, 2024. "Risk premium and rough volatility," Papers 2403.11897, arXiv.org.
  • Handle: RePEc:arx:papers:2403.11897
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    References listed on IDEAS

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    1. Mikkel Bennedsen & Asger Lunde & Mikko S Pakkanen, 2022. "Decoupling the Short- and Long-Term Behavior of Stochastic Volatility [Multifactor Approximation of Rough Volatility Models]," Journal of Financial Econometrics, Oxford University Press, vol. 20(5), pages 961-1006.
    2. Paul Gassiat, 2018. "On the martingale property in the rough Bergomi model," Papers 1811.10935, arXiv.org, revised Apr 2019.
    3. Charles Smithson & Betty J. Simkins, 2005. "Does Risk Management Add Value? A Survey of the Evidence," Journal of Applied Corporate Finance, Morgan Stanley, vol. 17(3), pages 8-17, June.
    4. Jin-Chuan Duan & Weiqi Zhang, 2014. "Forward-Looking Market Risk Premium," Management Science, INFORMS, vol. 60(2), pages 521-538, February.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Graham, John R. & Harvey, Campbell R., 2005. "The long-run equity risk premium," Finance Research Letters, Elsevier, vol. 2(4), pages 185-194, December.
    7. Julien Guyon & Jordan Lekeufack, 2023. "Volatility is (mostly) path-dependent," Post-Print hal-04373380, HAL.
    8. Julien Guyon & Jordan Lekeufack, 2023. "Volatility is (mostly) path-dependent," Quantitative Finance, Taylor & Francis Journals, vol. 23(9), pages 1221-1258, September.
    9. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    10. Antoine Jacquier & Claude Martini & Aitor Muguruza, 2018. "On VIX futures in the rough Bergomi model," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 45-61, January.
    11. Hiroaki Kaido & Halbert White, 2009. "Inference on Risk-Neutral Measures for Incomplete Markets," Journal of Financial Econometrics, Oxford University Press, vol. 7(3), pages 199-246, Summer.
    12. McDonald, Robert & Siegel, Daniel, 1984. "Option Pricing When the Underlying Asset Earns a Below-Equilibrium Rate of Return: A Note," Journal of Finance, American Finance Association, vol. 39(1), pages 261-265, March.
    13. Fousseni Chabi-Yo, 2012. "Pricing Kernels with Stochastic Skewness and Volatility Risk," Management Science, INFORMS, vol. 58(3), pages 624-640, March.
    14. Bansal, Ravi & Lundblad, Christian, 2002. "Market efficiency, asset returns, and the size of the risk premium in global equity markets," Journal of Econometrics, Elsevier, vol. 109(2), pages 195-237, August.
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