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The Price of the Smile and Variance Risk Premia

Author

Listed:
  • Peter H. GRUBER

    (University of Lugano)

  • Claudio TEBALDI

    (Bocconi University, IGIER and CAREFIN)

  • Fabio TROJANI

    (University of Geneva and Swiss Finance Institute)

Abstract

In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a downward sloping term structure of low-frequency variance risk premia in normal times. In periods of distress, the term structure is upward sloping and dominated by a high-frequency premium for jump variance. This dichotomy is consistent with the puzzling skew sensitivities of option markets with credit-constrained intermediaries and it builds a challenge for many reduced-form and structural models of stochastic volatility.

Suggested Citation

  • Peter H. GRUBER & Claudio TEBALDI & Fabio TROJANI, 2015. "The Price of the Smile and Variance Risk Premia," Swiss Finance Institute Research Paper Series 15-36, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1536
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    Cited by:

    1. Bardgett, Chris & Gourier, Elise & Leippold, Markus, 2019. "Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets," Journal of Financial Economics, Elsevier, vol. 131(3), pages 593-618.
    2. Chavas, Jean-Paul & Li, Jian & Wang, Linjie, 2024. "Option pricing revisited: The role of price volatility and dynamics," Journal of Commodity Markets, Elsevier, vol. 33(C).
    3. Claudia Yeap & Simon S Kwok & S T Boris Choy, 2018. "A Flexible Generalized Hyperbolic Option Pricing Model and Its Special Cases," Journal of Financial Econometrics, Oxford University Press, vol. 16(3), pages 425-460.
    4. Bai, Jennie & Goldstein, Robert S. & Yang, Fan, 2019. "The leverage effect and the basket-index put spread," Journal of Financial Economics, Elsevier, vol. 131(1), pages 186-205.
    5. Rombouts, Jeroen V.K. & Stentoft, Lars & Violante, Francesco, 2020. "Variance swap payoffs, risk premia and extreme market conditions," Econometrics and Statistics, Elsevier, vol. 13(C), pages 106-124.
    6. McGee, Richard J. & McGroarty, Frank, 2017. "The risk premium that never was: A fair value explanation of the volatility spread," European Journal of Operational Research, Elsevier, vol. 262(1), pages 370-380.
    7. Rombouts, Jeroen V.K. & Stentoft, Lars & Violante, Francesco, 2020. "Dynamics of variance risk premia: A new model for disentangling the price of risk," Journal of Econometrics, Elsevier, vol. 217(2), pages 312-334.
    8. He, Yunhao & Leippold, Markus, 2020. "Short-run risk, business cycle, and the value premium," Journal of Economic Dynamics and Control, Elsevier, vol. 120(C).
    9. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2020. "The Pricing of Tail Risk and the Equity Premium: Evidence From International Option Markets," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 662-678, July.
    10. Simon Scheidegger & Adrien Treccani, 2021. "Pricing American Options under High-Dimensional Models with Recursive Adaptive Sparse Expectations [Telling from Discrete Data Whether the Underlying Continuous-Time Model Is a Diffusion]," Journal of Financial Econometrics, Oxford University Press, vol. 19(2), pages 258-290.
    11. Jeroen V.K. Rombouts & Lars Stentoft & Francesco Violante, 2017. "Dynamics of Variance Risk Premia, Investors' Sentiment and Return Predictability," CREATES Research Papers 2017-10, Department of Economics and Business Economics, Aarhus University.
    12. Chavas, Jean-Paul & Li, Jian & Wang, Linjie, 2024. "Option Pricing Revisited: The Role of Price Volatility and Dynamics," 2024 Annual Meeting, July 28-30, New Orleans, LA 343544, Agricultural and Applied Economics Association.
    13. Yifan Ye & Zheqi Fan & Xinfeng Ruan, 2025. "Modeling the Implied Volatility Smirk in China: Do Non‐Affine Two‐Factor Stochastic Volatility Models Work?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 45(6), pages 612-636, June.

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    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • 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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