IDEAS home Printed from https://ideas.repec.org/p/chf/rpseri/rp1536.html

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
    as

    Download full text from publisher

    File URL: http://ssrn.com/abstract=2648288
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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. 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.
    5. Fabozzi, Frank J. & Recchioni, Maria Cristina & Renò, Roberto, 2025. "Fifty years at the interface between financial modeling and operations research," European Journal of Operational Research, Elsevier, vol. 327(1), pages 1-21.
    6. He, Yunhao & Leippold, Markus, 2020. "Short-run risk, business cycle, and the value premium," Journal of Economic Dynamics and Control, Elsevier, vol. 120(C).
    7. 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.
    8. 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.
    9. 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.
    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. 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.
    12. 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.
    13. repec:ags:aaea22:343544 is not listed on IDEAS
    14. Hyung Joo Kim & Dong Hwan Oh, 2025. "Local Estimation for Option Pricing: Improving Forecasts with Market State Information," Finance and Economics Discussion Series 2025-076, Board of Governors of the Federal Reserve System (U.S.).
    15. 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.
    16. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:chf:rpseri:rp1536. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ridima Mittal (email available below). General contact details of provider: https://edirc.repec.org/data/fameech.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.