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The Price of the Smile and Variance Risk Premia

Author

Listed:
  • Peter H. Gruber

    (Istituto di finanza, Università della Svizzera Italiana, 6900 Lugano, Switzerland;)

  • Claudio Tebaldi

    (Department of Finance, Università L. Bocconi, 20132 Milano, Italy; IGIER; Baffi-Carefin; LTI@UniTO, Università di Torino)

  • Fabio Trojani

    (University of Geneva, 1211 Geneva 4, Switzerland; Swiss Finance Institute)

Abstract

Using a new specification of multifactor volatility, we estimate the hidden risk factors spanning S&P 500 index (SPX) implied volatility surfaces and the risk premia of volatility-sensitive payoffs. SPX implied volatility surfaces are well-explained by three dependent state variables reflecting (i) short- and long-term implied volatility risks and (ii) short-term implied skewness risk. The more persistent volatility factor and the skewness factor support a downward sloping term structure of variance risk premia in normal times, whereas the most transient volatility factor accounts for an upward sloping term structure in periods of distress. Our volatility specification based on a matrix state process is instrumental to obtaining a tractable and flexible model for the joint dynamics of returns and volatilities, which improves pricing performance and risk premium modeling with respect to recent three-factor specifications based on standard state spaces.

Suggested Citation

  • Peter H. Gruber & Claudio Tebaldi & Fabio Trojani, 2021. "The Price of the Smile and Variance Risk Premia," Management Science, INFORMS, vol. 67(7), pages 4056-4074, July.
    • Handle: RePEc:inm:ormnsc:v:67:y:2021:i:7:p:4056-4074
    DOI: 10.1287/mnsc.2020.3689
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    References listed on IDEAS

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