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The term structure of the price of variance risk

Author

Listed:
  • Marianne Andries
  • Thomas M Eisenbach
  • R Jay Kahn
  • Martin C Schmalz

Abstract

We empirically investigate the term structure of variance risk pricing and how it varies over time. We estimate the aversion to variance risk in a stochastic-volatility option pricing model separately for options of different maturities and find that variance risk pricing decreases in absolute value with maturity but remains significantly different from zero up to the nine-month horizon. We find consistent non-parametric results using estimates from Sharpe ratios of delta-neutral straddles. We further show that the term structure is downward sloping both during normal times and in times of stress, when required compensation for variance risk increases and its term structure steepens further.

Suggested Citation

  • Marianne Andries & Thomas M Eisenbach & R Jay Kahn & Martin C Schmalz, 2025. "The term structure of the price of variance risk," Review of Finance, European Finance Association, vol. 29(6), pages 1699-1720.
    • Handle: RePEc:oup:revfin:v:29:y:2025:i:6:p:1699-1720.
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    File URL: http://hdl.handle.net/10.1093/rof/rfaf029
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    2. 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.
    3. Peter Van Tassel & Erik Vogt, 2016. "Global variance term premia and intermediary risk appetite," Staff Reports 789, Federal Reserve Bank of New York.
    4. Baeho Kim & Da‐Hea Kim & Haehean Park, 2020. "Informed options trading on the implied volatility surface: A cross‐sectional approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(5), pages 776-803, May.
    5. Hoyong Choi & Philippe Mueller & Andrea Vedolin, 2017. "Bond Variance Risk Premiums," Review of Finance, European Finance Association, vol. 21(3), pages 987-1022.
    6. Peter Van Tassel, 2020. "The Law of One Price in Equity Volatility Markets," Staff Reports 953, Federal Reserve Bank of New York.
    7. Dew-Becker, Ian & Giglio, Stefano & Kelly, Bryan, 2021. "Hedging macroeconomic and financial uncertainty and volatility," Journal of Financial Economics, Elsevier, vol. 142(1), pages 23-45.
    8. van Binsbergen, Jules H. & Koijen, Ralph S.J., 2017. "The term structure of returns: Facts and theory," Journal of Financial Economics, Elsevier, vol. 124(1), pages 1-21.
    9. Veronica Cappelli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Stefania Minardi, 2021. "Sources of Uncertainty and Subjective Prices," Journal of the European Economic Association, European Economic Association, vol. 19(2), pages 872-912.
    10. Peter Van Tassel, 2018. "Equity Volatility Term Premia," Staff Reports 867, Federal Reserve Bank of New York.
    11. Fabian Hollstein & Marcel Prokopczuk & Chardin Wese Simen, 2019. "The term structure of systematic and idiosyncratic risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(4), pages 435-460, April.
    12. Eisenbach, Thomas M. & Schmalz, Martin C., 2016. "Anxiety in the face of risk," Journal of Financial Economics, Elsevier, vol. 121(2), pages 414-426.

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    Keywords

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    JEL classification:

    • 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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