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VIX maturity interpolation

Author

Listed:
  • Torben G. Andersen

    (Northwestern University
    NBER
    Canadian Derivatives Institute
    Center for Research in Energy)

  • Oleg Bondarenko

    (University of Illinois at Chicago)

  • Maria T. Gonzalez-Perez

    (Banco de España
    Center for Economic and Financial Studies)

Abstract

The VIX index is computed as a weighted average of two model-free option-implied variance measures for maturities around 30 days. This induces an interpolation error which, prior to 2014 (old VIX), could be sizable and especially pertinent under stressed market conditions. We quantify the VIX interpolation errors and identify underlying sources. We show the change to include weekly options for the VIX calculation in 2014 (new VIX) led to a tenfold average error reduction, eliminating them as a practical concern. Thus, the gap between the old and new VIX measure is a good proxy for the interpolation error. Moreover, the new Cboe VIX calculation is not backdated, so the series displays different statistical properties before and after 2014. Our analysis is relevant for a broad set of VIX-style indices worldwide, since nearly all such measures are computed exclusively from monthly options. In addition, there is growing interest in shorter-horizon VIX indices, and for such measures the interpolation errors amplify notably. Our analysis facilitates assessment of these errors and offers guidance for new robust computational algorithms. We exemplify this via an analysis of the 9-day VIX index. Finally, we compare the interpolation scheme for VIX to a pair of existing alternatives also based on monthly options. We find that such modifications can reduce the average errors, but they are neither uniformly superior nor do they resolve the basic issue satisfactorily.

Suggested Citation

  • Torben G. Andersen & Oleg Bondarenko & Maria T. Gonzalez-Perez, 2025. "VIX maturity interpolation," Review of Derivatives Research, Springer, vol. 28(1), pages 1-40, April.
    • Handle: RePEc:kap:revdev:v:28:y:2025:i:1:d:10.1007_s11147-025-09210-x
    DOI: 10.1007/s11147-025-09210-x
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    References listed on IDEAS

    as
    1. Ian W. R. Martin & Christian Wagner, 2019. "What Is the Expected Return on a Stock?," Journal of Finance, American Finance Association, vol. 74(4), pages 1887-1929, August.
    2. Torben G. Andersen & Oleg Bondarenko & Maria T. Gonzalez-Perez, 2015. "Exploring Return Dynamics via Corridor Implied Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 28(10), pages 2902-2945.
    3. Stamatis Leontsinis & Carol Alexander, 2017. "Arithmetic variance swaps," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 551-569, April.
    4. Ian Martin, 2017. "What is the Expected Return on the Market?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(1), pages 367-433.
    5. Bondarenko, Oleg, 2014. "Variance trading and market price of variance risk," Journal of Econometrics, Elsevier, vol. 180(1), pages 81-97.
    6. Martin G. Haas & Franziska J. Peter, 2024. "Implementing Intraday Model-Free Implied Volatility for Individual Equities to Analyze the Return–Volatility Relationship," JRFM, MDPI, vol. 17(1), pages 1-19, January.
    7. Gonzalez-Perez, Maria T. & Guerrero, David E., 2013. "Day-of-the-week effect on the VIX. A parsimonious representation," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 243-260.
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