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Asymptotic extrapolation of model-free implied variance: exploring structural underestimation in the VIX Index

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  • Philip Stahl

    (Technische Universität Darmstadt
    Deka Investment GmbH)

Abstract

We show that the VIX Index structurally underestimates model-free implied volatility because its implementation omits extrapolation of the volatility smile in the tails. We use the asymptotic behavior of the volatility surface to construct a correction term that is model-independent and only requires option prices at the two outermost strikes. We show how to apply this correction to the VIX Index ex-post as well as how to modify its implementation accordingly. Furthermore, we show that the degree of underestimation varies over time. For the S&P 500 Index and the DJIA Index the error is larger in periods of sustained low volatility. This cannot be observed for the Volatility-of-VIX Index.

Suggested Citation

  • Philip Stahl, 2022. "Asymptotic extrapolation of model-free implied variance: exploring structural underestimation in the VIX Index," Review of Derivatives Research, Springer, vol. 25(3), pages 315-339, October.
    • Handle: RePEc:kap:revdev:v:25:y:2022:i:3:d:10.1007_s11147-022-09190-2
    DOI: 10.1007/s11147-022-09190-2
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    References listed on IDEAS

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    More about this item

    Keywords

    Model-free implied volatility; Volatility smile; VIX index; Variance swaps;
    All these 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

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