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Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models

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  • Stefan Gerhold
  • I. Cetin Gülüm
  • Arpad Pinter

Abstract

We consider the at-the-money (ATM) strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behaviour of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity ATM digital call options, using Mellin transform asymptotics. Finally, we discuss when the ATM slope is consistent with the steepness of the smile wings, as given by Lee’s moment formula.

Suggested Citation

  • Stefan Gerhold & I. Cetin Gülüm & Arpad Pinter, 2016. "Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(2), pages 135-157, March.
    • Handle: RePEc:taf:apmtfi:v:23:y:2016:i:2:p:135-157
    DOI: 10.1080/1350486X.2016.1197041
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    Cited by:

    1. Jean-Philippe Aguilar, 2021. "The value of power-related options under spectrally negative Lévy processes," Review of Derivatives Research, Springer, vol. 24(2), pages 173-196, July.
    2. Paolo Pigato, 2019. "Extreme at-the-money skew in a local volatility model," Finance and Stochastics, Springer, vol. 23(4), pages 827-859, October.
    3. Federico De Olivera & José Fajardo & Ernesto Mordecki, 2018. "Skewed Lévy Models And Implied Volatility Skew," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-16, March.
    4. Jean-Philippe Aguilar, 2019. "The value of power-related options under spectrally negative L\'evy processes," Papers 1910.07971, arXiv.org, revised Jan 2021.

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