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Normalization for Implied Volatility

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  • Masaaki Fukasawa

Abstract

We study specific nonlinear transformations of the Black-Scholes implied volatility to show remarkable properties of the volatility surface. Model-free bounds on the implied volatility skew are given. Pricing formulas for the European options which are written in terms of the implied volatility are given. In particular, we prove elegant formulas for the fair strikes of the variance swap and the gamma swap.

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  • Masaaki Fukasawa, 2010. "Normalization for Implied Volatility," Papers 1008.5055, arXiv.org, revised Sep 2010.
    • Handle: RePEc:arx:papers:1008.5055
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    Cited by:

    1. Masaaki Fukasawa, 2020. "Volatility has to be rough," Papers 2002.09215, arXiv.org.
    2. Christian Bayer & Fabian Andsem Harang & Paolo Pigato, 2020. "Log-modulated rough stochastic volatility models," Papers 2008.03204, arXiv.org, revised May 2021.
    3. Paolo Pigato, 2019. "Extreme at-the-money skew in a local volatility model," Finance and Stochastics, Springer, vol. 23(4), pages 827-859, October.
    4. Arianna Mingone, 2022. "Smiles in delta," Papers 2209.00406, arXiv.org.
    5. Stefano De Marco, 2020. "On the harmonic mean representation of the implied volatility," Papers 2007.03585, arXiv.org.
    6. Stefano De Marco & Claude Martini, 2017. "Moment generating functions and Normalized implied volatilities: unification and extension via Fukasawa's pricing formula," Papers 1703.00957, arXiv.org, revised May 2017.

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