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Mass at zero in the uncorrelated SABR model and implied volatility asymptotics

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  • Archil Gulisashvili
  • Blanka Horvath
  • Antoine Jacquier

Abstract

We study the mass at the origin in the uncorrelated SABR stochastic volatility model, and derive several tractable expressions, in particular when time becomes small or large. As an application--in fact the original motivation for this paper--we derive small-strike expansions for the implied volatility when the maturity becomes short or large. These formulae, by definition arbitrage free, allow us to quantify the impact of the mass at zero on existing implied volatility approximations, and in particular how correct/erroneous these approximations become.

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  • Archil Gulisashvili & Blanka Horvath & Antoine Jacquier, 2015. "Mass at zero in the uncorrelated SABR model and implied volatility asymptotics," Papers 1502.03254, arXiv.org, revised Nov 2016.
    • Handle: RePEc:arx:papers:1502.03254
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    Cited by:

    1. Blanka Horvath & Oleg Reichmann, 2018. "Dirichlet Forms and Finite Element Methods for the SABR Model," Papers 1801.02719, arXiv.org.
    2. Christian Bayer & Peter K. Friz & Archil Gulisashvili & Blanka Horvath & Benjamin Stemper, 2017. "Short-time near-the-money skew in rough fractional volatility models," Papers 1703.05132, arXiv.org, revised Mar 2018.

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