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The Right Wing of the SABR Smile with an Absorbing Boundary: Resolution of Conjectures of Henry-Labord\`ere

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  • Zeyu Cao
  • Shaosai Huang

Abstract

We determine the leading logarithmic asymptotics of the fixed-maturity right tail of the SABR model with $\beta\in(0,1)$ and absorption at zero, for every correlation $\rho\in(-1,1)$. If $P(k)$ is the probability that the terminal forward is at least $f_0e^k$, then $-k^{-2}\ln P(k)\to(1-\beta)^2/(2\nu^2T(1-(\rho\wedge0)^2))$ as $k\to\infty$. For $\rho\ge0$ this is the rate predicted by the unrestricted hyperbolic geometry. For $\rho

Suggested Citation

  • Zeyu Cao & Shaosai Huang, 2026. "The Right Wing of the SABR Smile with an Absorbing Boundary: Resolution of Conjectures of Henry-Labord\`ere," Papers 2610.04209, arXiv.org.
    • Handle: RePEc:arx:papers:2610.04209
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    References listed on IDEAS

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    1. Leif Andersen & Vladimir Piterbarg, 2007. "Moment explosions in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(1), pages 29-50, January.
    2. Archil Gulisashvili & Blanka Horvath & Antoine Jacquier, 2018. "Mass at zero in the uncorrelated SABR model and implied volatility asymptotics," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1753-1765, October.
    3. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2013. "Shapes of implied volatility with positive mass at zero," Papers 1310.1020, arXiv.org, revised May 2017.
    4. Nian Yang & Xiangwei Wan, 2018. "The survival probability of the SABR model: asymptotics and application," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1767-1779, October.
    5. S. Benaim & P. Friz, 2009. "Regular Variation And Smile Asymptotics," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 1-12, January.
    6. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
    7. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2017. "Shapes of implied volatility with positive mass at zero," Working Papers 2017-77, Center for Research in Economics and Statistics.
    8. Nan Chen & Nian Yang, 2019. "The principle of not feeling the boundary for the SABR model," Quantitative Finance, Taylor & Francis Journals, vol. 19(3), pages 427-436, March.
    9. Kun Gao & Roger Lee, 2014. "Asymptotics of implied volatility to arbitrary order," Finance and Stochastics, Springer, vol. 18(2), pages 349-392, April.
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