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

Zeyu Cao and Shaosai Huang

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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

Date: 2026-10
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