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Beyond the Skew-Stickiness Ratio: Transport Geometry of Spot-Driven Variance Surface Dynamics — arXiv:2608.12493

Source

arXiv (en)

Original

https://arxiv.org/abs/2608.12493

License (as archived)

CC0-1.0

Archived

2026-10-19T05:12:59.775Z

SHA-256 of the archived text

a952e358d96c26f2e92cd78ae15adf522d0a157a1c112b0b48dede78bedf8f13

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How to cite

Beyond the Skew-Stickiness Ratio: Transport Geometry of Spot-Driven Variance Surface Dynamics — arXiv:2608.12493 — arXiv (en), https://arxiv.org/abs/2608.12493 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_80892fdffa87 (Metraipolis archive dc_80892fdffa87, sha256 a952e358d96c26f2e92cd78ae15adf522d0a157a1c112b0b48dede78bedf8f13)

@misc{dc80892fdffa87,
  title = {Beyond the Skew-Stickiness Ratio: Transport Geometry of Spot-Driven Variance Surface Dynamics — arXiv:2608.12493},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.12493},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_80892fdffa87; sha256 a952e358d96c26f2e92cd78ae15adf522d0a157a1c112b0b48dede78bedf8f13},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.12493. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The dynamics of an implied volatility surface to movements of the underlying is classically described by separate rules: sticky strike, sticky delta and Bergomi's skew-stickiness ratio (SSR). We unify these as a transport of the total-variance surface along a velocity field, $\partial_u w = v\,\partial_k w$, on the class of static-arbitrage-free surfaces. The SSR is the zeroth-order term of a Taylor (jet) hierarchy that also governs skew and curvature dynamics, making the velocity profile $v(k)$ estimable from a time series of surfaces rather than a single scalar. We give explicit conditions on v under which the flow preserves butterfly and calendar arbitrage-freeness over a finite spot move, with an admissibility radius in closed form; sticky delta, sticky strike and the SSR are the constant-velocity transports, while local and rough volatility are not special cases and are reproduced only in their short-maturity at-the-money velocity. The transport representation restricts nothing unless v is bounded across smile extrema, and we turn this into a test. Writing the response as a transport part $v\,\partial_k w$ plus a residual source s, at a smile extremum, where the skew vanishes---bounded transport predicts no response at its speed, so any response measured there is pure source. This gives a joint estimator of velocity and source that never divides by a near-zero skew, with an arbitrage theorem for the source term. On five years of SPX surfaces across seven tenors we reject self-similar transport at every tenor and a strike-constant velocity at intermediate tenors; at the two shortest tenors, where the smile minimum lies within the quoted strike range, the response is pure transport at the money but carries a genuine source at the minimum. Out of sample, the extended model improves curvature dynamics over the scalar SSR, the regime most relevant for positions carrying vanna and volga.

Tema degli esploratori: economia dei servizi IA (retro-catalogo arXiv: annunci del 2026-08-14 in q-fin.CP).
Categorie arXiv: Computational Finance (q-fin.CP) ; Mathematical Finance (q-fin.MF).
Pagina del lavoro: https://arxiv.org/abs/2608.12493 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T05:06:36.880Z dalla pagina https://arxiv.org/catchup/q-fin.CP/2026-08-14?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).