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Dyson-Schwinger Effective-Action Methods for Rough Volatility: A Correlation-Response Architecture for Calibration, Exotics and Risk — arXiv:2609.37741

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.37741
License (as archived): CC0-1.0
Archived: 2026-10-07T20:45:34.148Z
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How to cite

Dyson-Schwinger Effective-Action Methods for Rough Volatility: A Correlation-Response Architecture for Calibration, Exotics and Risk — arXiv:2609.37741 — arXiv (en), https://arxiv.org/abs/2609.37741 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_5cd282dcda60 (Metraipolis archive dc_5cd282dcda60, sha256 0e9fc702dd0bded3eace8274f141857fe7c7d71a20c5b396ae5784ae54d6289e)

BibTeX

@misc{dc5cd282dcda60,
  title = {Dyson-Schwinger Effective-Action Methods for Rough Volatility: A Correlation-Response Architecture for Calibration, Exotics and Risk — arXiv:2609.37741},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.37741},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_5cd282dcda60; sha256 0e9fc702dd0bded3eace8274f141857fe7c7d71a20c5b396ae5784ae54d6289e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.37741. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We develop a non-perturbative framework for stochastic-volatility option pricing built on the two-particle-irreducible (2PI) effective action and the Dyson-Schwinger gap equations of quantum field theory. In log-price, log-volatility or Lamperti coordinates, the joint law of the state variables is approximated by a self-consistent Gaussian whose mean and effective diffusion follow from the 2PI stationarity conditions, with the exponential and CEV vertices evaluated through the exact Gaussian moment-generating function rather than a Taylor cut. For exponential vertices the skeletons beyond this level sum in closed form: in exp-OU the evaluated melon level cuts the Hartree error by 20-130x, to 0.01-0.11 bp. Whether the dressed inverse propagator is local in time separates Markovian models, where the gap equation collapses to a few ODEs, from rough (Volterra) models, where the full two-time propagator is retained. At nonzero correlation the field is integrated deterministically by conditioning on its two leading Gaussian modes, with exact conditional moments and a moment-matched law for the integrated variance and leverage integral; in the CEV models the correlated drift enters a Dyson equation around the exact absorbed-CEV propagator, resummed by jumps along the variance clock. These closures match Monte Carlo references for rough Bergomi approximately at their resolution (0.01-0.1 bp) down to H=0.07, rho=-0.9, and price SABR to 0.97 bp over a 72-cell grid with maturities to ten years (75 bp for Hagan's expansion) and rough SABR to 0.92 bp. Conditional on the volatility field, forward-start smiles and continuously-monitored barriers reduce to field-only quadratures on the native Volterra field, and the causal response block yields the impulse-vega curve in one adjoint contraction. Derivations, extended benchmarks and secondary applications are in an ancillary technical supplement.

Tema degli esploratori: economia dei servizi IA (retro-catalogo arXiv: annunci del 2026-09-30 in q-fin.CP).
Categorie arXiv: Mathematical Finance (q-fin.MF) ; Computational Finance (q-fin.CP); Pricing of Securities (q-fin.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.37741 — 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 2026-10-07T20:06:07.734Z dalla pagina https://arxiv.org/catchup/q-fin.CP/2026-09-30?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).