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Amortizing the Calibration Triple: A Projection-Consistent Neural Operator for Local-Stochastic Volatility

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Listed:
  • Xiaozhen Wang
  • Anais Despr'es
  • Martin Dureau
  • Francois Buet-Golfouse

Abstract

Local-stochastic volatility (LSV) combines vanilla marginals with richer smile dynamics, but calibration requires a slow, noisy and sequential McKean--Vlasov fixed point. We learn a projection-consistent operator for the calibration triple. Given finite quotes and a stochastic-volatility (SV) backbone, it jointly returns an implied-volatility surface subject to static-arbitrage constraints, its Dupire local volatility, LSV leverage and the conditional moment required by the projection identity. Starting from option-price marginals, we derive a division-free Dupire residual in log-implied-variance coordinates and a quotient Fokker--Planck equation after Gy\"ongy projection. Deep Operator Network (DeepONet) and Fourier Neural Operator (FNO) implementations enforce quote fit, static-arbitrage, Dupire and projection constraints. For the witness-augmented residual system, we prove conditional identification and empirical consistency under LSV existence and inverse residual stability. In controlled synthetic tests, forward-start and cliquet errors differ from a particle method by 0.1 and 0.2 percentage points, while calibration latency falls from 98.5 to 0.6 ms. Compared with the tested baselines, local-volatility root-mean-square error (RMSE) falls by 36% and leverage RMSE by 7-16%. These results support amortizing the LSV fixed point: the expensive solve moves offline, while online calibration reduces to a single projection-consistent operator evaluation.

Suggested Citation

  • Xiaozhen Wang & Anais Despr'es & Martin Dureau & Francois Buet-Golfouse, 2026. "Amortizing the Calibration Triple: A Projection-Consistent Neural Operator for Local-Stochastic Volatility," Papers 2608.01217, arXiv.org.
    • Handle: RePEc:arx:papers:2608.01217
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    References listed on IDEAS

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