Arbitrage-Free Implied Volatility Surface Reconstruction via Additive Martingales

Abstract:This work focuses on reconstructing a continuous implied volatility (IV) surface from a small number of option quotes, a fundamental task for option pricing and risk management. We propose Additive Martingale (AddMart), a few-shot IV surface reconstruction framework that satisfies static no-arbitrage conditions by construction. Rather than predicting IVs directly, AddMart maps sparse quotes to non-negative increment densities of an exponential additive martingale, from which valid risk-neutral marginals and IVs are recovered. By incorporating the no-arbitrage structure directly into its architecture, rather than enforcing it through regularization in the learning objective, AddMart produces IV surfaces that satisfy static no-arbitrage conditions throughout the domain. Extensive experiments on ten real-option datasets demonstrate that AddMart achieves competitive reconstruction accuracy with no material static arbitrage violations, while directly enabling the estimation of VaR, CVaR, and crash probabilities.

41 pages, 15 figures. Includes supplementary proofs and experimental analyses in the appendices

Computational Finance (q-fin.CP); Machine Learning (cs.LG)

arXiv:2610.25671 [q-fin.CP]

(or arXiv:2610.25671v1 [q-fin.CP] for this version)

https://doi.org/10.48550/arXiv.2610.25671 Focus to learn more arXiv-issued DOI via DataCite

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