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Building arbitrage-free implied volatility: Sinkhorn's algorithm and variants

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arxiv 1902.04456 v3 pith:ENLM6ZNZ submitted 2019-02-12 q-fin.CP

Hadrien De March (ECOLE POLYTECHNIQUE , QANTEV) , Pierre Henry-Labordere (SOCIETE GENERALE) This is my paper · ORCID
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keywords algorithmarbitrage-freebuildingimpliedsinkhornvolatilitybeenbid-ask
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We consider the classical problem of building an arbitrage-free implied volatility surface from bid-ask quotes. We design a fast numerical procedure, for which we prove the convergence, based on the Sinkhorn algorithm that has been recently used to solve efficiently (martingale) optimal transport problems.

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Cited by 2 Pith papers

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    An empirical KL minimizer over log-potentials estimates Schrödinger bridge potentials with terminal excess KL risk O(log^2 n / n) in the realizable case, even when the target distribution has unbounded support.

  2. Arbitrage-Free Multi-Maturity Risk-Neutral Marginals

    q-fin.CP 2026-07 accept novelty 6.0 of 10

    An explicit piecewise-constant-curvature construction with power-law tails converts discrete arbitrage-free call prices into full risk-neutral marginal laws that exactly reprice inputs and are free of butterfly and ca...

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