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Mixture-Preserving, Arbitrage-Free Interpolation for Volatility-Surface Models

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  • Thijs van den Berg

Abstract

Given risk-neutral densities of a tradeable forward, fitted as $N$-component mixtures at a finite set of expiration pillars, we look for a continuous-time interpolation that is (i) \emph{mixture-preserving}, remaining a mixture of the same kernel (generically with more components than either pillar), and (ii) \emph{arbitrage-free} across expiries. The second requirement is the \emph{peacock} (convex-order) property, equivalently a non-negative Dupire local volatility; for full-support kernels (Gaussian, lognormal) it gives a unique continuous local-volatility diffusion (Lowther). We construct such an interpolation in a fixed $2N$-component family, freezing both pillars' components and moving only their weights. Applied to mixture term-structure models, it lifts Brigo--Mercurio to time-varying weights and reaches the free-per-strike-width generality of SANOS at additive cost.

Suggested Citation

  • Thijs van den Berg, 2026. "Mixture-Preserving, Arbitrage-Free Interpolation for Volatility-Surface Models," Papers 2606.12717, arXiv.org, revised Jun 2026.
    • Handle: RePEc:arx:papers:2606.12717
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    References listed on IDEAS

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    1. Mathias Beiglbock & Gudmund Pammer & Walter Schachermayer, 2021. "From Bachelier to Dupire via Optimal Transport," Papers 2106.12395, arXiv.org.
    2. Damiano Brigo & Fabio Mercurio, 2002. "Lognormal-Mixture Dynamics And Calibration To Market Volatility Smiles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 427-446.
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