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SANOS Smooth strictly Arbitrage-free Non-parametric Option Surfaces

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Listed:
  • Hans Buehler
  • Blanka Horvath
  • Anastasis Kratsios
  • Yannick Limmer
  • Raeid Saqur

Abstract

We present a simple, numerically efficient but highly flexible non-parametric method to construct representations of option price surfaces which are both smooth and strictly arbitrage-free across time and strike. The method can be viewed as a smooth generalization of the widely-known linear interpolation scheme, and retains the simplicity and transparency of that baseline. Calibration of the model to observed market quotes is formulated as a linear program, allowing bid-ask spreads to be incorporated directly via linear penalties or inequalities, and delivering materially lower computational cost than most of the currently available implied-volatility surface fitting routines. As a further contribution, we derive an equivalent parameterization of the proposed surface in terms of strictly positive "discrete local volatility" variables. This yields, to our knowledge, the first construction of smooth, strictly arbitrage-free option price surfaces while requiring only trivial parameter constraints (positivity). We illustrate the approach using S&P 500 index options

Suggested Citation

  • Hans Buehler & Blanka Horvath & Anastasis Kratsios & Yannick Limmer & Raeid Saqur, 2026. "SANOS Smooth strictly Arbitrage-free Non-parametric Option Surfaces," Papers 2601.11209, arXiv.org, revised Feb 2026.
    • Handle: RePEc:arx:papers:2601.11209
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    References listed on IDEAS

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    1. Hans Buehler & Phillip Murray & Mikko S. Pakkanen & Ben Wood, 2021. "Deep Hedging: Learning to Remove the Drift under Trading Frictions with Minimal Equivalent Near-Martingale Measures," Papers 2111.07844, arXiv.org, revised Jan 2022.
    2. Hans Buehler, 2006. "Expensive martingales," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 207-218.
    3. René Carmona & Sergey Nadtochiy, 2012. "Tangent Lévy market models," Finance and Stochastics, Springer, vol. 16(1), pages 63-104, January.
    4. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    5. Magnus Wiese & Ben Wood & Alexandre Pachoud & Ralf Korn & Hans Buehler & Phillip Murray & Lianjun Bai, 2021. "Multi-Asset Spot and Option Market Simulation," Papers 2112.06823, arXiv.org.
    6. 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.
    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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