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Simulation of Arbitrage-Free Implied Volatility Surfaces

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  • Rama Cont
  • Milena Vuletić

Abstract

We present a computationally tractable method for simulating arbitrage-free implied volatility surfaces. We illustrate how our method may be combined with a data-driven model based on historical SPX implied volatility data to generate dynamic scenarios for arbitrage-free implied volatility surfaces. Our approach conciliates static arbitrage constraints with a realistic representation of statistical properties of implied volatility co-movements.

Suggested Citation

  • Rama Cont & Milena Vuletić, 2023. "Simulation of Arbitrage-Free Implied Volatility Surfaces," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(2), pages 94-121, March.
    • Handle: RePEc:taf:apmtfi:v:30:y:2023:i:2:p:94-121
    DOI: 10.1080/1350486X.2023.2277960
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    Cited by:

    1. Jian'an Zhang, 2025. "Risk-Sensitive Option Market Making with Arbitrage-Free eSSVI Surfaces: A Constrained RL and Stochastic Control Bridge," Papers 2510.04569, arXiv.org.
    2. Jing Wang & Shuaiqiang Liu & Cornelis Vuik, 2025. "Controllable Generation of Implied Volatility Surfaces with Variational Autoencoders," Papers 2509.01743, arXiv.org.
    3. Zhonghao Xian & Xing Yan & Cheuk Hang Leung & Qi Wu, 2024. "Risk-Neutral Generative Networks," Papers 2405.17770, arXiv.org.
    4. Herv'e Andr`es & Alexandre Boumezoued & Benjamin Jourdain, 2023. "The implied volatility surface (also) is path-dependent," Papers 2312.15950, arXiv.org, revised Oct 2025.

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