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Discovering parametrizations of implied volatility with symbolic regression

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  • Martin Keller-Ressel
  • Hannes Nikulski

Abstract

We investigate the data-driven discovery of parametric representations for implied volatility slices. Using symbolic regression, we search for simple analytic formulas that approximate the total implied variance as a function of log-moneyness and maturity. Our approach generates candidate parametrizations directly from market data without imposing a predefined functional form. We compare the resulting formulas with the widely used SVI parametrization in terms of accuracy and simplicity. Numerical experiments indicate that symbolic regression can identify compact parametrizations with competitive fitting performance.

Suggested Citation

  • Martin Keller-Ressel & Hannes Nikulski, 2026. "Discovering parametrizations of implied volatility with symbolic regression," Papers 2603.21892, arXiv.org.
    • Handle: RePEc:arx:papers:2603.21892
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    References listed on IDEAS

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    1. Milena Vuletić & Rama Cont, 2024. "VolGAN: A Generative Model for Arbitrage-Free Implied Volatility Surfaces," Applied Mathematical Finance, Taylor & Francis Journals, vol. 31(4), pages 203-238, July.
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    5. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    6. Matthias R. Fengler, 2005. "Semiparametric Modeling of Implied Volatility," Springer Finance, Springer, number 978-3-540-30591-0, December.
    7. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
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