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Volatility models in practice: Rough, Path-dependent or Markovian?

Author

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  • Eduardo Abi Jaber

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Shaun Xiaoyuan Li

    (UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

An extensive empirical study of the class of Volterra Bergomi models using SPX options data between 2011 and 2022 reveals the following fact-check on two fundamental claims echoed in the rough volatility literature: Do rough volatility models with Hurst index H ∈ (0, 1/2) really capture well SPX implied volatility surface with very few parameters? No, rough volatility models are inconsistent with the global shape of SPX smiles. They suffer from severe structural limitations imposed by the roughness component, with the Hurst parameter H ∈ (0, 1/2) controlling the smile in a poor way. In particular, the SPX at-the-money skew is incompatible with the power-law shape generated by rough volatility models. The skew of rough volatility models increases too fast on the short end, and decays too slow on the longer end where "negative" H is sometimes needed. Do rough volatility models really outperform consistently their classical Markovian counterparts? No, for short maturities they underperform their one-factor Markovian counterpart with the same number of parameters. For longer maturities, they do not systematically outperform the one-factor model and significantly underperform when compared to an under-parametrized two-factor Markovian model with only one additional calibratable parameter. On the positive side: our study identifies a (non-rough) path-dependent Bergomi model and an under-parametrized two-factor Markovian Bergomi model that consistently outperform their rough counterpart in capturing SPX smiles between one week and three years with only 3 to 4 calibratable parameters.

Suggested Citation

  • Eduardo Abi Jaber & Shaun Xiaoyuan Li, 2025. "Volatility models in practice: Rough, Path-dependent or Markovian?," Post-Print hal-04372797, HAL.
    • Handle: RePEc:hal:journl:hal-04372797
    Note: View the original document on HAL open archive server: https://hal.science/hal-04372797v2
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    References listed on IDEAS

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    1. Jean-Pierre Fouque & George Papanicolaou & Ronnie Sircar & Knut Solna, 2004. "Maturity cycles in implied volatility," Finance and Stochastics, Springer, vol. 8(4), pages 451-477, November.
    2. Eduardo Abi Jaber & Camille Illand & Shaun Xiaoyuan Li, 2024. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03902513, HAL.
    3. Eduardo Abi Jaber & Nathan de Carvalho, 2024. "Reconciling rough volatility with jumps," Post-Print hal-04295416, HAL.
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