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Volatility Models in Practice: Rough, Path‐Dependent, or Markovian?

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  • Eduardo Abi Jaber
  • Shaun (Xiaoyuan) Li

Abstract

We present an empirical study examining several claims related to option prices in rough volatility literature using SPX options data. Our results show that rough volatility models with the parameter H∈(0,1/2)$H \in (0,1/2)$ are inconsistent with the global shape of SPX smiles. In particular, the at‐the‐money SPX skew is incompatible with the power‐law shape generated by these models, which increases too fast for short maturities and decays too slowly for longer maturities. For maturities between 1 week and 3 months, rough volatility models underperform one‐factor Markovian models with the same number of parameters. When extended to longer maturities, rough volatility models do not consistently outperform one‐factor Markovian models. Our study identifies a non‐rough path‐dependent model and a two‐factor Markovian model that outperform their rough counterparts in capturing SPX smiles between 1 week and 3 years, with only three to four parameters.

Suggested Citation

  • Eduardo Abi Jaber & Shaun (Xiaoyuan) Li, 2025. "Volatility Models in Practice: Rough, Path‐Dependent, or Markovian?," Mathematical Finance, Wiley Blackwell, vol. 35(4), pages 796-817, October.
    • Handle: RePEc:bla:mathfi:v:35:y:2025:i:4:p:796-817
    DOI: 10.1111/mafi.12463
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    Cited by:

    1. Eduardo Abi Jaber & Louis-Amand Gérard, 2025. "Hedging with memory: shallow and deep learning with signatures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-05197836, HAL.
    2. Matthieu Garcin & Karl Sawaya & Thomas Valade, 2025. "Prediction of linear fractional stable motions using codifference, with application to non-Gaussian rough volatility," Papers 2507.15437, arXiv.org, revised Nov 2025.
    3. Eduardo Abi Jaber & Louis-Amand G'erard, 2025. "Hedging with memory: shallow and deep learning with signatures," Papers 2508.02759, arXiv.org.

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