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Asymmetric super-Heston-rough volatility model with Zumbach effect as scaling limit of quadratic Hawkes processes

Author

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  • Priyanka Chudasama
  • Srikanth Krishnan Iyer

Abstract

Hawkes processes were first introduced to obtain microscopic models for the rough volatility observed in asset prices. Scaling limits of such processes leads to the rough-Heston model that describes the macroscopic behavior. Blanc et al. (2017) show that Time-reversal asymmetry (TRA) or the Zumbach effect can be modeled using Quadratic Hawkes (QHawkes) processes. Dandapani et al. (2021) obtain a super-rough-Heston model as scaling limit of QHawkes processes in the case where the impact of buying and selling actions are symmetric. To model asymmetry in buying and selling actions, we propose a bivariate QHawkes process and derive a super-rough-Heston model as scaling limits for the price process in the stable and near-unstable regimes that preserves TRA. A new feature of the limiting process in the near-unstable regime is that the two driving Brownian motions exhibit a stochastic covariation that depends on the spot volatility.

Suggested Citation

  • Priyanka Chudasama & Srikanth Krishnan Iyer, 2025. "Asymmetric super-Heston-rough volatility model with Zumbach effect as scaling limit of quadratic Hawkes processes," Papers 2508.16566, arXiv.org.
    • Handle: RePEc:arx:papers:2508.16566
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    References listed on IDEAS

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    1. El Euch Omar & Fukasawa Masaaki & Rosenbaum Mathieu, 2016. "The microstructural foundations of leverage effect and rough volatility," Papers 1609.05177, arXiv.org.
    2. Aditi Dandapani & Paul Jusselin & Mathieu Rosenbaum, 2021. "From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect," Quantitative Finance, Taylor & Francis Journals, vol. 21(8), pages 1235-1247, August.
    3. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    4. Aditi Dandapani & Paul Jusselin & Mathieu Rosenbaum, 2019. "From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect," Papers 1907.06151, arXiv.org, revised Jan 2021.
    5. Gilles Zumbach, 2007. "Time reversal invariance in finance," Papers 0708.4022, arXiv.org.
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