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Rough-Heston Local-Volatility Model

Author

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  • Enrico Dall'Acqua
  • Riccardo Longoni
  • Andrea Pallavicini

Abstract

In industrial applications it is quite common to use stochastic volatility models driven by semi-martingale Markov volatility processes. However, in order to fit exactly market volatilities, these models are usually extended by adding a local volatility term. Here, we consider the case of singular Volterra processes, and we extend them by adding a local-volatility term to their Markov lift by preserving the stylized results implied by these models on plain-vanilla options. In particular, we focus on the rough-Heston model, and we analyze the small time asymptotics of its implied local-volatility function in order to provide a proper extrapolation scheme to be used in calibration.

Suggested Citation

  • Enrico Dall'Acqua & Riccardo Longoni & Andrea Pallavicini, 2022. "Rough-Heston Local-Volatility Model," Papers 2206.09220, arXiv.org.
    • Handle: RePEc:arx:papers:2206.09220
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    References listed on IDEAS

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    1. Florian Bourgey & Stefano De Marco & Peter K. Friz & Paolo Pigato, 2023. "Local volatility under rough volatility," Mathematical Finance, Wiley Blackwell, vol. 33(4), pages 1119-1145, October.
    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. Aitor Muguruza, 2019. "Not so Particular about Calibration: Smile Problem Resolved," Papers 1909.13366, arXiv.org.
    4. Christian Bayer & Simon Breneis, 2021. "Markovian approximations of stochastic Volterra equations with the fractional kernel," Papers 2108.05048, arXiv.org, revised Jul 2022.
    5. Elisa Al`os & David Garc'ia-Lorite & Makar Pravosud, 2022. "On the skew and curvature of implied and local volatilities," Papers 2205.11185, arXiv.org, revised Sep 2023.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Christian Bayer & Denis Belomestny & Oleg Butkovsky & John Schoenmakers, 2022. "A Reproducing Kernel Hilbert Space approach to singular local stochastic volatility McKean-Vlasov models," Papers 2203.01160, arXiv.org, revised Jan 2024.
    8. Christian Bayer & Peter K. Friz & Paul Gassiat & Jorg Martin & Benjamin Stemper, 2020. "A regularity structure for rough volatility," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 782-832, July.
    9. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    10. 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.
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