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Short-time near-the-money skew in rough fractional volatility models

Author

Listed:
  • C. Bayer
  • P. K. Friz
  • A. Gulisashvili
  • B. Horvath
  • B. Stemper

Abstract

We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the ‘rough’ regime of Hurst parameter $ H

Suggested Citation

  • C. Bayer & P. K. Friz & A. Gulisashvili & B. Horvath & B. Stemper, 2019. "Short-time near-the-money skew in rough fractional volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 19(5), pages 779-798, May.
    • Handle: RePEc:taf:quantf:v:19:y:2019:i:5:p:779-798
    DOI: 10.1080/14697688.2018.1529420
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    Citations

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    Cited by:

    1. Paolo Pigato, 2019. "Extreme at-the-money skew in a local volatility model," Finance and Stochastics, Springer, vol. 23(4), pages 827-859, October.
    2. Peter K. Friz & Paul Gassiat & Paolo Pigato, 2022. "Short-dated smile under rough volatility: asymptotics and numerics," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 463-480, March.
    3. 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.
    4. Aur'elien Alfonsi & Ahmed Kebaier, 2021. "Approximation of Stochastic Volterra Equations with kernels of completely monotone type," Papers 2102.13505, arXiv.org, revised Mar 2022.
    5. Stefan Gerhold & Christoph Gerstenecker & Archil Gulisashvili, 2020. "Large deviations for fractional volatility models with non-Gaussian volatility driver," Papers 2003.12825, arXiv.org.
    6. Qinwen Zhu & Grégoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian Approximation of the Rough Bergomi Model for Monte Carlo Option Pricing," Mathematics, MDPI, vol. 9(5), pages 1-21, March.
    7. Gerhold, Stefan & Gerstenecker, Christoph & Gulisashvili, Archil, 2021. "Large deviations for fractional volatility models with non-Gaussian volatility driver," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 580-600.
    8. Christian Bayer & Fabian Andsem Harang & Paolo Pigato, 2020. "Log-modulated rough stochastic volatility models," Papers 2008.03204, arXiv.org, revised May 2021.
    9. Paul Hager & Eyal Neuman, 2020. "The Multiplicative Chaos of $H=0$ Fractional Brownian Fields," Papers 2008.01385, arXiv.org.
    10. Jacquier, Antoine & Pannier, Alexandre, 2022. "Large and moderate deviations for stochastic Volterra systems," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 142-187.
    11. Markus Bibinger, 2024. "Probabilistic models and statistics for electronic financial markets in the digital age," Papers 2406.07388, arXiv.org.
    12. Qinwen Zhu & Gregoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian approximation of the rough Bergomi model for Monte Carlo option pricing," Post-Print hal-02910724, HAL.
    13. Giacomo Giorgio & Barbara Pacchiarotti & Paolo Pigato, 2023. "Short-Time Asymptotics for Non-Self-Similar Stochastic Volatility Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(3), pages 123-152, May.
    14. Solesne Bourguin & Thanh Dang & Konstantinos Spiliopoulos, 2023. "Moderate Deviation Principle for Multiscale Systems Driven by Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-57, March.
    15. Carsten Chong & Viktor Todorov, 2022. "Short-time expansion of characteristic functions in a rough volatility setting with applications," Papers 2208.00830, arXiv.org.
    16. Ranieri Dugo & Giacomo Giorgio & Paolo Pigato, 2024. "The Multivariate Fractional Ornstein-Uhlenbeck Process," CEIS Research Paper 581, Tor Vergata University, CEIS, revised 28 Aug 2024.
    17. Peter K. Friz & Thomas Wagenhofer, 2022. "Reconstructing Volatility: Pricing of Index Options under Rough Volatility," Papers 2212.07817, arXiv.org.
    18. Masaaki Fukasawa, 2020. "Volatility has to be rough," Papers 2002.09215, arXiv.org.
    19. Gulisashvili, Archil, 2021. "Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 37-79.
    20. Yaroslav Eumenius-Schulz, 2020. "Spot estimation for fractional Ornstein–Uhlenbeck stochastic volatility model: consistency and central limit theorem," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 355-380, July.
    21. Dupret, Jean-Loup & Barbarin, Jérôme & Hainaut, Donatien, 2021. "Impact of rough stochastic volatility models on long-term life insurance pricing," LIDAM Discussion Papers ISBA 2021017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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