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Volatility has to be rough

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  • Masaaki Fukasawa

Abstract

Under power-law blow-up of the short ATM skew, volatility must be rough in a viable market for the underlying asset

Suggested Citation

  • Masaaki Fukasawa, 2021. "Volatility has to be rough," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 1-8, January.
    • Handle: RePEc:taf:quantf:v:21:y:2021:i:1:p:1-8
    DOI: 10.1080/14697688.2020.1825781
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    Citations

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    Cited by:

    1. Daniele Angelini & Matthieu Garcin, 2024. "Market information of the fractional stochastic regularity model," Papers 2409.07159, arXiv.org.
    2. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Post-Print hal-02946146, HAL.
    3. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    4. Ofelia Bonesini & Giorgia Callegaro & Antoine Jacquier, 2021. "Functional quantization of rough volatility and applications to volatility derivatives," Papers 2104.04233, arXiv.org, revised Mar 2024.
    5. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Finance and Stochastics, Springer, vol. 26(4), pages 733-769, October.
    6. Giulia Di Nunno & Anton Yurchenko-Tytarenko, 2022. "Sandwiched Volterra Volatility model: Markovian approximations and hedging," Papers 2209.13054, arXiv.org, revised Jul 2024.
    7. 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.
    8. Masaaki Fukasawa, 2022. "On asymptotically arbitrage-free approximations of the implied volatility," Papers 2201.02752, arXiv.org, revised Jan 2022.
    9. Mohamed Ben Alaya & Martin Friesen & Jonas Kremer, 2024. "Ergodicity and Law-of-large numbers for the Volterra Cox-Ingersoll-Ross process," Papers 2409.04496, arXiv.org.
    10. Ulrich Horst & Wei Xu & Rouyi Zhang, 2023. "Convergence of Heavy-Tailed Hawkes Processes and the Microstructure of Rough Volatility," Papers 2312.08784, arXiv.org, revised Nov 2024.
    11. Ofelia Bonesini & Giorgia Callegaro & Martino Grasselli & Gilles Pag`es, 2023. "From elephant to goldfish (and back): memory in stochastic Volterra processes," Papers 2306.02708, arXiv.org, revised Sep 2023.
    12. Angelini, Daniele & Bianchi, Sergio, 2023. "Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    13. Peter K. Friz & William Salkeld & Thomas Wagenhofer, 2022. "Weak error estimates for rough volatility models," Papers 2212.01591, arXiv.org, revised Aug 2024.
    14. Giulia Di Nunno & Anton Yurchenko-Tytarenko, 2023. "Power law in Sandwiched Volterra Volatility model," Papers 2311.01228, arXiv.org.
    15. Eduardo Abi Jaber & Shaun & Li, 2024. "Volatility models in practice: Rough, Path-dependent or Markovian?," Papers 2401.03345, arXiv.org.
    16. Changqing Teng & Guanglian Li, 2024. "Unsupervised learning-based calibration scheme for Rough Bergomi model," Papers 2412.02135, arXiv.org, revised Dec 2024.
    17. Antoine Jacquier & Mugad Oumgari, 2023. "Interest rate convexity in a Gaussian framework," Papers 2307.14218, arXiv.org, revised Mar 2024.
    18. Carsten Chong & Marc Hoffmann & Yanghui Liu & Mathieu Rosenbaum & Gr'egoire Szymanski, 2022. "Statistical inference for rough volatility: Minimax Theory," Papers 2210.01214, arXiv.org, revised Feb 2024.
    19. Carsten Chong & Marc Hoffmann & Yanghui Liu & Mathieu Rosenbaum & Gr'egoire Szymanski, 2022. "Statistical inference for rough volatility: Central limit theorems," Papers 2210.01216, arXiv.org, revised Jun 2024.
    20. Carsten H. Chong & Viktor Todorov, 2022. "Short-time expansion of characteristic functions in a rough volatility setting with applications," Papers 2208.00830, arXiv.org, revised Nov 2024.
    21. Huy N. Chau & Duy Nguyen & Thai Nguyen, 2024. "On short-time behavior of implied volatility in a market model with indexes," Papers 2402.16509, arXiv.org, revised Apr 2024.
    22. Christian Bayer & Masaaki Fukasawa & Shonosuke Nakahara, 2022. "On the weak convergence rate in the discretization of rough volatility models," Papers 2203.02943, arXiv.org.
    23. Peng Wu & Jean-Franc{c}ois Muzy & Emmanuel Bacry, 2022. "From Rough to Multifractal volatility: the log S-fBM model," Papers 2201.09516, arXiv.org, revised Jul 2022.

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