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Functional quantization of rough volatility and applications to volatility derivatives

Author

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  • Ofelia Bonesini
  • Giorgia Callegaro
  • Antoine Jacquier

Abstract

We develop a product functional quantization of rough volatility. Since the quantizers can be computed offline, this new technique, built on the insightful works by Luschgy and Pages, becomes a strong competitor in the new arena of numerical tools for rough volatility. We concentrate our numerical analysis to pricing VIX Futures in the rough Bergomi model and compare our results to other recently suggested benchmarks.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2104.04233
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    References listed on IDEAS

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    1. Christian Bayer & Chiheb Ben Hammouda & Raul Tempone, 2018. "Hierarchical adaptive sparse grids and quasi Monte Carlo for option pricing under the rough Bergomi model," Papers 1812.08533, arXiv.org, revised Jan 2020.
    2. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    3. Peter Carr & Dilip B. Madan, 2014. "Joint modeling of VIX and SPX options at a single and common maturity with risk management applications," IISE Transactions, Taylor & Francis Journals, vol. 46(11), pages 1125-1131, November.
    4. Eduardo Abi Jaber & Omar El Euch, 2019. "Multi-factor approximation of rough volatility models," Post-Print hal-01697117, HAL.
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    6. Christian Bayer & Chiheb Ben Hammouda & Raúl Tempone, 2020. "Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model," Quantitative Finance, Taylor & Francis Journals, vol. 20(9), pages 1457-1473, September.
    7. Masaaki Fukasawa, 2021. "Volatility has to be rough," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 1-8, January.
    8. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    9. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    10. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2015. "Hybrid scheme for Brownian semistationary processes," Papers 1507.03004, arXiv.org, revised May 2017.
    11. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2017. "Hybrid scheme for Brownian semistationary processes," Finance and Stochastics, Springer, vol. 21(4), pages 931-965, October.
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    Citations

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    Cited by:

    1. Ofelia Bonesini & Antoine Jacquier & Alexandre Pannier, 2023. "Rough volatility, path-dependent PDEs and weak rates of convergence," Papers 2304.03042, arXiv.org.
    2. Florian Bourgey & Stefano De Marco, 2021. "Multilevel Monte Carlo simulation for VIX options in the rough Bergomi model," Papers 2105.05356, arXiv.org, revised Jun 2022.
    3. Antoine Jacquier & Aitor Muguruza & Alexandre Pannier, 2021. "Rough multifactor volatility for SPX and VIX options," Papers 2112.14310, arXiv.org, revised Nov 2023.
    4. Christa Cuchiero & Guido Gazzani & Sara Svaluto-Ferro, 2022. "Signature-based models: theory and calibration," Papers 2207.13136, arXiv.org.
    5. Eduardo Abi Jaber & Camille Illand & Shaun & Li, 2022. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Papers 2212.08297, arXiv.org, revised Dec 2024.
    6. Alexandre Pannier, 2023. "Path-dependent PDEs for volatility derivatives," Papers 2311.08289, arXiv.org, revised Jan 2024.

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