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Multi-factor approximation of rough volatility models

Author

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  • Eduardo Abi Jaber

    (CEREMADE)

  • Omar El Euch

Abstract

Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to simulate efficiently such models, which makes risk management of derivatives an intricate task. In this paper, we design tractable multi-factor stochastic volatility models approximating rough volatility models and enjoying a Markovian structure. Furthermore, we apply our procedure to the specific case of the rough Heston model. This in turn enables us to derive a numerical method for solving fractional Riccati equations appearing in the characteristic function of the log-price in this setting.

Suggested Citation

  • Eduardo Abi Jaber & Omar El Euch, 2018. "Multi-factor approximation of rough volatility models," Papers 1801.10359, arXiv.org, revised Apr 2018.
    • Handle: RePEc:arx:papers:1801.10359
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    File URL: http://arxiv.org/pdf/1801.10359
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    References listed on IDEAS

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    1. Eduardo Abi Jaber & Omar El Euch, 2018. "Markovian structure of the Volterra Heston model," Working Papers hal-01716696, HAL.
    2. Omar El Euch & Mathieu Rosenbaum, 2016. "The characteristic function of rough Heston models," Papers 1609.02108, arXiv.org.
    3. El Euch Omar & Fukasawa Masaaki & Rosenbaum Mathieu, 2016. "The microstructural foundations of leverage effect and rough volatility," Papers 1609.05177, arXiv.org.
    4. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394, arXiv.org.
    5. Omar El Euch & Mathieu Rosenbaum, 2017. "Perfect hedging in rough Heston models," Papers 1703.05049, arXiv.org.
    6. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    7. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    8. Philippe Carmona & Laure Coutin & G. Montseny, 2000. "Approximation of Some Gaussian Processes," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 161-171, January.
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    Cited by:

    1. Abi Jaber, Eduardo & El Euch, Omar, 2019. "Markovian structure of the Volterra Heston model," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 63-72.
    2. Eduardo Abi Jaber, 2018. "Lifting the Heston model," Papers 1810.04868, arXiv.org, revised Nov 2019.
    3. Eduardo Abi Jaber, 2019. "Lifting the Heston model," Post-Print hal-01890751, HAL.
    4. Eduardo Abi Jaber & Omar El Euch, 2018. "Markovian structure of the Volterra Heston model," Working Papers hal-01716696, HAL.
    5. Ryan McCrickerd, 2019. "On spatially irregular ordinary differential equations and a pathwise volatility modelling framework," Papers 1902.01673, arXiv.org, revised Sep 2021.
    6. Eduardo Abi Jaber, 2018. "Lifting the Heston model," Working Papers hal-01890751, HAL.
    7. Jim Gatheral & Radoš Radoičić, 2019. "Rational Approximation Of The Rough Heston Solution," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-19, May.
    8. Eduardo Abi Jaber & Omar El Euch, 2019. "Markovian structure of the Volterra Heston model," Post-Print hal-01716696, HAL.

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