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From microscopic price dynamics to multidimensional rough volatility models

Author

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  • Mehdi Tomas
  • Mathieu Rosenbaum

Abstract

Rough volatility is a well-established statistical stylised fact of financial assets. This property has lead to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried out in the mono-asset case. In this work, we show that some specific multivariate rough volatility models arise naturally from microstructural properties of the joint dynamics of asset prices. To do so, we use Hawkes processes to build microscopic models that reproduce accurately high frequency cross-asset interactions and investigate their long term scaling limits. We emphasize the relevance of our approach by providing insights on the role of microscopic features such as momentum and mean-reversion on the multidimensional price formation process. We in particular recover classical properties of high-dimensional stock correlation matrices.

Suggested Citation

  • Mehdi Tomas & Mathieu Rosenbaum, 2019. "From microscopic price dynamics to multidimensional rough volatility models," Papers 1910.13338, arXiv.org, revised Oct 2019.
    • Handle: RePEc:arx:papers:1910.13338
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    References listed on IDEAS

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    7. Thibault Jaisson & Mathieu Rosenbaum, 2013. "Limit theorems for nearly unstable Hawkes processes," Papers 1310.2033, arXiv.org, revised Mar 2015.
    8. Paul Jusselin & Mathieu Rosenbaum, 2018. "No-arbitrage implies power-law market impact and rough volatility," Papers 1805.07134, arXiv.org.
    9. Reigneron, Pierre-Alain & Allez, Romain & Bouchaud, Jean-Philippe, 2011. "Principal regression analysis and the index leverage effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(17), pages 3026-3035.
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    11. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Post-Print hal-01313995, HAL.
    12. Pierre-Alain Reigneron & Romain Allez & Jean-Philippe Bouchaud, 2010. "Principal Regression Analysis and the index leverage effect," Papers 1011.5810, arXiv.org, revised Feb 2011.
    13. Giulia Livieri & Saad Mouti & Andrea Pallavicini & Mathieu Rosenbaum, 2018. "Rough volatility: Evidence from option prices," IISE Transactions, Taylor & Francis Journals, vol. 50(9), pages 767-776, September.
    14. Christa Cuchiero & Josef Teichmann, 2019. "Markovian lifts of positive semidefinite affine Volterra type processes," Papers 1907.01917, arXiv.org, revised Sep 2019.
    15. repec:dau:papers:123456789/10911 is not listed on IDEAS
    16. Omar Euch & Masaaki Fukasawa & Mathieu Rosenbaum, 2018. "The microstructural foundations of leverage effect and rough volatility," Finance and Stochastics, Springer, vol. 22(2), pages 241-280, April.
    17. 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.
    18. Omar El Euch & Jim Gatheral & Radov{s} Radoiv{c}i'c & Mathieu Rosenbaum, 2018. "The Zumbach effect under rough Heston," Papers 1809.02098, arXiv.org.
    19. Blanka Horvath & Aitor Muguruza & Mehdi Tomas, 2019. "Deep Learning Volatility," Papers 1901.09647, arXiv.org, revised Aug 2019.
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    Citations

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    Cited by:

    1. Eduardo Abi Jaber & Enzo Miller & Huy^en Pham, 2020. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Papers 2006.13539, arXiv.org, revised Jan 2021.
    2. Eduardo Abi Jaber & Enzo Miller & Huyên Pham, 2021. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Post-Print hal-02877569, HAL.
    3. Bastien Baldacci, 2020. "High-frequency dynamics of the implied volatility surface," Papers 2012.10875, arXiv.org.
    4. Mathieu Rosenbaum & Mehdi Tomas, 2021. "A characterisation of cross-impact kernels," Papers 2107.08684, arXiv.org.
    5. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2020. "How to build a cross-impact model from first principles: Theoretical requirements and empirical results," Working Papers hal-02567489, HAL.
    6. Eduardo Abi Jaber & Enzo Miller & Huyên Pham, 2020. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Working Papers hal-02877569, HAL.
    7. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2022. "How to build a cross-impact model from first principles: Theoretical requirements and empirical results," Post-Print hal-02567489, HAL.
    8. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2020. "How to build a cross-impact model from first principles: Theoretical requirements and empirical results," Papers 2004.01624, arXiv.org, revised Mar 2022.
    9. Eduardo Abi Jaber & Enzo Miller & Huyên Pham, 2021. "Markowitz portfolio selection for multivariate affine and quadratic Volterra models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02877569, HAL.

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