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The Zumbach effect under rough Heston

Author

Listed:
  • Omar El Euch
  • Jim Gatheral
  • Radov{s} Radoiv{c}i'c
  • Mathieu Rosenbaum

Abstract

Previous literature has identified an effect, dubbed the Zumbach effect, that is nonzero empirically but conjectured to be zero in any conventional stochastic volatility model. Essentially this effect corresponds to the property that past squared returns forecast future volatilities better than past volatilities forecast future squared returns. We provide explicit computations of the Zumbach effect under rough Heston and show that they are consistent with empirical estimates. In agreement with previous conjectures however, the Zumbach effect is found to be negligible in the classical Heston model.

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  • 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.
    • Handle: RePEc:arx:papers:1809.02098
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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. P. Blanc & J. Donier & J.-P. Bouchaud, 2017. "Quadratic Hawkes processes for financial prices," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 171-188, February.
    3. Rémy Chicheportiche & Jean-Philippe Bouchaud, 2014. "The fine-structure of volatility feedback I: Multi-scale self-reflexivity," Post-Print hal-00722261, HAL.
    4. Jim Gatheral & Roel Oomen, 2010. "Zero-intelligence realized variance estimation," Finance and Stochastics, Springer, vol. 14(2), pages 249-283, April.
    5. Gilles Zumbach, 2009. "Time reversal invariance in finance," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 505-515.
    6. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    7. Lisa Borland & Jean-Philippe Bouchaud & Jean-Francois Muzy & Gilles Zumbach, 2005. "The Dynamics of Financial Markets -- Mandelbrot's multifractal cascades, and beyond," Papers cond-mat/0501292, arXiv.org.
    8. Gilles Zumbach, 2004. "Volatility processes and volatility forecast with long memory," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 70-86.
    9. 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.
    10. Lisa Borland & Jean-Philippe Bouchaud & Jean-Francois Muzy & Gilles Zumbach, 2005. "The Dynamics of Financial Markets -- Mandelbrot's multifractal cascades, and beyond," Science & Finance (CFM) working paper archive 500061, Science & Finance, Capital Fund Management.
    11. Zumbach, Gilles & Lynch, Paul, 2001. "Heterogeneous volatility cascade in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 521-529.
    12. Paul Lynch & Gilles Zumbach, 2003. "Market heterogeneities and the causal structure of volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 320-331.
    13. Gilles Zumbach & Paul Lynch, 2001. "Heterogeneous volatility cascade in financial markets," Papers cond-mat/0105162, arXiv.org.
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    Cited by:

    1. Siow Woon Jeng & Adem Kiliçman, 2021. "On Multilevel and Control Variate Monte Carlo Methods for Option Pricing under the Rough Heston Model," Mathematics, MDPI, vol. 9(22), pages 1-32, November.
    2. Mehdi Tomas & Mathieu Rosenbaum, 2019. "From microscopic price dynamics to multidimensional rough volatility models," Papers 1910.13338, arXiv.org, revised Oct 2019.
    3. 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.

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