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Heterogeneous volatility cascade in financial markets

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  • Gilles Zumbach
  • Paul Lynch

Abstract

Using high frequency data, we have studied empirically the change of volatility, also called volatility derivative, for various time horizons. In particular, the correlation between the volatility derivative and the volatility realized in the next time period is a measure of the response function of the market participants. This correlation shows explicitly the heterogeneous structure of the market according to the characteristic time horizons of the differents agents. It reveals a volatility cascade from long to short time horizons, with a structure different from the one observed in turbulence. Moreover, we have developed a new ARCH-type model which incorporates the different groups of agents, with their characteristic memory. This model reproduces well the empirical response function, and allows us to quantify the importance of each group.

Suggested Citation

  • Gilles Zumbach & Paul Lynch, 2001. "Heterogeneous volatility cascade in financial markets," Papers cond-mat/0105162, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0105162
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    References listed on IDEAS

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    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. Gilles Zumbach & Ulrich Müller, 2001. "Operators On Inhomogeneous Time Series," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 147-177.
    3. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
    4. Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
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    Cited by:

    1. Clark, Andrew, 2004. "Evidence of log-periodicity in corporate bond spreads," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 585-595.
    2. Julien Idier, 2011. "Long-term vs. short-term comovements in stock markets: the use of Markov-switching multifractal models," The European Journal of Finance, Taylor & Francis Journals, vol. 17(1), pages 27-48.
    3. Gilles Zumbach, 2011. "Characterizing heteroskedasticity," Quantitative Finance, Taylor & Francis Journals, vol. 11(9), pages 1357-1369, October.
    4. 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.
    5. Gilles Zumbach, 2007. "Time reversal invariance in finance," Papers 0708.4022, arXiv.org.
    6. Damien Challet & Vincent Ragel, 2023. "Recurrent Neural Networks with more flexible memory: better predictions than rough volatility," Working Papers hal-04165354, HAL.
    7. Nicolas Boitout & Loredana Ureche-Rangau, 2004. "Towards A Multifractal Paradigm Of Stochastic Volatility?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(07), pages 823-851.
    8. David Mcmillan & Alan Speight, 2008. "Long-memory in high-frequency exchange rate volatility under temporal aggregation," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 251-261.
    9. Blanc, Pierre & Chicheportiche, Rémy & Bouchaud, Jean-Philippe, 2014. "The fine structure of volatility feedback II: Overnight and intra-day effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 58-75.
    10. Marcus Cordi & Serge Kassibrakis & Damien Challet, 2018. "The market nanostructure origin of asset price time reversal asymmetry," Working Papers hal-01966419, HAL.
    11. Marcus Cordi & Damien Challet & Serge Kassibrakis, 2021. "The market nanostructure origin of asset price time reversal asymmetry," Quantitative Finance, Taylor & Francis Journals, vol. 21(2), pages 295-304, February.
    12. Daniel Fricke & Thomas Lux, 2015. "The effects of a financial transaction tax in an artificial financial market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(1), pages 119-150, April.
    13. Ramazan Gencay & Nikola Gradojevic & Faruk Selcuk & Brandon Whitcher, 2010. "Asymmetry of information flow between volatilities across time scales," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 895-915.
    14. Milan Bašta, 2014. "Simulating Bivariate Stationary Processes with Scale-Specific Characteristics," Acta Oeconomica Pragensia, Prague University of Economics and Business, vol. 2014(1), pages 3-26.
    15. Charles Guy Njike Leunga & Donatien Hainaut, 2024. "Affine Heston model style with self-exciting jumps and long memory," Annals of Finance, Springer, vol. 20(1), pages 1-43, March.
    16. Gilles Zumbach, 2010. "Volatility conditional on price trends," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 431-442.
    17. Wang, Xunxiao & Wu, Chongfeng & Xu, Weidong, 2015. "Volatility forecasting: The role of lunch-break returns, overnight returns, trading volume and leverage effects," International Journal of Forecasting, Elsevier, vol. 31(3), pages 609-619.
    18. Gilles Zumbach, 2009. "Volatility forecasts and the at-the-money implied volatility: a multi-components ARCH approach and its relation with market models," Papers 0901.2275, arXiv.org.

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