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Turbulence in financial markets: the surprising explanatory power of simple cascade models

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  • T. Lux
Abstract
Price changes in financial markets have been found to share many of the features characterizing turbulent flows. In particular, a number of recent contributions have highlighted that time series from both stock and foreign exchange markets possess multifractal statistics, i.e. the scaling behaviour of absolute moments is described by a convex function. These findings have stimulated the application of certain cascade models from statistical physics to financial data. Extant work in this area has so far been confined to parameter estimation and visual comparison of empirical and theoretical scaling properties. The lack of rigorous statistical measures of goodness of fit in the literature on turbulence has, however, impeded a comparison of these new models with standard approaches in empirical finance. Here we try to fill this gap and provide a first assessment of two elementary cascade models based on elementary goodness-of-fit criteria. As it turns out, these relatively simple one-parameter models are not only capable of accommodating the multiscaling behaviour of price changes, but also provide a perplexingly good fit of the unconditional distribution of the data. In a double-blind test, we would, in fact, be unable to reject identity of the data-generating processes underlying empirical records and simulated data from stochastic cascades.

Suggested Citation

  • T. Lux, 2001. "Turbulence in financial markets: the surprising explanatory power of simple cascade models," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 632-640.
    • Handle: RePEc:taf:quantf:v:1:y:2001:i:6:p:632-640
    DOI: 10.1088/1469-7688/1/6/305
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    Citations

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    Cited by:

    1. T. Di Matteo & T. Aste & M. M. Dacorogna, 2003. "Using the Scaling Analysis to Characterize Financial Markets," Papers cond-mat/0302434, arXiv.org.
    2. Segnon, Mawuli & Lux, Thomas, 2013. "Multifractal models in finance: Their origin, properties, and applications," Kiel Working Papers 1860, Kiel Institute for the World Economy (IfW Kiel).
    3. Matteo, T. Di & Aste, T. & Dacorogna, Michel M., 2005. "Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 827-851, April.
    4. Vindel, Jose M. & Trincado, Estrella, 2010. "The timing of information transmission in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5749-5758.
    5. 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.
    6. Thomas Lux, 2003. "The Multi-Fractal Model of Asset Returns:Its Estimation via GMM and Its Use for Volatility Forecasting," Computing in Economics and Finance 2003 14, Society for Computational Economics.
    7. Vortelinos, Dimitrios I., 2016. "Incremental information of stock indicators," International Review of Economics & Finance, Elsevier, vol. 41(C), pages 79-97.
    8. Trincado, Estrella & Vindel, José María, 2015. "An application of econophysics to the history of economic thought: The analysis of texts from the frequency of appearance of key words," Economics Discussion Papers 2015-51, Kiel Institute for the World Economy (IfW Kiel).
    9. Carlo Campajola & Fabrizio Lillo & Daniele Tantari, 2019. "Unveiling the relation between herding and liquidity with trader lead-lag networks," Papers 1909.10807, arXiv.org, revised Mar 2020.
    10. Wyart, Matthieu & Bouchaud, Jean-Philippe, 2007. "Self-referential behaviour, overreaction and conventions in financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 63(1), pages 1-24, May.
    11. Marcus Cordi & Serge Kassibrakis & Damien Challet, 2018. "The market nanostructure origin of asset price time reversal asymmetry," Working Papers hal-01966419, HAL.
    12. 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.
    13. L. Borland & J. -Ph. Bouchaud, 2005. "On a multi-timescale statistical feedback model for volatility fluctuations," Papers physics/0507073, arXiv.org.
    14. Lisa Borland & Jean-Philippe Bouchaud, 2005. "On a multi-timescale statistical feedback model for volatility fluctuations," Science & Finance (CFM) working paper archive 500059, Science & Finance, Capital Fund Management.
    15. Kartono, Agus & Febriyanti, Marina & Wahyudi, Setyanto Tri & Irmansyah,, 2020. "Predicting foreign currency exchange rates using the numerical solution of the incompressible Navier–Stokes equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    16. Bacry, Emmanuel & Kozhemyak, Alexey & Muzy, Jean-François, 2006. "Are asset return tail estimations related to volatility long-range correlations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 119-126.
    17. Matthieu Wyart & Jean-Philippe Bouchaud, 2003. "Self-referential behaviour, overreaction and conventions in financial markets," Science & Finance (CFM) working paper archive 500020, Science & Finance, Capital Fund Management.
    18. Miśkiewicz, Janusz, 2012. "Economy with the time delay of information flow—The stock market case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1388-1394.

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