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A distribution‐based method to gauge market liquidity through scale invariance between investment horizons

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  • Sergio Bianchi
  • Augusto Pianese
  • Massimiliano Frezza

Abstract

A nonparametric method is developed to detect self‐similarity among the rescaled distributions of the log‐price variations over a number of time scales. The procedure allows to test the statistical significance of the scaling exponent that possibly characterizes each pair of time scales and to analyze the link between self‐similarity and liquidity, the core assumption of the fractal market hypothesis. The method can support financial operators in the selection of the investment horizons as well as regulators in the adoption of guidelines to improve the stability of markets. The analysis performed on the S&P500 reveals a very complex, time‐changing scaling structure, which confirms the link between market liquidity and self‐similarity.

Suggested Citation

  • Sergio Bianchi & Augusto Pianese & Massimiliano Frezza, 2020. "A distribution‐based method to gauge market liquidity through scale invariance between investment horizons," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(5), pages 809-824, September.
    • Handle: RePEc:wly:apsmbi:v:36:y:2020:i:5:p:809-824
    DOI: 10.1002/asmb.2531
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    References listed on IDEAS

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    1. S. Bianchi & A. Pantanella & A. Pianese, 2013. "Modeling stock prices by multifractional Brownian motion: an improved estimation of the pointwise regularity," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1317-1330, July.
    2. Frezza, Massimiliano, 2012. "Modeling the time-changing dependence in stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1510-1520.
    3. Benoit Mandelbrot & Howard M. Taylor, 1967. "On the Distribution of Stock Price Differences," Operations Research, INFORMS, vol. 15(6), pages 1057-1062, December.
    4. Anderson, Nicola & Noss, Joseph, 2013. "Financial Stability Paper No 23: The Fractal Market Hypothesis and its implications for the stability of financial markets," Bank of England Financial Stability Papers 23, Bank of England.
    5. Bianchi, Sergio & Pianese, Augusto, 2014. "Multifractional processes in finance," Risk and Decision Analysis, IOS Press, issue 5, pages 1-22.
    6. Rama Cont & Marc Potters & Jean-Philippe Bouchaud, 1997. "Scaling in stock market data: stable laws and beyond," Science & Finance (CFM) working paper archive 9705087, Science & Finance, Capital Fund Management.
    7. Bianchi, Sergio, 2004. "A new distribution-based test of self-similarity," MPRA Paper 16640, University Library of Munich, Germany.
    8. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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    1. Frezza, Massimiliano & Bianchi, Sergio & Pianese, Augusto, 2021. "Fractal analysis of market (in)efficiency during the COVID-19," Finance Research Letters, Elsevier, vol. 38(C).

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