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Dimensional Analysis and Market Microstructure Invariance

Author

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  • Albert S. Kyle

    (Robert H. Smith School of Business, University of Maryland)

  • Anna Obizhaeva

    (New Economic School)

Abstract

Market microstructure is the subfield of finance and econophysics1 which studies how prices result from the process of trading securities. Large trades move prices2 and incur trading costs. Here we combine dimensional analysis, leverage neutrality, and a principle of market microstructure invariance to derive scaling laws which express transaction costs functions, bid-ask spreads, bet sizes, number of bets, and other financial variables in terms of trading volume and volatility. For example, market liquidity is proportional to the cube root of the ratio of dollar volume to return variance. We illustrate the scaling by showing that bid-ask spreads in Russian stocks indeed scale with the cube root. In addition to being of interest to risk managers and traders, these scaling laws provide scientific benchmarks for evaluating controversial issues related to high frequency trading, market crashes, and liquidity measurement as well as guidelines for designing policies in the aftermath of financial crisis.

Suggested Citation

  • Albert S. Kyle & Anna Obizhaeva, 2017. "Dimensional Analysis and Market Microstructure Invariance," Working Papers w0234, New Economic School (NES).
    • Handle: RePEc:abo:neswpt:w0234
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    File URL: https://www.nes.ru/files/Preprints-resh/WP234.pdf
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    Cited by:

    1. Frédéric Bucci & Fabrizio Lillo & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Are trading invariants really invariant? Trading costs matter," Post-Print hal-02323318, HAL.
    2. Fr'ed'eric Bucci & Fabrizio Lillo & Jean-Philippe Bouchaud & Michael Benzaquen, 2019. "Are trading invariants really invariant? Trading costs matter," Papers 1902.03457, arXiv.org.
    3. Mathias Pohl & Alexander Ristig & Walter Schachermayer & Ludovic Tangpi, 2018. "Theoretical and empirical analysis of trading activity," Papers 1803.04892, arXiv.org, revised Oct 2018.
    4. Giacomo Toscano & Maria Cristina Recchioni, 2020. "Bias optimal vol-of-vol estimation: the role of window overlapping," Papers 2004.04013, arXiv.org, revised Jul 2021.
    5. Giacomo Toscano & Maria Cristina Recchioni, 2022. "Bias-optimal vol-of-vol estimation: the role of window overlapping," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 137-185, June.
    6. Frédéric Bucci & Fabrizio Lillo & Jean-Philippe Bouchaud & Michael Benzaquen, 2019. "Are trading invariants really invariant? Trading costs matter," Working Papers hal-02323318, HAL.
    7. Kyle, Albert S. & Obizhaeva, Anna A. & Tuzun, Tugkan, 2020. "Microstructure invariance in U.S. stock market trades," Journal of Financial Markets, Elsevier, vol. 49(C).

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