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Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets

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  • Matthieu Wyart
  • Jean-Philippe Bouchaud
  • Julien Kockelkoren
  • Marc Potters
  • Michele Vettorazzo

Abstract

We show that the cost of market orders and the profit of infinitesimal market-making or -taking strategies can be expressed in terms of directly observable quantities, namely the spread and the lag-dependent impact function. Imposing that any market taking or liquidity providing strategies is at best marginally profitable, we obtain a linear relation between the bid-ask spread and the instantaneous impact of market orders, in good agreement with our empirical observations on electronic markets. We then use this relation to justify a strong, and hitherto unnoticed, empirical correlation between the spread and the volatility_per trade_, with R^2s exceeding 0.9. This correlation suggests both that the main determinant of the bid-ask spread is adverse selection, and that most of the volatilitycomes from trade impact. We argue that the role of the time-horizon appearing in the definition of costs is crucial and that long-range correlations in the order flow, overlooked in previous studies, must be carefully factored in. We find that the spread is significantly larger on the nyse, a liquid market with specialists, where monopoly rents appear to be present.

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  • Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2006. "Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets," Papers physics/0603084, arXiv.org, revised Mar 2007.
  • Handle: RePEc:arx:papers:physics/0603084
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    References listed on IDEAS

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    Cited by:

    1. Willis, Geoff, 2011. "Why money trickles up – wealth & income distributions," MPRA Paper 30851, University Library of Munich, Germany.
    2. Gilles Zumbach, 2009. "Time reversal invariance in finance," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 505-515.
    3. Challet, Damien, 2008. "Feedback and efficiency in limit order markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3831-3836.
    4. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    5. Zoltan Eisler & Janos Kertesz & Fabrizio Lillo & Rosario Mantegna, 2009. "Diffusive behavior and the modeling of characteristic times in limit order executions," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 547-563.
    6. Takero Ibuki & Jun-ichi Inoue, 2011. "Response of double-auction markets to instantaneous Selling–Buying signals with stochastic Bid–Ask spread," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 6(2), pages 93-120, November.
    7. Moutot, Philippe, 2011. "Systemic risk and financial development in a monetary model," Working Paper Series 1352, European Central Bank.
    8. J. Doyne Farmer & John Geanakoplos, 2008. "The Virtues and Vices of Equilibrium and the Future of Financial Economics," Levine's Working Paper Archive 122247000000002067, David K. Levine.
    9. G.-F. Gu & W. Chen & W.-X. Zhou, 2007. "Quantifying bid-ask spreads in the Chinese stock market using limit-order book data," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(1), pages 81-87, May.
    10. Gilles Zumbach, 2007. "Time reversal invariance in finance," Papers 0708.4022, arXiv.org.

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