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

Author

Listed:
  • Matthieu Wyart

    (CEA Saclay;)

  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

  • Julien Kockelkoren

    (Capital Fund Management)

  • Marc Potters

    (Science & Finance, Capital Fund Management)

  • Michele Vettorazzo

Abstract

We argue that on electronic markets, limit and market orders should have equal effective costs on average. This symmetry implies a linear relation between the bid-ask spread and the average impact of market orders. Our empirical observations on different markets are consistent with this hypothesis. We then use this relation to justify a simple, and hitherto unnoticed, proportionality relation between the spread and the volatility_per trade_. We provide convincing empirical evidence for this relation. This suggests that the main determinant of the bid-ask spread is adverse selection, if one considers that the volatility per trade is a measure of the amount of `information' included in prices at each transaction. Symmetry between market and limit orders stems from the self-organization of liquidity in electronic markets. Our results appear to hold approximately on liquid specialist markets as well, although the spread is significantly larger.

Suggested Citation

  • Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2006. "Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets," Science & Finance (CFM) working paper archive 500067, Science & Finance, Capital Fund Management.
  • Handle: RePEc:sfi:sfiwpa:500067
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Geoff Willis, 2011. "Why Money Trickles Up - Wealth & Income Distributions," Papers 1105.2122, arXiv.org, revised May 2011.
    4. J. Doyne Farmer & John Geanakoplos, 2008. "The virtues and vices of equilibrium and the future of financial economics," Papers 0803.2996, arXiv.org.
    5. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    6. Challet, Damien, 2008. "Feedback and efficiency in limit order markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3831-3836.
    7. Gilles Zumbach, 2007. "Time reversal invariance in finance," Papers 0708.4022, arXiv.org.
    8. Moutot, Philippe, 2011. "Systemic risk and financial development in a monetary model," Working Paper Series 1352, European Central Bank.
    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.

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