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Agent-based models for latent liquidity and concave price impact

Author

Listed:
  • Iacopo Mastromatteo
  • Bence Toth
  • Jean-Philippe Bouchaud
Abstract
We revisit the "epsilon-intelligence" model of Toth et al.(2011), that was proposed as a minimal framework to understand the square-root dependence of the impact of meta-orders on volume in financial markets. The basic idea is that most of the daily liquidity is "latent" and furthermore vanishes linearly around the current price, as a consequence of the diffusion of the price itself. However, the numerical implementation of Toth et al. was criticised as being unrealistic, in particular because all the "intelligence" was conferred to market orders, while limit orders were passive and random. In this work, we study various alternative specifications of the model, for example allowing limit orders to react to the order flow, or changing the execution protocols. By and large, our study lends strong support to the idea that the square-root impact law is a very generic and robust property that requires very few ingredients to be valid. We also show that the transition from super-diffusion to sub-diffusion reported in Toth et al. is in fact a cross-over, but that the original model can be slightly altered in order to give rise to a genuine phase transition, which is of interest on its own. We finally propose a general theoretical framework to understand how a non-linear impact may appear even in the limit where the bias in the order flow is vanishingly small.

Suggested Citation

  • Iacopo Mastromatteo & Bence Toth & Jean-Philippe Bouchaud, 2013. "Agent-based models for latent liquidity and concave price impact," Papers 1311.6262, arXiv.org, revised Dec 2014.
    • Handle: RePEc:arx:papers:1311.6262
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    References listed on IDEAS

    as
    1. P. Weber & B. Rosenow, 2005. "Order book approach to price impact," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 357-364.
    2. Eric Smith & J Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2003. "Statistical theory of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 481-514.
    3. Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters, 2006. "Random walks, liquidity molasses and critical response in financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 115-123.
    4. David Eliezer & Ian I. Kogan, 1998. "Scaling Laws for the Market Microstructure of the Interdealer Broker Markets," Papers cond-mat/9808240, arXiv.org, revised Sep 1998.
    5. J. Doyne Farmer & Paolo Patelli & Ilija I. Zovko, 2003. "The Predictive Power of Zero Intelligence in Financial Markets," Papers cond-mat/0309233, arXiv.org, revised Feb 2004.
    6. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
    7. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    8. Bak, P. & Paczuski, M. & Shubik, M., 1997. "Price variations in a stock market with many agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 430-453.
    9. Andre Cardoso Barato & Iacopo Mastromatteo & Marco Bardoscia & Matteo Marsili, 2011. "Impact of meta-order in the Minority Game," Papers 1112.3908, arXiv.org, revised Nov 2012.
    10. Biais, Bruno & Hillion, Pierre & Spatt, Chester, 1995. "An Empirical Analysis of the Limit Order Book and the Order Flow in the Paris Bourse," Journal of Finance, American Finance Association, vol. 50(5), pages 1655-1689, December.
    11. F. Lillo & Szabolcs Mike & J. Doyne Farmer, 2004. "A theory for long-memory in supply and demand," Papers cond-mat/0412708, arXiv.org, revised Mar 2005.
    12. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    13. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    14. Esteban Moro & Javier Vicente & Luis G. Moyano & Austin Gerig & J. Doyne Farmer & Gabriella Vaglica & Fabrizio Lillo & Rosario N. Mantegna, 2009. "Market impact and trading profile of large trading orders in stock markets," Papers 0908.0202, arXiv.org.
    15. Sandas, Patrik, 2001. "Adverse Selection and Competitive Market Making: Empirical Evidence from a Limit Order Market," The Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 705-734.
    16. Nataliya Bershova & Dmitry Rakhlin, 2013. "The non-linear market impact of large trades: evidence from buy-side order flow," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1759-1778, November.
    17. Zoltán Eisler & Jean-Philippe Bouchaud & Julien Kockelkoren, 2012. "The price impact of order book events: market orders, limit orders and cancellations," Quantitative Finance, Taylor & Francis Journals, vol. 12(9), pages 1395-1419, September.
    18. Maslov, Sergei, 2000. "Simple model of a limit order-driven market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(3), pages 571-578.
    19. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Henri Waelbroeck, 2013. "How efficiency shapes market impact," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1743-1758, November.
    20. A. C. Barato & I. Mastromatteo & M. Bardoscia & M. Marsili, 2013. "Impact of meta-order in the Minority Game," Quantitative Finance, Taylor & Francis Journals, vol. 13(9), pages 1343-1352, September.
    21. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2008. "Relation between bid-ask spread, impact and volatility in order-driven markets," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 41-57.
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