Statistical theory of the continuous double auction
Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the assumption of IID random order flow, and analyze it using simulation, dimensional analysis, and theoretical tools based on mean field approximations. The model makes testable predictions for basic properties of markets, such as price volatility, the depth of stored supply and demand vs. price, the bid-ask spread, the price impact function, and the time and probability of filling orders. These predictions are based on properties of order flow and the limit order book, such as share volume of market and limit orders, cancellations, typical order size, and tick size. Because these quantities can all be measured directly there are no free parameters. We show that the order size, which can be cast as a nondimensional granularity parameter, is in most cases a more significant determinant of market behavior than tick size. We also provide an explanation for the observed highly concave nature of the price impact function. On a broader level, this work suggests how stochastic models based on zero-intelligence agents may be useful to probe the structure of market institutions. Like the model of perfect rationality, a stochastic-zero intelligence model can be used to make strong predictions based on a compact set of assumptions, even if these assumptions are not fully believable.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- P. Bak & M. Paczuski & Martin Shubik, 1996. "Price Variations in a Stock Market with Many Agents," Cowles Foundation Discussion Papers 1132, Cowles Foundation for Research in Economics, Yale University.
- P. Bak & M. Paczuski & M. Shubik, 1996. "Price Variations in a Stock Market with Many Agents," Working Papers 96-09-075, Santa Fe Institute.
- anonymous, 1992. "Interview with Gyo Obata," The Region, Federal Reserve Bank of Minneapolis, issue Sep.
- 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.
- Carl Chiarella & Giulia Iori, 2002. "A simulation analysis of the microstructure of double auction markets," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 346-353.
- Anonymous, 1992. "Honorary Life Member Award," Northeastern Journal of Agricultural and Resource Economics, Northeastern Agricultural and Resource Economics Association, vol. 21(2), October.
- Challet, Damien & Stinchcombe, Robin, 2001. "Analyzing and modeling 1+1d markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(1), pages 285-299.
- Damien Challet & Robin Stinchcombe, 2001. "Analyzing and modelling 1+1d markets," Papers cond-mat/0106114, arXiv.org, revised Jun 2001.
- Unknown, 1992. "Newsletter Fall 1992," Institute on Global Conflict and Cooperation, Working Paper Series qt9b58d3pn, Institute on Global Conflict and Cooperation, University of California.
- Gode, Dhananjay K & Sunder, Shyam, 1993. "Allocative Efficiency of Markets with Zero-Intelligence Traders: Market as a Partial Substitute for Individual Rationality," Journal of Political Economy, University of Chicago Press, vol. 101(1), pages 119-137, February.
- 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.
- Anonymous, 1992. "Book Reviews," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 36(03), December.
- 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.
- Anonymous, 1992. "Book Reviews," Journal of Agricultural Cooperation, National Council of Farmer Cooperatives, vol. 7.
- anonymous, 1992. "Interview with Paul A. Volcker," The Region, Federal Reserve Bank of Minneapolis, issue Dec.
- Anonymous, 1992. "Book Reviews," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 60(02), August.
- Bollerslev, Tim & Domowitz, Ian & Wang, Jianxin, 1997. "Order flow and the bid-ask spread: An empirical probability model of screen-based trading," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1471-1491, June.
- Anonymous, 1992. "Book Reviews," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 36(02), August.
- Domowitz, Ian & Wang, Jianxin, 1994. "Auctions as algorithms : Computerized trade execution and price discovery," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 29-60, January.
- anonymous, 1992. "Interview with Milton Friedman," The Region, Federal Reserve Bank of Minneapolis, issue June.
- Vasiliki Plerou & Parameswaran Gopikrishnan & Xavier Gabaix & H. Eugene Stanley, 2001. "Quantifying Stock Price Response to Demand Fluctuations," Papers cond-mat/0106657, arXiv.org.
- Anonymous, 1992. "Book Reviews," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 36(01), April. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:arx:papers:cond-mat/0210475. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.