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# Scaling Laws for the Market Microstructure of the Interdealer Broker Markets

## Author

Listed:
• David Eliezer
• Ian I. Kogan

## Abstract

We propose a series of simple models for the microstructure of a double auction market without intermediaries. We specialize to those markets, such interdealer broker markets, which are dominated by professional traders, who trade mainly through limit orders, watch markets closely, and move their limit order prices frequently. We model these markets as a set of buyers and a set of sellers diffusing in price space and interacting through an annihilation interaction. We seek to compute the purely statistical effects of the presence of large numbers of traders, as scaling laws on various measures of liquidity, and to this end we allow our model very few parameters. We find that the bid-offer spread scales as $\sqrt{1/{\rm Deal Rate}}$.In addition we investigate the scaling of other intuitive relationships, such as the relation between fluctuations of the best bid/offer and the density of buyers/sellers. We then study this model and its scaling laws under the influence of random disturbances to trader drift, trader volatility, and entrance rate. We also study possible extensions to the model, such as the addition of market order traders, and an interaction that models momentum-type trading. Finally, we discuss how detailed simulations may be carried out to study scaling in all of these settings, and how the models may be tested inactual markets.

## Suggested Citation

• 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.
• Handle: RePEc:arx:papers:cond-mat/9808240
as

File URL: http://arxiv.org/pdf/cond-mat/9808240

## References listed on IDEAS

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1. Seha M. Tinic, 1972. "The Economics of Liquidity Services," The Quarterly Journal of Economics, Oxford University Press, vol. 86(1), pages 79-93.
2. Tinic, Seha M & West, Richard R, 1974. "Marketability of Common Stocks in Canada and the U.S.A.: A Comparison of Agent versus Dealer Dominated Markets," Journal of Finance, American Finance Association, vol. 29(3), pages 729-746, June.
3. Oldfield, George Jr. & Rogalski, Richard J. & Jarrow, Robert A., 1977. "An autoregressive jump process for common stock returns," Journal of Financial Economics, Elsevier, vol. 5(3), pages 389-418, December.
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## Citations

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Cited by:

1. Mike, Szabolcs & Farmer, J. Doyne, 2008. "An empirical behavioral model of liquidity and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 200-234, January.
2. J. Doyne Farmer, 2002. "Market force, ecology and evolution," Industrial and Corporate Change, Oxford University Press, vol. 11(5), pages 895-953, November.
3. Szabolcs Mike & J. Doyne Farmer, 2005. "An empirical behavioral model of price formation," Papers physics/0509194, arXiv.org, revised Oct 2005.
4. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
5. 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.
6. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
7. 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.
8. Hendrik J. Blok, 2000. "On the nature of the stock market: Simulations and experiments," Papers cond-mat/0010211, arXiv.org.

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