Scaling Laws for the Market Microstructure of the Interdealer Broker Markets

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Abstract
We discuss a series of simple models for microstructure of a double auction without intermediaries. We specialize to those markets, such as 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, whose numbers vary in time, and who diffuse in price space and interact 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 1 over the square root of the deal rate. In addition we investigate the scaling of other intuitive relationships, such as the relationship between the fluctuations of the best bid/offer and the density of buyers and sellers. We then study this model and its scaling laws under the influence of random disturbances to trader drift, 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 simulations may be carried out to study scaling in all of these settings, and how the models may be tested in actual markets.

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