arXiv1998
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.