A Random Order Placement Model of Price Formation in the Continuous Double Auction

Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this chapter we use a microscopic dynamical statistical model for the continuous double auction under the assumption of IID random order flow. The analysis is based on simulation, dimensional analysis, and theoretical tools based on mean-field approximations. The model makes testable predictions for all the basic properties of markets, including price volatility, the depth of stored supply and demand, 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 such as share volume of market and limit orders, cancellations, typical order size, and tick size. Because these quantities can all be measured directly in real data sets 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 im-