A steady-state model of the continuous double auction

A model of the continuous double auction is constructed and analysed. Given the underlying supply and demand functions, the analysis yields steady-state probability distributions for the best ask, best bid and transaction prices. Under fairly general assumptions it is found that these prices are confined to a clearly defined window. Expressions are also obtained for the depth of the order book at arbitrary prices, and for the expected time-to-execution of a given order. These can be used to calculate the optimal order price for a trader with a specified level of impatience, to determine when a market order is preferable to a limit order, and hence in some cases to detect the presence of irrational or ill-informed traders in the market. It is conjectured that, in a market of rational and well-informed traders, the two sides of the order book should be statistically independent.