Order Flow and the Bid-Ask Spread : An Empirical Probability Model of Screen-Based Trading

A probabilistic framework for the analysis of screen-based trading activity in financial markets is presented. Conditional probability functions are derived for the stationary distributions of the best bid and offer in the market, given the order flows and the acceptance rates of bids and offers. These flows are conditioned on observable screen information. A two-step method is developed for the estimation of the conditional probability functions. The estimation allows for the separate identification of the unobservable order and acceptance flows, which in turn may be used to predict the stationary distributions of the bid- ask spreads, transaction prices, and other market statistics. A formal comparison of the predicted and the sample bid-ask spread distribution provides a stringent test of the model. The necessary econometric methods for conducting such a test, taking into account the parameter estimation error uncertainty, is developed. The methodology is applied to the screen-based interbank foreign exchange market, using a newly available dataset that consists of continuously recorded bid and ask quotes on the Deutschemark/U.S. Dollar exchange rate. The model is found to provide a good description of the salient probabilistic features of the market structure, even though the formal prediction based test for the spread distribution, with more than 29,000 out-of-sample quotations, rejects the exact parametric formulation of the order flows