Modeling Electronic FX Brokerage as a Fast Order-Driven Marketunder Heterogeneous Private Values and Information

The paper develops a theoretical framework for studying price formation in brokered foreign exchange markets with very high order arrival frequency (to be followed by an application to real data on Czech koruna transactions in subsequent work). I construct a model of an order-driven market with very volatile motives for trade and a large number of (nearly) simultaneous limit and market order submissions. The model is applicable to very frequently traded securities such as high-grade bonds or FX. Investors have a non-trivial distribution of private values for the traded asset as well as heterogeneous information about the parameters of this distribution across traders. I investigate the properties of the mapping from the histogram of private asset values and private information endowments to the inside bid and ask price. Basic relationships between the limit order book, market sell and market buy order flow distributions, expected market order execution prices and the probabilities of a limit order execution at a given price, all as functions of private information, are derived. Traders are risk neutral as long as the transacted quantities are small, so that the limit and the market order decisions within one trading round do not feed back into private values. I formulate the equations that characterize the best ask and bid prices in this environment, as well as establish a number of properties of the equilibrium order book.