Continuous Time Decision-Making in a Partially Decentralized Multiple Dealership Forex Market and Equilibrium Exchange Rate

The paper introduces a model of bid/ask price formation in an imperfectly centralized forex dealership market in continuous time. The dealers have costly access to best quotes while interpreting signals from the joint dealer-customer order flow and deciding upon their own price quotes and activities in the inter-dealer market. The lowest ask/highest bid price of a foreign currency becomes the single transaction price in equilibrium. Each dealer uses the observed order flow to improve the subjective estimates of relevant aggregate variables, which are the sources of uncertainty. These are: returns on domestic and foreign assets, the equilibrium FX transaction price and the size of the aggregate dealer transactions in the FX market. These uncertainties have diffusion form and are dealt with according to principles of portfolio optimization in continuous time. The price information content of the local order flow observed by the dealer, has to do with the existence of "global" investors in the dealer's customer base. Global investors have access to bid-ask quotes of more than one dealer, along with superior information about fundamentals. These two factors help them generate better estimates of the future inter-dealer transactions than both the "local" investors (i.e. those who only trade with their single local dealer) and any of the dealers themselves. I obtain the formula for the dealer spread around the equilibrium price. I also show how informational customer-dealer asymmetries generate non-stationary cumulative order flows as well as deviations of the inter-dealer transaction price from uncovered parity of national asset returns.