Optimal Spread with Heterogeneous Expectations in Foreign Exchange Market

Our subject is foreign exchange auction through market makers. We consider market maker’s policy to choose bid and ask as an optimization problem. We show that if traders’ expectations are more heterogeneous, the market maker widens bid and ask spread. He can take advantage of the heterogeneous expectations. We derive an equation of expected transaction prices. This equation makes it possible that our representative market maker sets bid and ask so that expected profit per transaction is maximized. We apply our model to derive such bid and ask. Meanwhile the underlying model is about generation of order flow. Various authors, including Evans and Lyons (2002) documented significant effects of order flow in FX market. We fill what the existing literature lacks. We have mechanisms which generate stochastic arrivals of orders. Two sources generate orders; FX dealers’ revisions of expectations and retail transactions. Dealers with heterogeneous views as a whole absorb unbalanced arrivals of retail transactions. This determines path of transaction prices. FX market is not transparent. Dealers have to inquire market makers for quote. Only by that, they can obtain immediately executable quotes. Quotes may change during the search for another quotes. Using such an expected change, dealers determine reservation prices. As the expectations become more heterogeneous, so do reservation prices. They are dispersed over a wider range. Market makers can exploit it by wider spread.