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Stochastic Structure of Brokered Foreign Exchange Auctions

This paper models stochastic order flow generations in a FX market. Trading volume and volatility are endogenous. We circumvent an issue of defining equilibrium. Yet we provide a model of auctions process where rational FX dealers choose actions and transactions continue. Our features of our microstructure are handling (i) dealer's own choosing of price expectation believing others', (ii) asynchronous transactions (iii) characterizing sources of trading. Our approach makes use of instruments related to continuous time Markov process. We define a set of market states. Each one has an associated distribution of bid rate. Bid rate is a proxy for the transaction price. We construct an infinitesimal operator of Markov transitions between market states. Use of infinitesimal operator makes derivation of stochastic properties of bid rate possible. What determine trading volume and volatility are "dealers" expectation revision process, distribution of dealer's reservation prices and retail transactions. We show volume and volatility can change separately or together. FX auctions poses theoretical issues. Like other financial asset markets, in order for a trader to have perspective on price, he must take other traders' perspectives into consideration. In our model, he tries to fathom unobservable distribution of reservation prices and chooses his own. Meanwhile traders have transactions with retail customers. These retail transactions are passed onto wholesale market. Thus prices are formed through the interactions between heterogeneous price perspectives and the order flow from macro economy. The second issue is how to define equilibrium when the auctions are continuous. We do not have truistic point of time to define liquidation value. Also applying demand and supply on their asynchronous transactions is difficult. We use alternative benchmark value. The peak or trough of price, trader expects first in a row is the key variable. That value determines his present action.