| Budget Amount *help |
¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2006: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
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| Research Abstract |
Our subject is continuous auctions in foreign exchange market. We have two papers. (1)"Stochastic Structure of Brokered Foreign Exchange Auctions" and (2)"Optimal Spread with Heterogeneous Expectations in Foreign Exchange Market." We describe arrivals of orders in the market as continuous time stochastic processes. Both of our papers start with these stochastic order generations. There are two sources of order generations. One is foreign exchange dealer's expectation revising and the other is retail transactions with customers. We presuppose that dealers have heterogeneous expectations. Knowing it, they choose their actions. Our model assumes that dealers may agree on price determination mechanism but that they have different estimates on relevant parameters.
In paper (1), dealers submit heterogeneous limit orders. Basic mechanism of price determination is that transaction price changes enough to absorb unbalanced arrivals of orders. For a given unbalanced arrivals, price has to change
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more when expectations are more heterogeneous. As for mathematical description, we consider that all combinations of the dealers' positions constitute a finite set of states. Transactions in the market correspond to Markov transitions between these states. We construct a matrix called infinitesimal operator. From this, we derive probability distribution of the states. We apply our model on volume and volatility correlation. Paper (2) is about market maker's optimal bid-ask spread. We show that as dealers have more heterogeneous expectations, a market maker widens spread so that he can exploit the heterogeneity of expectations. Usually, an adverse selection is key issue for the spread determination. However, in the intra-day transactions, a definition of equilibrium is not truism. The heterogeneous expectations influence actual transaction prices. We circumvent this difficulty. Assuming such an environment, we derive an expected time path of transaction prices. The intra-day expected time is what had been lacking in the existing literature. Less
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