An Integrated Model of Market and Limit Orders

Abstract

We develop an integrated model in which a risk neutral informed trader optimally chooses any combination of: a market buy, a market sell, a limit buy including the optimal limit buy price, and a limit sell including the optimal limit sell price. We allow orders to cross with one another without involving the market maker. This generates transactions inside the bid-ask spread, corresponding to what is observed in practice. Using minimal distributional assumptions, we are able to characterize the informed trader's optimal strategy. We find that he sometimes chooses to submit market orders when the terminal risky asset value is inside the bid-ask spread. This results from the fact that a market buy submitted by the informed trader sometimes executes at a price below the ask by crossing with a limit sell submitted by an uninformed trader and it never executes above the ask in our single period model. Thus, the expected execution price of the informed trader's market buy is below the ask. Hence, there are some terminal asset values, above the expected execution price and below the ask, for which it is optimal for the informed trader to submit a market buy. In addition, with a richer menu of strategies to choose from, the informed trader is able to exploit mutually beneficial interactions between opposite order types. For example, any time the terminal asset value is above the bid, a combined market buy-limit sell is more profitable than a market buy only. Sometimes the two orders will cross against one another and the informed trader will end up with a zero net trade. This is beneficial because the combination eliminates states in which the same market buy submitted in isolation would have executed at a loss. In this sense, the limit sell acts as a "safety-net" for the accompanying market buy--an intuition that has not been captured in the extant theoretical microstructure literature. Adding specific distributional assumptions, we obtain an analytic solution and explore the comparative statics of the informed trader's limit price strategy.

JEL Classification: D40, D82, G12, G14