Market Microstructure

2

Order Choice and Information in Limit Order Markets

Ioanid Rou

2.1 INTRODUCTION

In recent years, trading via limit orders and market orders has become the dominant form of trading in most exchanges around the world, whether these are pure electronic limit order markets or hybrid markets in which limit order traders are in competition with floor traders, specialists, or dealers.

A pure limit order market is defined as a market in which there are essentially only limit orders and market orders. A market order demands immediate execution, irrespective of the price. A limit order is an instruction to buy or sell only at a pre-specified price, and is placed in a queue based on price/time priority. A limit order is usually executed only after a market order clears it from the queue. A limit order that gets immediate execution because the price is already met is called a marketable order and is not differentiated from a market order. A sell limit order is also called an ask (or offer), while a buy limit order is also called a bid. The limit order book, or simply the book, is the collection of all outstanding limit orders. The lowest ask in the book is called the ask price, or simply ask, and the highest bid is called the bid price, or simply bid.1 This chapter does not discuss hidden limit orders, which are limit orders for which some of the quantity is not visible to the market.

Given the importance of limit order markets, there have been relatively few models that describe price formation and order choice in these markets. The main reason for this scarcity is the difficulty of the problem. In dealer or specialist markets, liquidity provision is restricted to one or several individuals, who are easier to model, especially if they are assumed to be uninformed.2 In contrast, in limit order markets, liquidity provision is open to everyone via limit orders. Therefore, in order to achieve the tractability of previous models, one may assume, as in Glosten (1994), Rock (1996), Seppi (1997), or Biais et al. (2000), that limit order traders are uninformed. If instead informed traders are allowed to choose how to trade, the problem becomes significantly more difficult, especially in dynamic models. This chapter focuses on the order choice; therefore we do not discuss the literature in which traders cannot choose between market orders and limit orders.

The author has benefited from some excellent surveys on the market microstructure literature, e.g., O'Hara (1995), Madhavan (2000), Biais et al. (2005), and especially Parlour and Seppi (2008), which focuses on limit order markets.

This survey begins by an analysis of order choice in the presence of symmetric information (Section 2.2) and then discusses the same choice under asymmetric information (Section 2.3). The next section discusses the empirical literature on order choice, as well as on the information content and price impact of various types of orders (Section 2.4). The survey ends with some questions for future research (Section 2.5).

2.2 ORDER CHOICE WITH SYMMETRIC INFORMATION

In the absence of asymmetric information, the choice between market orders and limit orders is decided by comparing the certain execution of market orders at possibly disadvantageous prices with the uncertain execution of limit orders at more advantageous prices. If, moreover, limit orders cannot be freely canceled or modified, one additional cost of limit orders is that they can be picked off by the new traders.

The intuition for the trade-off between price and time goes back to Demsetz (1968), but it was first modeled explicitly in Cohen et al. (1981). This paper assumes an exogenous price process that determines whether a limit order becomes executed by the next period or not, in which case the limit order is canceled. The model produces a nonzero bid-ask spread. Moreover, if the market has a smaller trading intensity (it is thinner), the equilibrium bid-ask spread is larger. To understand these results, consider an investor who contemplates placing a limit buy order below the ask. Due to the frictions in the model, the probability of execution is always significantly less than one, while the price improvement converges to zero as the limit buy order approaches the ask. This “gravitational pull” makes it certain that above a certain price below the ask it is always more advantageous to buy with a market order than with a limit order. Thus, there is a minimum distance between the bid and the ask, i.e., a minimum bid-ask spread. One can see also that this minimum spread must be larger when the probability of execution of the limit order gets smaller, which happens when the market is thinner.

Parlour (1998) presents a model of a limit order book in which there are only two prices: the bid, B, and the ask, A. The buy limit orders a queue at B and the limit orders a queue at A. The trading day is divided into T + 1 subperiods, t = 0, 1, ... ,T. On each trading subperiod, one trader arrives, that is either a seller (with probability ), a buyer (with probability ), or neither. A buyer can make one of three choices: submit a market buy order, submit a limit buy order, or stay out of the market. Each trader is characterized by a parameter (with ), which determines the trade-off between consumption on the trading day and on the next day, when the asset value is realized. The parameter can be interpreted as an impatience coefficient, or alternatively as a private valuation for the asset. Traders with extreme values of prefer to trade immediately, and use market orders. Traders with intermediate values of prefer to wait, and use limit orders. A low indicates that the trader prefers consumption today to consumption tomorrow, which means that, given the choice, he or she prefers to sell the asset to get cash today. Similarly, high characterizes a propensity to buy. A trader arriving at t has only one opportunity to submit an order. Once submitted, orders cannot be modified or canceled.

The model leads to a stochastic sequential game and has a cutoff equilibrium. For example, buyers with high submit a market buy order; with intermediate submit a limit buy order; and with low stay out of the market. The model produces interesting liquidity dynamics, and in particular it provides an explanation for the diagonal effect of Biais et al. (1995), who find that, for example, buy market orders (BMOs) are more likely after a BMO than after sell market orders (SMOs). To see this, consider the arrival of a BMO at t. This reduces the liquidity available at the ask by one unit, and, if the next trader is a seller, the trader is more likely to submit a sell limit order (SLO) than a sell market order (SMO). This in turn makes future buyers prefer a BMO to a BLO. Note that this type of dynamics also involve a correlation between a BMO and an SLO, which provides an additional empirical prediction.

Foucault et al. (2005) explicitly model waiting costs as linear in the expected waiting time. Limit orders cannot be canceled and must be submitted inside the existing bid-ask spread. Prices are constrained in a fundamental band [B, A]: a competitive fringe of traders stands ready to buy at B and sell at A an unlimited number of shares. Traders arrive according to a Poisson process with parameter λ, and can trade only one unit. Traders can be either patient, by incurring a waiting cost of per unit of time, or impatient, with a waiting cost of . The fraction of impatient traders out of the total population is .

The assumption that limit orders must always improve the spread implies that the only relevant state variable is the bid-ask spread, which is an integer multiple of the minimum tick size, Δ. This in turn means that a limit order can be characterized simply by the bid-ask spread that it creates after being submitted: a z-limit order is a limit order that results in a bid-ask spread of size jΔ. The resulting Markov perfect equilibrium depends on the current spread: if the spread is below a cutoff, both patient and impatient traders submit market orders; if the spread is above a cutoff, both types of traders submit limit orders and if the spread is of intermediate size, the patient traders submit limit orders and impatient traders submit market orders.

Foucault et al. (2005) focus on the case when it is never optimal for impatient traders to submit limit orders. Not all spreads can exist in equilibrium, but only a subset: . Then a patient trader facing a spread between and is to submit an nh-limit order. The expected time to execution of such a limit order has a closed-form expression: , where is the ratio of the proportions of patient and impatient traders. Relatively more patient traders (higher ρ) induce more competition for providing liquidity, and hence a higher expected waiting time for limit orders. Aware of this, each patient trader submits more aggressive orders and consequently reduces the spread more quickly.

The paper discusses the notion of resiliency: e.g., the propensity for the bid-ask spread to revert to its lower level after a market order has consumed liquidity in the book. Note that in the context of the model there is no pressure to revert to the former level, which would be due, for example, to the arrival of more liquidity providers when the bid-ask spread becomes wider....