Limit Order Book as a Market for LiquidityWe develop a dynamic model of an order-driven market populated by discretionary liquidity traders. These traders differ by their impatience and seek to minimize their trading costs by optimally choosing between market and limit orders. We characterize the equilibrium order placement strategies and the waiting times for limit orders. In equilibrium less patient traders are likely to demand liquidity, more patient traders are more likely to provide it. We find that the resiliency of the limit order book increases with the proportion of patient traders and decreases with the order arrival rate. Furthermore, the spread is negatively related to the proportion of patient traders and the order arrival rate. We show that these findings yield testable predictions on the relation between the trading intensity and the spread. Moreover, the model generates predictions for time-series and cross-sectional variation in the optimal order-submission strategies.Finally, we find that imposing a minimum price variation improves the resiliency of a limit order market. For this reason, reducing the minimum price variation does not necessarily reduce the average spread in limit order markets.

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We study the relation between asset liquidity and stock liquidity. Our model shows that the relation may be either positive or negative depending on parameter values. Asset liquidity improves stock liquidity more for firms that are less likely to reinvest their liquid assets (i.e., firms with less growth opportunities and financially constrained firms). Empirically, we find a positive and economically large relation between asset liquidity and stock liquidity. Consistent with our model, the relation is more positive for firms that are less likely to reinvest their liquid assets. Our results also shed light on the value of holding liquid assets.

PHONE: [972]-2-6584135 FAX: [972]-2-6513681 E-MAIL: ratio@math.huji.ac.il URL: http://www.ratio.huji.ac.il/ Abstract Limit Order Book as a Market for LiquidityWe develop a dynamic model of an order-driven market populated by discretionary liquidity traders. These traders differ by their impatience and seek to minimize their trading costs by optimally choosing between market and limit orders. We characterize the equilibrium order placement strategies and the waiting times for limit orders. In equilibrium less patient traders are likely to demand liquidity, more patient traders are more likely to provide it. We find that the resiliency of the limit order book increases with the proportion of patient traders and decreases with the order arrival rate. Furthermore, the spread is negatively related to the proportion of patient traders and the order arrival rate. We show that these findings yield testable predictions on the relation between the trading intensity and the spread. Moreover, the model generates predictions for time-series and cross-sectional variation in the optimal order-submission strategies.Finally, we find that imposing a minimum price variation improves the resiliency of a limit order market. For this reason, reducing the minimum price variation does not necessarily reduce the average spread in limit order markets.3 Empirical analyses of limit order markets include . 4 In extant models, traders who submit limit orders may be seen as infinitely patient, while those who submit market orders may be seen as extremely impatient. We consider a less polar case.5 Several other approaches exist to modeling the limit order book: Angel (1994), Domowitz and Wang (1994),and Harris (1995) study models with exogenous order flow. Using queuing theory, Domowitz and Wang (1994) analyze the stochastic properties of the book. Angel (1994) and Harris (1998) study how the optimal choice between market and limit orders varies with market conditions such as the state of the book, and the order arrival rate. We use more restrictive assumptions on the primitives of the model that enable us to endogenize the market conditions

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