Resilient price impact of trading and the cost of illiquidity

We construct a model for liquidity risk and price impacts in a limit order book setting, and derive a wealth equation and a characterization of illiquidity costs for liquidity providers. The model has desirable stylized facts justified by empirical studies and contains all three components identified by Kyle (1985). We give conditions under which the model is arbitrage free. By considering the standard utility maximization problem, we obtain a stochastic discount factor and an asset pricing formula which is consistent with the empirical findings of Brennan & Subrahmanyam (1996) and Amihud & Mendelson (1986). Furthermore, we show that in limiting cases for some parameters of the model, we derive many existing liquidity models present in the arbitrage pricing literature, including Çetin et al. (2004) and Rogers and Singh (2010). This offers a classification of different types of liquidity costs in terms of the depth and resilience of prices.