Modeling the bid/ask spread: Measuring the inventory-holding premium

The need to understand and measure the determinants of market maker bid/ask spreads is crucial in evaluating the merits of competing market structures and the fairness of market maker rents. This study develops a simple, parsimonious model for the market maker's spread that accounts for the effects of price discreteness induced by minimum tick size, order-processing costs, inventory-holding costs, adverse selection, and competition. The inventory-holding and adverse selection cost components of spread are modeled as an option with a stochastic time to expiration. This inventory-holding premium embedded in the spread represents compensation for the price risk borne by the market maker while the security is held in inventory. The premium is partitioned in such a way that the inventory-holding and adverse selection cost components, as well as the probability of an informed trade, are identified. The model is tested empirically using Nasdaq stocks in three distinct minimum tick size regimes and is shown to perform well both in an absolute sense and relative to competing specifications.