Modeling the Bid/Ask Spread: Measuring the Inventory-Holding Premium

Abstract

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. After providing a brief review of past work, 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 and the probability of an informed trade are identified. The model is tested empirically on a sample of NASDAQ stocks over three distinct tick size regimes and is shown to perform well.

Keywords: market microstructure, determinants of spread, option value

JEL Classification: G13, G24