Optimal execution in a limit order book and an associated microstructure market impact model∗

We model an electronic limit order book as a multi-class queueing system under fluid dynamics, and formulate and solve a problem of limit and market order placement to optimally buy a block of shares over a short, predetermined time horizon. Using the structure of the optimal execution policy, we identify microstructure variables that affect trading costs over short time horizons and propose a resulting microstructure-based model of market impact costs. We use a proprietary data set to estimate this cost model, and highlight its insightful structure and increased accuracy over conventional (macroscopic) market impact models that estimate the cost of a trade based on its normalized size but disregarding measurements of limit order book variables.