Optimal liquidity-based trading tactics

TL;DR

This paper develops an optimal trading strategy using limit orders, market orders, and cancellations in a high-frequency setting, modeled through an order book and utility maximization, outperforming naive methods.

Contribution

It introduces a novel order book model and derives equations for optimal high-frequency trading tactics considering liquidity and price impact.

Findings

Optimal strategy derived and numerically solved.

Significant outperformance over naive execution strategies.

Model effectively captures high-frequency trading dynamics.

Abstract

We consider an agent who needs to buy (or sell) a relatively small amount of asset over some fixed short time interval. We work at the highest frequency meaning that we wish to find the optimal tactic to execute our quantity using limit orders, market orders and cancellations. To solve the agent's control problem, we build an order book model and optimize an expected utility function based on our price impact. We derive the equations satisfied by the optimal strategy and solve them numerically. Moreover, we show that our optimal tactic enables us to outperform significantly naive execution strategies.