Optimal Execution in a Multiplayer Model of Transient Price Impact

TL;DR

This paper analyzes how order anticipation strategies affect optimal trade execution in a multi-investor setting with transient price impact, providing a Nash equilibrium solution and insights into execution costs and price overshooting.

Contribution

It introduces a model with quadratic transaction costs, proves existence and uniqueness of Nash equilibrium, and derives a closed-form solution for exponential decay kernels.

Findings

Order anticipation strategies increase execution costs significantly.

Typically, order anticipation does not lead to price overshooting.

Provides a closed-form Nash equilibrium for exponential decay kernels.

Abstract

Trading algorithms that execute large orders are susceptible to exploitation by order anticipation strategies. This paper studies the influence of order anticipation strategies in a multi-investor model of optimal execution under transient price impact. Existence and uniqueness of a Nash equilibrium is established under the assumption that trading incurs quadratic transaction costs. A closed-form representation of the Nash equilibrium is derived for exponential decay kernels. With this representation, it is shown that while order anticipation strategies raise the execution costs of a large order significantly, they typically do not cause price overshooting in the sense of Brunnermeier and Pedersen.