Optimal Execution with Dynamic Order Flow Imbalance

TL;DR

This paper develops a continuous-time stochastic control model for optimal trade execution that incorporates both market impact and informational costs related to order flow imbalance, allowing for dynamic adjustment of trading horizon.

Contribution

It introduces a novel model integrating order flow imbalance into optimal execution, with tractable approximations and a dynamic receding horizon approach linked to existing frameworks.

Findings

Receding horizon control approximations are highly accurate.

Model captures the influence of order flow on execution strategies.

Links to Almgren-Chriss framework and empirical order flow features.

Abstract

We examine optimal execution models that take into account both market microstructure impact and informational costs. Informational footprint is related to order flow and is represented by the trader's influence on the flow imbalance process, while microstructure influence is captured by instantaneous price impact. We propose a continuous-time stochastic control problem that balances between these two costs. Incorporating order flow imbalance leads to the consideration of the current market state and specifically whether one's orders lean with or against the prevailing order flow, key components often ignored by execution models in the literature. In particular, to react to changing order flow, we endogenize the trading horizon $T$. After developing the general indefinite-horizon formulation, we investigate several tractable approximations that sequentially optimize over price impact and over $T$. These approximations, especially a dynamic version based on receding horizon control, are shown to be very accurate and connect to the prevailing Almgren-Chriss framework. We also discuss features of empirical order flow and links between our model and "Optimal Execution Horizon" by Easley et al (Mathematical Finance, 2013).