Optimal Execution with Dynamic Order Flow Imbalance and Trading Horizons

Summary

This paper develops an optimal execution model that accounts for both instantaneous price impact and informational costs linked to a trader’s influence on order flow imbalance. The imbalance represents the prevailing direction of market flow, so the model considers whether a trader’s orders align with or oppose current conditions. It frames execution as a continuous-time stochastic control problem balancing these costs and allows the trading horizon to adjust dynamically as order flow changes.

The authors first present an indefinite-horizon formulation, then study tractable approximations that optimize price impact and execution horizon in sequence. They report that the approximations, particularly a receding-horizon version, are very accurate and relate to the Almgren–Chriss framework. The discussion also covers empirical features of order flow and connections to prior work on execution horizons. The supplied description gives no datasets, error measures, or specific market conditions, so the stated accuracy cannot be assessed beyond the authors’ characterization.

Key ideas

• The execution objective balances instantaneous price impact against informational costs tied to order flow imbalance.
• The model accounts for whether a trader’s orders lean with or against prevailing order flow.
• The trading horizon is allowed to change in response to market conditions.
• Tractable approximations optimize price impact and horizon sequentially, including a receding-horizon approach.
• The authors connect the model to Almgren–Chriss and discuss empirical order-flow features, but provide no quantitative evidence in the supplied description.

Tags

# Optimal Execution with Dynamic Order Flow Imbalance


# Optimal Execution with Dynamic Order Flow Imbalance









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).

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