Optimal Trade Execution Under Endogenous Order Flow

We consider an optimal liquidation model in which an investor is required to execute meta-orders during intraday trading periods, and his trading activity triggers child orders and endogenously affects future order flow, both instantaneously and permanently. Under the assumptions of risk neutrality and deterministic constants of the impact parameters, we provide closed-form solutions and illustrate the relationship between trading strategies and feedback effects. The optimal trading strategy is of hyperbolic form if the feedback effect of current trading on future order flow is not too strong. If the feedback effect becomes too dominating, a cyclic strategy with possible beneficial round-trips may emerge. Our results extend to risk-averse investors for which semiclosed form solutions involving inverse Laplace transforms are obtained. We set up an estimation framework so that parameter estimates can be made directly from public data and are consistent with the theoretical model. When implementing our model on 110 NASDAQ stocks, the empirical analysis shows that as the level of endogeneity increases, our strategy provides increasingly better performance than the commonly adopted trading strategy. The empirical analysis also shows that too strong feedback effects do not exist in practice, thus ruling out statistical arbitrage.

Funding: The authors thank the Ministry of Education Singapore for research funding [Project A-8000014-00-00]. This research project is supported by the National Research Foundation Singapore under its Industry Alignment Fund–Prepositioning Funding Initiative, and the Monetary Authority of Singapore [Grant A-0003504-17-00]. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not reflect the views of National Research Foundation, Singapore, or of the Monetary Authority of Singapore. U. Horst acknowledges funding from the German Research Foundation through [CRC TRR 190 Grant 280092119].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2023.0151.