Optimal Trade Execution Strategy and Implementation with Deterministic Market Impact Parameters

In this paper, we present an explicit solution for a continuous optimal trade execution problem, considering deterministic instantaneous, permanent, and temporary market impacts. Using a calculus of variations approach, we solve a system of ordinary differential equations. The unified model draws connections to benchmark optimal trade execution models proposed by Almgren and Chriss (2001. “Optimal execution of portfolio transactions.” Journal of Risk 3:5–40) and Obizhaeva and Wang (2013. “Optimal trading strategy and supply/demand dynamics.” Journal of Financial Markets 16:1–31. https://doi.org/10.1016/j.finmar.2012.09.001), treating them as special cases. We introduce a methodology to estimate parameters for implementing order-splitting strategies, leveraging limit order book data instead of proprietary datasets. We posit that instantaneous impact is shaped by market depth through limit order arrivals and cancellations, whereas permanent and temporary impacts arise from mid-price shifts, driven by the anticipation of forthcoming order flows. To validate the utility of our framework, we calibrate market impacts for 100 NASDAQ stocks and compute order-splitting strategies using real data. Numerical evaluations indicate potential cost savings of up to 8.760% compared to other optimal strategies. This research provides valuable insights into understanding and optimizing liquidation strategies in financial markets, emphasizing the role of market impacts and the importance of limit order book data.