Fast and slow optimal trading with exogenous information

Journal article

Abstract:: We model the interaction between an investor executing trades at low frequency and a high-frequency trader as a multiperiod stochastic Stackelberg game. The high-frequency trader exploits price information more frequently and is subject to periodic inventory constraints. We are able to explicitly compute the equilibrium strategies, in two steps. We first derive the optimal strategy of the high-frequency trader given any strategy adopted by the investor. Then we solve the problem of the investor given the optimal strategy of the high-frequency trader, in terms of the resolvent of a Fredholm integral equation. Our results show that the high-frequency trader adopts a predatory strategy whenever the value of the trading signal is high, and follows a cooperative strategy otherwise. We also show that there is a net gain in performance for the investor from taking into account the order flow of the high-frequency trader. A U-shaped intraday pattern in trading volume is shown to arise endogenously as a result of the strategic behaviour of the agents.

Files:: Cont_et_al_2025_Fast_and_slow.pdf

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Language:: English
Keywords:: market microstructure

high-frequency trading

optimal stochastic control

stochastic games

price impact

Fredholm integral equations

trading signals

Stackelberg equilibrium
Pubs id:: 2095308
Local pid:: pubs:2095308
Deposit date:: 2025-03-19
ARK identifier:: ark:/29072/ora_265528bfae284fd8afbd9d6d652ec4f2

Copyright holder:: Cont et al.
Rights statement:: Copyright © 2025, The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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