Fast and slow optimal trading with exogenous information

• Published in: Finance and stochastics Vol. 29; no. 2; pp. 553 - 607
• Main Authors: Cont, Rama, Micheli, Alessandro, Neuman, Eyal
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2025; Springer Nature B.V
• Subjects: Competition; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Electronic trading systems; Equilibrium; Finance; Fredholm equations; Games; High frequency trading; Institutional investments; Insurance; Integral equations; Inventory; Investors; Management; Mathematics; Mathematics and Statistics; Probability Theory and Stochastic Processes; Quantitative Finance; Statistics for Business; Strategy; Trading; High-frequency trading; Trading signals; 60H30; C02; G11; Price impact; Market microstructure; Stochastic games; 91A65; 93E20; 45B05; Stackelberg equilibrium; 49N70; Optimal stochastic control; 49N90; Fredholm integral equations; C73; C61
• ISSN: 0949-2984; 1432-1122
• DOI: 10.1007/s00780-025-00560-w

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.