Fast and Slow Optimal Trading with Exogenous Information

TL;DR

This paper models a strategic interaction between a high-frequency trader and an institutional investor, deriving explicit optimal strategies and equilibrium solutions in a stochastic game with information asymmetry and inventory constraints.

Contribution

It introduces a novel coupled stochastic control framework to explicitly solve for the multi-period Stackelberg equilibrium in a trading game with exogenous information.

Findings

High-frequency trader can adopt predatory or cooperative strategies.

Institutional investor's strategy becomes more profitable considering high-frequency trader's order-flow.

Explicit equilibrium solutions are derived using Fredholm integral equations.

Abstract

We consider a stochastic game between a slow institutional investor and a high-frequency trader who are trading a risky asset and their aggregated order-flow impacts the asset price. We model this system by means of two coupled stochastic control problems, in which the high-frequency trader exploits the available information on a price predicting signal more frequently, but is also subject to periodic "end of day" inventory constraints. We first derive the optimal strategy of the high-frequency trader given any admissible strategy of the institutional investor. Then, we solve the problem of the institutional investor given the optimal signal-adaptive strategy of the high-frequency trader, in terms of the resolvent of a Fredholm integral equation, thus establishing the unique multi-period Stackelberg equilibrium of the game. Our results provide an explicit solution to the game, which shows that the high-frequency trader can adopt either predatory or cooperative strategies in each period, depending on the tradeoff between the order-flow and the trading signal. We also show that the institutional investor's strategy is considerably more profitable when the order-flow of the high-frequency trader is taken into account in her trading strategy.