Stackelberg Trading Strategies for Fast and Slow Investors

Summary

This paper models interaction between a slow institutional investor and a high-frequency trader whose combined orders affect an asset’s price. The faster trader observes a price-predicting signal more often but faces periodic end-of-day inventory constraints. Their decisions are represented as coupled stochastic control problems, with the high-frequency trader’s strategy optimized first and the institution’s strategy solved in response.

The authors characterize a multi-period Stackelberg equilibrium through the solution of a Fredholm integral equation. In the resulting model, the high-frequency trader may act predatively or cooperatively in a given period, depending on the balance between order-flow effects and the predictive signal. The analysis also finds that the institution earns more when its strategy accounts for the high-frequency trader’s order flow. These are theoretical results from the specified game; the document gives no empirical test, calibration, or evidence that the strategies retain their properties in live markets.

Key ideas

• The model treats a slow institution and a high-frequency trader as strategic players whose orders influence price.
• The faster trader uses a predictive signal more frequently and must satisfy periodic inventory constraints.
• The institution’s optimal strategy accounts for the faster trader’s signal-adaptive order flow.
• The equilibrium solution allows predatory or cooperative behavior depending on signal and order-flow effects.
• The profitability result is theoretical and depends on the assumptions of the model.

Tags

# Fast and Slow Optimal Trading with Exogenous Information


# Fast and Slow Optimal Trading with Exogenous Information









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.