Mean Field Game of High-Frequency Anticipatory Trading

TL;DR

This paper models the strategic interactions between high-frequency traders and a large trader using mean field game theory, revealing how HFTs' behaviors influence market impact and the large trader's optimal execution strategy.

Contribution

It introduces a mean field game framework to analyze anticipatory high-frequency trading with discrete large trader transactions, incorporating HFTs' inventory preferences.

Findings

HFTs' anticipatory trading reduces LT's costs under certain market impact conditions.

Repeated liquidity provision by HFTs leads to more uniform trading strategies for LT.

Market impact dynamics are significantly affected by HFTs' inventory aversion.

Abstract

The interactions between a large population of high-frequency traders (HFTs) and a large trader (LT) who executes a certain amount of assets at discrete time points are studied. HFTs are faster in the sense that they trade continuously and predict the transactions of LT. A jump process is applied to model the transition of HFTs' attitudes towards inventories and the equilibrium is solved through the mean field game approach. When the crowd of HFTs is averse to running (ending) inventories, they first take then supply liquidity at each transaction of LT (throughout the whole execution period). Inventory-averse HFTs lower LT's costs if the market temporary impact is relatively large to the permanent one. What's more, the repeated liquidity consuming-supplying behavior of HFTs makes LT's optimal strategy close to uniform trading.