Inventory Management for High-Frequency Trading with Imperfect Competition

TL;DR

This paper analyzes the strategic behavior of high-frequency traders with inventory aversion in discrete trading settings, revealing how competition influences trading volume, price impact, and market liquidity.

Contribution

It provides a novel equilibrium analysis of inventory-averse HFTs in discrete trading, deriving explicit solutions and contrasting competitive and cooperative scenarios.

Findings

Optimal inventories are mean-reverting and diminish with more trading rounds.

Risk-adjusted profits and price impact converge to risk-neutral levels.

Nash competition causes excess trading, reducing market liquidity.

Abstract

We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit information about future price changes. For discrete trading rounds, the HFTs' optimal trading strategies and their equilibrium price impact are described by a system of nonlinear equations; explicit solutions obtain around the continuous-time limit. Unlike in the risk-neutral case, the optimal inventories become mean-reverting and vanish as the number of trading rounds becomes large. In contrast, the HFTs' risk-adjusted profits and the equilibrium price impact converge to their risk-neutral counterparts. Compared to a social-planner solution for cooperative HFTs, Nash competition leads to excess trading, so that marginal transaction taxes in fact decrease market liquidity.