Inventory Management for High-Frequency Trading with Imperfect Competition
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.
Keywords
Cite
@article{arxiv.1808.05169,
title = {Inventory Management for High-Frequency Trading with Imperfect Competition},
author = {Sebastian Herrmann and Johannes Muhle-Karbe and Dapeng Shang and Chen Yang},
journal= {arXiv preprint arXiv:1808.05169},
year = {2019}
}
Comments
25 pages, 5 figures