Inventory Management for High-Frequency Trading With Imperfect Competition

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: High-Frequency Trading, Information Asymmetry, Inventory Management, Imperfect Competition

JEL Classification: G14, G11, C61, C68

Suggested Citation: Suggested Citation

Herrmann, Sebastian and Muhle-Karbe, Johannes and Shang, Dapeng and Yang, Chen, Inventory Management for High-Frequency Trading With Imperfect Competition (June 2, 2019). Available at SSRN: https://ssrn.com/abstract=3232037 or http://dx.doi.org/10.2139/ssrn.3232037