Inventory Management for High-Frequency Trading With Imperfect Competition

25 Pages Posted: 29 Aug 2018 Last revised: 4 Jun 2019

See all articles by Sebastian Herrmann

Sebastian Herrmann

University of Manchester

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics

Dapeng Shang

Boston University - Questrom School of Business

Chen Yang

ETH Zurich - Department of Mathematics

Date Written: June 2, 2019

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

JEL Classification: G14, G11, C61, C68

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

Sebastian Herrmann

University of Manchester ( email )

Oxford Road
Manchester, M13 9PL
United Kingdom

HOME PAGE: http://personalpages.manchester.ac.uk/staff/sebastian.herrmann

Johannes Muhle-Karbe (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Dapeng Shang

Boston University - Questrom School of Business ( email )

595 Commonwealth Ave
Boston, MA 02466
United States

Chen Yang

ETH Zurich - Department of Mathematics ( email )

R¨amistrasse 101
Z¨urich, 8092
Switzerland

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