TY - JOUR
T1 - Inventory Management for High-Frequency Trading with Imperfect Competition
AU - Herrmann, Sebastian
AU - Muhle-Karbe, Johannes
AU - Shang, Dapeng
AU - Yang, Chen
N1 - Funding Information:
∗Received by the editors August 16, 2018; accepted for publication (in revised form) October 25, 2019; published electronically January 8, 2020. Parts of this paper were written while this author was visiting the Forschungsinstitut für Mathematik at ETH Zürich. https://doi.org/10.1137/18M1207776 Funding: The second author’s research was partially supported by the CFM-Imperial Institute for Quantitative Finance. The fourth author was partly supported by Swiss National Foundation grant SNF 200020 172815. †Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK (sebastian.herrmann@ manchester.ac.uk). ‡Department of Mathematics, Imperial College London, London, SW7 1NE, UK ([email protected]). §Questrom School of Business, Boston University, Boston, MA 02215 ([email protected]). ¶Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Hong Kong ([email protected]).
Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/1/15
Y1 - 2020/1/15
N2 - 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 are obtained around the high-frequency 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 cooperative HFTs, Nash competition leads to excess trading, so that marginal transaction taxes in fact decrease market liquidity.
AB - 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 are obtained around the high-frequency 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 cooperative HFTs, Nash competition leads to excess trading, so that marginal transaction taxes in fact decrease market liquidity.
KW - high-frequency trading
KW - information asymmetry
KW - inventory management
KW - imperfect competition
UR - https://www.scopus.com/pages/publications/85083261396
U2 - 10.1137/18M1207776
DO - 10.1137/18M1207776
M3 - Article
VL - 11
SP - 1
EP - 26
JO - SIAM Journal on Financial Mathematics
JF - SIAM Journal on Financial Mathematics
IS - 1
ER -