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Inventory Management for High-Frequency Trading with Imperfect Competition

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  • Sebastian Herrmann
  • Johannes Muhle-Karbe
  • Dapeng Shang
  • Chen Yang

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.

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  • Sebastian Herrmann & Johannes Muhle-Karbe & Dapeng Shang & Chen Yang, 2018. "Inventory Management for High-Frequency Trading with Imperfect Competition," Papers 1808.05169, arXiv.org, revised Jun 2019.
    • Handle: RePEc:arx:papers:1808.05169
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    References listed on IDEAS

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