A Market Impact Game Under Transient Price Impact

Alexander Schied () and Tao Zhang ()
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Alexander Schied: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1 Canada; and Department of Mathematics, University of Mannheim, 68131 Mannheim, Germany
Tao Zhang: Department of Mathematics, University of Mannheim, 68131 Mannheim, Germany

Mathematics of Operations Research, 2019, vol. 44, issue 1, 102-121

Abstract: We consider a Nash equilibrium between two high-frequency traders (HFTs) in a simple market impact model with transient price impact and additional quadratic transaction costs. We prove existence and uniqueness of the Nash equilibrium and show that, for small transaction costs, the HFTs engage in a “hot potato game,” in which the same asset position is sold back and forth. We then identify a critical value for the size of the transaction costs above, for which all oscillations disappear and strategies become buy only or sell only. Numerical simulations show that, for both traders, the expected costs can be lower with transaction costs than without. Moreover, the costs can increase with the trading frequency if there are no transaction costs but decrease with the trading frequency if transaction costs are sufficiently high. We argue that these effects occur due to the need for protection against predatory trading in the regime of low transaction costs.

Keywords: market impact game; high-frequency trading; Nash equilibrium; transient price impact; market impact; predatory trading; M -matrix; inverse-positive matrix; Kaluza sign criterion (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (19)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:44:y:2019:i:1:p:102-121

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