Instabilities in multi-asset and multi-agent market impact games

Francesco Cordoni () and Fabrizio Lillo ()
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Francesco Cordoni: Royal Holloway University of London
Fabrizio Lillo: Scuola Normale Superiore

Annals of Operations Research, 2024, vol. 336, issue 1, No 16, 505-539

Abstract: Abstract We consider the general problem of a set of agents trading a portfolio of assets in the presence of transient price impact and additional quadratic transaction costs and we study, with analytical and numerical methods, the resulting Nash equilibria. Extending significantly the framework of Schied and Zhang (2019) and Luo and Schied (2020), who considered the single asset case, we prove the existence and uniqueness of the corresponding Nash equilibria for the related mean-variance optimization problem. We then focus our attention on the conditions on the model parameters making the trading profile of the agents at equilibrium, and as a consequence the price trajectory, wildly oscillating and the market unstable. While Schied and Zhang (2019) and Luo and Schied (2020) highlighted the importance of the value of transaction cost in determining the transition between a stable and an unstable phase, we show that also the scaling of market impact with the number of agents J and the number of assets M determines the asymptotic stability (in J and M) of markets.

Keywords: Market impact; Game theory and Nash equilibria; Transaction costs; Market microstructure; High frequency trading; Cross-impact (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-022-05066-8

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