Instabilities in Multi-Asset and Multi-Agent Market Impact Games

43 Pages Posted: 4 May 2020 Last revised: 29 Nov 2021

See all articles by Francesco Cordoni

Francesco Cordoni

University of London, Royal Holloway College - Department of Economics

Fabrizio Lillo

Università di Bologna

Date Written: April 7, 2020

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 & Zhang (2019) and Luo & 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 & Zhang
(2019) and Luo & 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

JEL Classification: C70,D53,G11

Suggested Citation

Cordoni, Francesco and Lillo, Fabrizio, Instabilities in Multi-Asset and Multi-Agent Market Impact Games (April 7, 2020). Available at SSRN: https://ssrn.com/abstract=3570691 or http://dx.doi.org/10.2139/ssrn.3570691

Francesco Cordoni (Contact Author)

University of London, Royal Holloway College - Department of Economics ( email )

Royal Holloway College
Egham
Surrey, Surrey TW20 0EX
United Kingdom

Fabrizio Lillo

Università di Bologna ( email )

Via Zamboni, 33
Bologna, 40126
Italy

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