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

37 Pages Posted: 4 May 2020 Last revised: 22 Dec 2020

See all articles by Francesco Cordoni

Francesco Cordoni

University of Pisa - Department of Economics and Management

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 and Zhang (2018) and Luo and Schied (2020), who considered the one
asset case, we focus our attention on the conditions on the value of transaction cost making
the trading profile of the agents, and as a consequence the price trajectory, wildly oscillating
and the market unstable. We prove the existence and uniqueness of the corresponding Nash
equilibria for the related mean-variance optimization problem. We find that the presence
of more assets and a large number of agents make the market more prone to large oscillations and instability. When the number of assets is fixed, a more complex structure of the
cross-impact matrix, i.e. the existence of multiple factors for liquidity, makes the market
less stable compared to the case when a single liquidity factor exists.

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 Pisa - Department of Economics and Management ( email )

Italy

Fabrizio Lillo

Università di Bologna ( email )

Via Zamboni, 33
Bologna, 40126
Italy

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