Instabilities in Multi-Asset and Multi-Agent Market Impact Games
43 Pages Posted: 4 May 2020 Last revised: 29 Nov 2021
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: Suggested Citation