Periodic Trading Activities in Financial Markets: Mean-field Liquidation Game with Major-Minor Players

TL;DR

This paper models periodic trading activities in financial markets using a mean-field game with major and minor traders, revealing how strategic interactions influence market periodicity and trader behaviors.

Contribution

It introduces a novel major-minor mean-field liquidation game that captures periodic trading patterns and analyzes equilibrium properties and strategic behaviors.

Findings

Minor traders exhibit front-running behaviors reducing major trader profits.

Strategic interactions weaken the periodicity in trading volume and asset prices.

The model explains observed periodic trading phenomena in markets.

Abstract

Motivated by recent empirical findings on the periodic phenomenon of aggregated market volumes in equity markets, we aim to understand the causes and consequences of periodic trading activities through a game-theoretic perspective, examining market interactions among different types of participants. Specifically, we introduce a new mean-field liquidation game involving major and minor traders, where the major trader evaluates her strategy against a periodic targeting strategy while a continuum of minor players trade against her. We establish the existence and uniqueness of an open-loop Nash equilibrium. In addition, we prove an O(1/sqrt N) approximation rate of the mean-field solution to the Nash equilibrium in a major-minor game with N minor players. In equilibrium, minor traders exhibit front-running behaviors in both the periodic and trend components of their strategies, reducing the major trader's profit. Such strategic interactions diminish the strength of periodicity in both overall trading volume and asset prices. Our model rationalizes observed periodic trading activities in the market and offers new insights into market dynamics.