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

Paper: arXiv 2408.09505

Authors: Yufan Chen, Lan Wu, Renyuan Xu, Ruixun Zhang

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical formulation combining extended mean-field games with major-minor players to explain high-frequency periodicity in financial markets. It features deep mathematical proofs and open-loop Nash equilibrium derivations, but lacks empirical backtesting on real-world market tick data.

Research Flowchart

  flowchart TD
    A[Research Goal: Explain & Analyze Periodic Trading Activities in Equity Markets] --> B[Model Setup: Major-Minor Game Framework]
    
    subgraph Methodology & Inputs
        B --> C[Inputs: Major Trader Periodic Strategy & Continuum of N Minor Traders]
        C --> D[Solve Open-Loop Nash Equilibrium via Mean-Field Game Theory]
    ]
    
    subgraph Computational Analysis
        D --> E[Prove Existence, Uniqueness & O1/sqrt N Approximation Rate]
    ]
    
    E --> F[Key Outcome 1: Minor Traders Exhibit Front-Running Behavior]
    E --> G[Key Outcome 2: Strategic Interactions Dampen Volume & Price Periodicity]

    style A fill:#f9f,stroke:#333,stroke-width:2px
    style F fill:#bbf,stroke:#333,stroke-width:1px
    style G fill:#bbf,stroke:#333,stroke-width:1px