Paper: arXiv 2305.17830

Authors: Yuanyuan Chang, Dena Firoozi, David Benatia

Abstract

This paper presents a dynamic game framework to analyze the role of large banks in interbank markets. By extending existing models, we incorporate a large bank as a dynamic decision-maker interacting with multiple small banks. Using the mean-field game methodology and convex analysis, best-response trading strategies are derived, leading to an approximate equilibrium for the interbank market. We investigate the influence of the large bank on the market stability by examining individual default probabilities and systemic risk, through the use of Monte Carlo simulations. Our findings reveal that, when the size of the major bank is not excessively large, it can positively contribute to market stability. However, there is also the potential for negative spillover effects in the event of default, leading to an increase in systemic risk. The magnitude of this impact is further influenced by the size and trading rate of the major bank. Overall, this study provides valuable insights into the management of systemic risk in interbank markets.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper relies heavily on advanced mathematical modeling, utilizing mean-field games and convex analysis to model major-minor bank interactions. However, its empirical rigor is limited as the findings are validated through synthetic Monte Carlo simulations rather than real-world historical interbank market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze Large Bank Impact on Interbank Market & Systemic Risk] --> B[Model Formulation: Mean-Field Game Framework]
    B --> C[Inputs: Major Bank Size, Trading Rates, & Interbank Liquidity Parameters]
    C --> D[Analytical Derivation: Convex Analysis for Best-Response Trading Strategies]
    D --> E[Computational Process: Monte Carlo Simulations of Default Probabilities]
    E --> F[Key Findings: Moderate Major Banks Enhance Stability; Excess Size/Default Triggers Systemic Risk]