Large Banks and Systemic Risk: Insights from a Mean-Field Game Model

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.