🤖 AI Summary
This paper investigates the systemic role of large banks in interbank markets and its implications for financial stability and risk. We develop the first mean-field game framework in which large banks are modeled as endogenous decision-makers, integrating convex analysis and Monte Carlo simulation to characterize their dynamic interactions with numerous small banks. Theoretically, we show that both the size and trading intensity of large banks exert a non-monotonic effect on systemic risk: moderate scale enhances market stability, yet default by a large bank triggers substantial negative spillovers; risk escalates nonlinearly with increases in either dimension. Our key contribution lies in moving beyond the conventional exogenous treatment of large banks—instead, we endogenize their strategic decisions within a mean-field game setting for the first time. This enables precise identification of the mechanistic boundaries under which large banks act either as stabilizers or as risk amplifiers, thereby providing a rigorous theoretical foundation for macroprudential regulation.
📝 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.
