Stability in a Model of Interbank Lending

We propose a simple model of the banking system and analyze stochastic stability of inter-bank lending. The monetary reserves of banks are modeled as a system of interacting Feller diffusions. The model is simple enough for mathematical analysis, yet captures how lending preferences of banks affect possible multiple bank failures. In our model we quantify the lending preference from one bank to another as a function of all the reserves and find an extreme example that only k out of n banks can survive after the multiple bank failures. This banking system induces a class of random graph processes in continuous time exhibiting some stability property. Our analysis reveals quantities which can be used as indicators by regulators to assess the systemic risk.