Mean Field Equilibrium for a Model of Interbank Lending

We study the formation of short-term interest rates in the interbank lending market where banks are modeled as agents with bounded rationality. We propose a novel model which is based on bilateral contracts between risk-neutral profit-maximizing agents. To render the model tractable for large financial networks, we assume that banks' beliefs about the borrowing alternatives in the market are governed by a common reference interest rate, which is a function of the rates offered in the bilateral contracts. We show how this reference rate can be determined endogenously from a suitable mean field equilibrium and provide sufficient conditions for the existence of such an equilibrium together with an algorithm to compute it. Using simulation, we study the dependence of the equilibrium on the model parameters.