A Price-Differentiation Model of the Interbank Market and Its Application to a Financial Crisis

Rate curves for overnight loans between bank pairs, as functions of loan values, can be used to infer valuation of reserves by banks. The inferred valuation can be used to interpret shifts in rate curves between bank pairs, for example, in response to a financial crisis. This paper proposes a model of lending by a small bank to a large monopolistic bank to generate a tractable rate curve. An explicit calibration procedure for model parameters is developed and applied to a dataset from Mexico around the 2008 financial crisis. During the crisis, relatively small banks were lending to large banks at lower rates than usual, and the calibration suggests that a broad decline in valuation of reserves is responsible for this outcome, rather than a general increase in the supply of lending or compositional effects.