Systemic Risk: the Effect of Market Confidence

Abstract

In a crisis, when faced with insolvency, banks can sell stock in a dilutive offering in the
stock market and borrow money in order to raise funds. We propose a simple model to find the
maximum amount of new funds the banks can raise in these ways. To do this, we incorporate
market confidence of the bank together with market confidence of all the other banks in the
system into the overnight borrowing rate. Additionally, for a given cash shortfall, we find the
optimal mix of borrowing and stock selling strategy. We show the existence and uniqueness of
Nash equilibrium point for all these problems. Finally, using this model we investigate if banks
have become safer since the crisis. We calibrate this model with market data and conduct an
empirical study to assess safety of the financial system before, during after the last financial
crisis.

Keywords: Systemic risk, market confidence, overnight interest rate, Nash equilibrium

JEL Classification: G32