Incorporating Confidence into Systemic Risk

In a crisis when faced with insolvency, banks can issue shares/sell their treasury stock 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 bank can raise in this way. To do this we incorporate market confidence of the bank together with market confidence of all the other banks into the overnight borrowing rate. Additionally, for a given shortfall, we find the optimal mix of borrowing and stock selling. We show that the existence and uniqueness of Nash equilibrium strategy for all these problems. We then calibrate this model to market data and conduct an empirical study to access whether the current financial system is safer than it was before the last financial crisis.

In a related model of financial contagion in a network subject to fire sales and price impacts, we allow for firms to borrow to cover their shortfall as well. We consider both uncollateralized and collateralized loans. The main results of this work are providing sufficient conditions for existence and uniqueness of the clearing solutions (i.e., payments, liquidations, and borrowing); in such a setting any clearing solution is the Nash equilibrium of an aggregation game.