Mathematical Modeling of Systemic Risk

Abstract

Since the onset of the financial crisis in 2007, more than 370 of the almost 8000 US banks insured by the Federal Deposit Insurance Corporation have failed. By comparison, between 2000 and 2004 there were around 30 failures and no failures occurred between 2005 and the beginning of 2007.

We focus on the mathematical modeling of such episodes of default contagion, by which an economic shock causing initial losses and defaults of a few institutions is amplified due to complex financial linkages, leading to large scale defaults.

We introduce a detailed model of balance sheets, that allows for joint modeling of insolvency and illiquidity cascades on the financial network. We present asymptotic results on the size of a default cascade. These results can be applied to several channels of distress propagation.

Keywords: Systemic risk, Financial networks

JEL Classification: G21, G28