Vulnerability Analysis of the Financial Network

Since the financial crisis in 2007-2008, the vulnerability of a financial system has become a major concern in financial engineering. In this paper, we analyze the vulnerability of a financial network based on the linear optimization model introduced by Eisenberg and Noe (2001), where the right hand side of the constraints is subject to market shock and only partial information regarding the liability matrix is revealed. We conduct a new sensitivity analysis to characterize the conditions under which a single bank is solvent, default or bankrupted, and estimate the probability that some financial institute in the network will be bankrupted under mild assumptions on the market shock and the network structure. We also present some numerical experiments to verify the theoretical conclusions in the paper.