Contagion in financial networks: A threat index

An intricate web of claims and obligations ties together the balance sheets of a wide variety of financial institutions. Under the occurrence of default, these interbank claims generate externalities across institutions and possibly disseminate defaults and bankruptcy. Building on a simple model for the joint determination of the repayments of interbank claims, this paper introduces a measure of the threat that a bank poses to the system. Such a measure, called threat index, may be helpful to determine how to inject cash into banks so as to increase debt reimbursement, or to assess the contributions of individual institutions to the risk in the system. Although the threat index and the default level of a bank both reflect some form of weakness and are affected by the whole liability network, the two indicators differ. As a result, injecting cash into the banks with the largest default level may not be optimal.