Systemic Risk in Financial Networks

We consider default by firms that are part of a single clearing mechanism. The obligations of all firms within the system are determined simultaneously in a fashion consistent with the priority of debt claims and the limited liability of equity. We first show, via a fixed-point argument, that there always exists a clearing payment vector that clears the obligations of the members of the clearing system; under mild regularity conditions, this clearing vector is unique. Next, we develop an algorithm that both clears the financial network in a computationally efficient fashion and provides information on the systemic risk faced by individual system firms. Finally, we produce qualitative comparative statics for financial networks. These comparative statics imply that, in contrast to single-firm results, unsystematic, nondissipative shocks to the system will lower the total value of the network and may lower the value of the equity of some of the individual network firms