Systemic risk in financial systems

We consider default by firms that are part of a single clearing mechanism. The obligations of all firms within the system are determined simultaneousl y 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 a lways exists a "clearing payment vector" that clears the obligations of the members of the clearing system; under mild regularity conditions, this cle aring vector is unique. Next, we develop an algorithm that both clears the financial system in a computationally efficient fashion and provides inform ation on the systemic risk faced by the individual system firms. Finally, w e produce qualitative comparative statics for financial systems. These comp arative statics imply that, in contrast to single-firm results, even unsyst ematic, nondissipative shocks to the system will lower the total value of t he system and may lower the value of the equity of some of the individual s ystem firms.