Systemic Risk in Financial Systems

Abstract

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 system in a computationally efficient fashion and provides information on the systemic risk faced by the individual system firms. Finally, we produce qualitative comparative statics for financial systems. These comparative statics imply that, in contrast to single-firm results, even unsystematic, nondissipative shocks to the system will lower the total value of the system and may lower the value of the equity of some of the individual system firms.Credit Risk, Default, Clearing Systems

Decentralized Clearing in Financial Networks

“…An important application concerns financial networks, where Eisenberg and Noe (2001) is the seminal paper. Recent crisis on financial markets triggered by the Lehman bankruptcy as well as sovereign debt problems of European countries provide prime examples of why the network perspective is important.…”

“…There is also a substantial literature that relates the number and magnitude of defaults to the network topology and that characterizes those structures that tend to propagate default, see Gai and Kapadia (2010), Elliott et al (2014), Acemoglu et al (2015), Capponi et al (2015), and Glasserman and Young (2015). The basic setup of Eisenberg and Noe (2001) has also been extended in various directions, for instance in Cifuentes et al (2005) and Shin (2008) by allowing for liquidity considerations or in Rogers and Veraart (2013) by allowing for costs of default.…”

“…Following the seminal paper by Eisenberg and Noe (2001), the literature on systemic risk in financial networks has adopted proportional rules specifying payment ratios less than one in case of default. In reality, not all the liabilities are of the same seniority and some of the liabilities are more senior than others.…”

“…Priority of creditors requires that if an agent is not paying all of its liabilities, then a higher payment should lead to a negative equity level. Contrary to the divisible case, where Eisenberg and Noe (2001) formulate the property of absolute priority, our notion of priority of creditors sometimes allows an agent to have positive equity even if some outstanding liabilities remain.…”

“…Examples of such algorithms are presented in Eisenberg and Noe (2001), Rogers and Veraart (2013), and Elliott et al (2014). These algorithms correspond to centralized procedures for finding a clearing payment matrix.…”