Managing Default Contagion in Inhomogeneous Financial Networks

Detering, Nils; Meyer-Brandis, Thilo ; Panagiotou, Konstantinos und Ritter, Daniel (2019): Managing Default Contagion in Inhomogeneous Financial Networks. In: SIAM Journal on Financial Mathematics, Bd. 10, Nr. 2: S. 578-614

Abstract

The aim of this paper is to quantify and manage systemic risk caused by default contagion in the interbank market. We model the market as a random directed network, where the vertices represent financial institutions and the weighted edges monetary exposures. Our model captures the strong degree of heterogeneity observed in empirical data and the parameters can easily be fitted to real data sets. Our first main result allows us to determine the impact of local shocks, where initially some banks default, on the entire system and the wider economy. Here the impact is measured by some index of total systemic importance of all eventually defaulted institutions. As a central application, we characterize resilient and nonresilient cases. In particular, for the prominent case where the network has a degree sequence without second moment, we show that a small number of initially defaulted banks can trigger a substantial default cascade. Our results complement and extend earlier findings derived in the configuration model, where the existence of a second moment of the degree distribution was assumed. As a second main contribution, paralleling regulatory discussions, we determine minimal capital requirements for financial institutions sufficient to make the network resilient to small shocks. An appealing feature of these capital requirements is that they can be determined locally by each institution without knowing the complete network structure, as they depend only on the institution's exposures to its counterparties.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik ; Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1945-497X
• Sprache: Englisch