Managing Default Contagion in Inhomogeneous Financial Networks

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 between them. Our model captures the strong degree of heterogeneity observed in empirical data and the parameters can easily be fitted to real data sets. One of our main results allows us to determine the impact of local shocks, where initially some banks default, to 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 non-resilient 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 significantly earlier findings derived in the configuration model where the existence of a second moment of the degree distribution is 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 basically only depend on the institution's exposures to its counterparties.

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“…No matter the Eisenberg–Noe model, or the Gai–Kapadia model or the Amini framework, they all belong to static cascade models, which assume the structure and scale of the network itself be static. While networks can evolve due to the interactions of participants’ inter-connections of assets and shocks from the outside, so random graph models are brought in [ 6 , 132 , 140 , 142 , 167 , 168 , 169 ].…”

An integrated model for fire sales and default contagion

“…Another line of research, which started in [23] and continued for example in [16,17,19], uses asymptotic random graph techniques. Similarly to [1,2,9], the objective is to gain understanding of which network structures promote systemic risk and which capital requirements are suitable to prevent large cascades.…”

Bootstrap Percolation in Directed Inhomogeneous Random Graphs

“…the electronic journal of combinatorics 26(3) (2019), #P3.12 the fraction of the absolute relevance lost due to the percolation process. In [16], where a financial network is studied, the number r i comprises several properties that make a financial institution relevant to society, as for example the amount of debt issued to the real economy or its contribution to the infrastructure of the payment system. In Section 7 we demonstrate how our results can be extended to that setting.…”