Publication

Systemic Risk in Networks with a Central Node

Abstract

We examine the effects on a financial network of clearing all contracts though a central node (CN), thereby transforming the original network into a star-shaped one. The CN is capitalized with external equity and a guaranty fund. We introduce a structural systemic risk measure that captures the shortfall of end users. We show that it is possible to simultaneously improve the expected surplus of the banks and the CN as well as decrease the shortfall of end users. We determine the CN's equity and guaranty fund policies as a Nash bargaining solution. We illustrate our findings on simulated credit default swap networks compatible with aggregate market data.

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Related concepts (16)
Centrality
In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, super-spreaders of disease, and brain networks. Centrality concepts were first developed in social network analysis, and many of the terms used to measure centrality reflect their sociological origin.
Private equity
In the field of finance, private equity (PE) is an investment fund, usually a limited partnership, which invests in and restructures private companies. A private-equity fund is both a type of ownership of assets (financial equity) and is a class of assets (debt securities and equity securities), which function as modes of financial management for operating private companies that are not publicly traded in a stock exchange.
Katz centrality
In graph theory, the Katz centrality or alpha centrality of a node is a measure of centrality in a network. It was introduced by Leo Katz in 1953 and is used to measure the relative degree of influence of an actor (or node) within a social network. Unlike typical centrality measures which consider only the shortest path (the geodesic) between a pair of actors, Katz centrality measures influence by taking into account the total number of walks between a pair of actors. It is similar to Google's PageRank and to the eigenvector centrality.
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