Systemic risk in networks with a central node

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