Controlling systemic risk: Network structures that minimize it and node properties to calculate it.

Evaluation of systemic risk in networks of financial institutions in general requires information of interinstitution financial exposures. In the framework of the DebtRank algorithm, we introduce an approximate method of systemic risk evaluation which requires only node properties, such as total assets and liabilities, as inputs. We demonstrate that this approximation captures a large portion of systemic risk measured by DebtRank. Furthermore, using Monte Carlo simulations, we investigate network structures that can amplify systemic risk. Indeed, while no topology in general sense is a priori more stable if the market is liquid (i.e., the price of transaction creation is small) [T. Roukny et al., Sci. Rep. 3, 2759 (2013)10.1038/srep02759], a larger complexity is detrimental for the overall stability [M. Bardoscia et al., Nat. Commun. 8, 14416 (2017)10.1038/ncomms14416]. Here we find that the measure of scalar assortativity correlates well with level of systemic risk. In particular, network structures with high systemic risk are scalar assortative, meaning that risky banks are mostly exposed to other risky banks. Network structures with low systemic risk are scalar disassortative, with interactions of risky banks with stable banks.