Fair immunization and network topology of complex financial ecosystems

The aftermath of the recent financial crisis has shown how expensive and unfair the stabilization of financial ecosystems can be. The main cause is the level of complexity of financial interactions that poses a problem for regulators. We provide an analytical framework that decomposes complex ecosystems in both their overall level of instability and the contribution of institutions to instability. These ingredients are then used to study the pathways of the ecosystems towards stability by means of immunization schemes. The latter can be designed to penalize institutions proportionally to their contribution to instability, and therefore enhance fairness. We show that fair immunization schemes can also be cost-efficient when employed on ecosystems characterized by a tiered network structure of interactions concentrated among few core nodes that at the same time form many closed cycles that exacerbate instability. For less tiered network topologies we observe a trade-off between fairness and dollar-cost of immunization, allowing regulators to choose the combination that best meets their objectives. The implementation of immunization schemes on real cross-border financial networks of the Bank of International Settlement (BIS) reporting country banking systems is also provided.