Stability of Financial Networks

The central focus of this paper is on understanding theoretically the effect of risk segregation in the financial network on the default contagion process. We extended the previous model introducing banks' heterogeneity in terms of their risk types and allowing for risk segregation in the financial network. First, with an updated model we derived the condition for the global default contagion to occur conditional on the risk segregation parameters and theoretically verified the existence of contagion connectivity window such that the default contagion is possible only if the average connectivity of the network is within this window. Secondly, it was shown that potential effect of the level of risk segregation in the financial network on the contagion process is not trivial. It is dependent on the level of resistance of each type of banks to the asset deterioration shocks and their standalone ability of contagion transmitting. For instance, we deduced that greater probability of Risky banks borrowing from Risky banks as well can facilitate the default contagion when Stable banks are resistant enough. At the same time higher probability of Risky banks borrowing from Stable ones can also enhance the default contagion process provided that Stable banks are not so resilient to shocks and are not significantly safer than Risky ones since it increases the probability that a contagion process started from nodes of one type will be transmitted to the other type which does not stop the cascades and hence increases the final extent of default contagion. Thirdly, we have derived the self-consistency equations for the probability of default contagion conditional on the default of one random bank in the financial network and the scale of default contagion given that the global contagion takes place and verified the "robust-yet-fragile" property of highly connected financial networks. We show that these important metrics are dependent on segregation levels.