We extend analytic large network results on default contagion in random graphs to capture a pronounced Block Model structure. This includes as a special case the Core-Periphery network structure , which plays a prominent role in recent research on systemic risk. Further, in the existing literature on systemic risk using random graph methods the problematic assumption that the distribution of liabilities solely depends on the creditor type seems to persist. Under this assumption a straightforward application of the law of large numbers allows to turn edge related random elements into deterministic vertex properties. Here we study a general setting in which the liabilities may depend on both the creditor and the debtor where this argument breaks down and a direct asymptotic analysis of the edge weighted random graph becomes necessary. Among several other applications our results allow us to obtain resilience conditions for the entire network (for example the global financial network ) based only on subnetwork conditions. Contrasting earlier research we also give an example that demonstrates how reshuffling edge weights to form blocks can in fact impact resilience even for otherwise very homogeneous networks .
One of the most defining features of modern financial networks is their inherent complex and intertwined structure. In particular the often observed core-periphery structure plays a prominent role . Here we study and quantify the impact that the complexity of networks has on contagion effects and system stability, and our focus is on the channel of default contagion that describes the spread of initial distress via direct balance sheet exposures. We present a general approach describing the financial network by a random graph, where we distinguish vertices (institutions) of different types - for example core/periphery - and let edge probabilities and weights (exposures) depend on the types of both the receiving and the sending vertex. Our main result allows to compute explicitly the systemic damage caused by some initial local shock event, and we derive a complete characterization of resilient respectively non-resilient financial systems. Due to the random graphs approach these results bear a considerable robustness to local uncertainties and small changes of the network structure over time. In particular, it is possible to condense the precise micro-structure of the network to macroscopic statistics. Applications of our theory demonstrate that indeed the features captured by our model can have significant impact on system stability; we derive resilience conditions for the global network based on subnetwork conditions only .
R
We extend analytic large network results on default contagion in random graphs to capture a pronounced Block Model structure. This includes as a special case the Core-Periphery network structure , which
One of the most defining features of modern financial networks is their inherent complex and intertwined structure. In particular the often observed core-periphery structure
R
in recent research on systemic risk. Further, in the existing literature on systemic risk using random graph methods the problematic assumption that the distribution of liabilities solely depends on the creditor type seems to persist. Under this assumption a straightforward application of the law of large numbers allows to turn edge related random elements into deterministic vertex properties. Here we study a general setting in which the liabilities may depend on both the creditor and the debtor where this argument breaks down and a direct asymptotic analysis of the edge weighted random graph becomes necessary. Among several other applications our results allow us to obtain resilience conditions for the entire network (for example the global financial network ) based only on subnetwork conditions. Contrasting earlier research we also give an example that demonstrates how reshuffling edge weights to form blocks can in fact impact resilience even for otherwise very homogeneous networks
. Here we study and quantify the impact that the complexity of networks has on contagion effects and system stability, and our focus is on the channel of default contagion that describes the spread of initial distress via direct balance sheet exposures. We present a general approach describing the financial network by a random graph, where we distinguish vertices (institutions) of different types - for example core/periphery - and let edge probabilities and weights (exposures) depend on the types of both the receiving and the sending vertex. Our main result allows to compute explicitly the systemic damage caused by some initial local shock event, and we derive a complete characterization of resilient respectively non-resilient financial systems. Due to the random graphs approach these results bear a considerable robustness to local uncertainties and small changes of the network structure over time. In particular, it is possible to condense the precise micro-structure of the network to macroscopic statistics. Applications of our theory demonstrate that indeed the features captured by our model can have significant impact on system stability; we derive resilience conditions for the global network based on subnetwork conditions only