Network Effects in Default Clustering for Large Systems

Abstract

We consider a large collection of dynamically interacting components defined on a weighted directed graph determining the impact of default of one component to another one. We prove a law of large numbers for the empirical measure capturing the evolution of the different components in the pool and from this we extract important information for quantities such as the loss rate in the overall pool as well as the mean impact on a given component from system wide defaults. A singular value decomposition of the adjacency matrix of the graph allows to coarse-grain the system by focusing on the highest eigenvalues which also correspond to the components with the highest contagion impact on the pool. Numerical simulations demonstrate the theoretical findings.arXiv:1812.07645v2 [q-fin.RM]

Dynamic Default Contagion in Heterogeneous Interbank Systems

“…To illustrate, k = 4 gives a simple way of splitting the system into four subgroups, where, e.g., u i = (0, u i 2 , 0, 0) says that bank i belongs to the second grouping of top-tier banks with the score u i 2 giving its relative importance, while u j = (0, 0, u j 3 , 0) says that bank j belongs to the first grouping of lower-tier banks with relative importance u j 3 , and so on; see Figure 2. In place of (3.4) serving as a model for the network structure, we note that one could also treat it as a form of principle component analysis of the network, similarly to the use of spectral decompositions for core-periphery detection [9] and related financial contagion models [1,26].…”

A Dynamic Default Contagion Model: From Eisenberg-Noe to the Mean Field

“…In relation to financial networks and systemic risk, simple aspects of this has, e.g., been utilised in contagion models , Cont and Schaanning [2019] and statistical methods for detecting core-periphery network structures Cucuringu et al [2016]. More recently, the preprint Spiliopoulos and Yang [2019] studies a reduced form model for default clustering (based on interacting default intensities), using a singular value decomposition of the adjacency matrix in a way that is completely analogous to what we do here; namely to study the large population limit of the system under a bounded rank assumption which allows for a more tractable reformulation of the interactions.…”