Network effects and default clustering for large systems: typical and atypical events
Embargo Date
2023-02-13
OA Version
Citation
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. The empirical measure captures the evolution of different components
in the system and from this we extract important information for quantities such as
the loss rate in the overall pool and the mean impact on a given component from
system wide defaults. We prove a law of large numbers and large deviations on
the empirical measure of the survival distribution in the system. In addition, we
study the typical and atypical behavior of statistics of interest under the combined
effect of default cluster and network structure. 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 system. Numerical simulations demonstrate the theoretical
findings in both the law of large number and in the large deviations principle.