Systemic Cascades On Inhomogeneous Random Financial Networks

TL;DR

This paper develops a mathematical framework for modeling systemic risk in heterogeneous financial networks, analyzing how shocks propagate and lead to cascades, with fixed point equations describing equilibrium states as the network size grows.

Contribution

It introduces a generalized inhomogeneous random network model with a new LTI property for Eisenberg-Noe cascades, providing explicit fixed point equations for large systems.

Findings

Derived fixed point equations for infinite network size

Proved LTI property for Eisenberg-Noe cascades

Framework applicable to diverse financial network structures

Abstract

This systemic risk paper introduces inhomogeneous random financial networks (IRFNs). Such models are intended to describe parts, or the entirety, of a highly heterogeneous network of banks and their interconnections, in the global financial system. Both the balance sheets and the stylized crisis behaviour of banks are ingredients of the network model. A systemic crisis is pictured as triggered by a shock to banks' balance sheets, which then leads to the propagation of damaging shocks and the potential for amplification of the crisis, ending with the system in a cascade equilibrium. Under some conditions the model has ``locally tree-like independence (LTI)'', where a general percolation theoretic argument leads to an analytic fixed point equation describing the cascade equilibrium when the number of banks $N$ in the system is taken to infinity. This paper focusses on mathematical properties of the framework in the context of Eisenberg-Noe solvency cascades generalized to account for fractional bankruptcy charges. New results including a definition and proof of the ``LTI property'' of the Eisenberg-Noe solvency cascade mechanism lead to explicit $N=\infty$ fixed point equations that arise under very general model specifications. The essential formulas are shown to be implementable via well-defined approximation schemes, but numerical exploration of some of the wide range of potential applications of the method is left for future work.