Systemic risk in a network fragility model analyzed with probability density evolution of persistent random walks

TL;DR

This paper analyzes systemic risk in financial networks using a mean field approximation of a cascade model, revealing how network density influences systemic risk and providing a method to compute the stable distribution of network fragility.

Contribution

It introduces a probability density evolution approach to analyze systemic risk, highlighting the non-monotonic relationship between network density and systemic risk in a mean field framework.

Findings

Systemic risk first decreases then increases with network density.

The probability density of network fragility converges to a unique stable distribution.

The model provides a numerical method to estimate systemic risk based on network parameters.

Abstract

We study the mean field approximation of a recent model of cascades on networks relevant to the investigation of systemic risk control in financial networks. In the model, the hypothesis of a trend reinforcement in the stochastic process describing the fragility of the nodes, induces a trade-off in the systemic risk with respect to the density of the network. Increasing the average link density, the network is first less exposed to systemic risk, while above an intermediate value the systemic risk increases. This result offers a simple explanation for the emergence of instabilities in financial systems that get increasingly interwoven. In this paper, we study the dynamics of the probability density function of the average fragility. This converges to a unique stable distribution which can be computed numerically and can be used to estimate the systemic risk as a function of the parameters of the model.