Collective firm bankruptcies and phase transition in rating dynamics

TL;DR

This paper introduces a model of firm rating evolution incorporating individual dynamics and inter-firm interactions, revealing a phase transition between independent bankruptcies and collective defaults influenced by interaction strength.

Contribution

The study demonstrates how phase transitions in firm ratings depend on interaction strength, highlighting systemic risk implications of collective defaults.

Findings

Phase transition between independent and collective defaults.

Existence of an optimal interaction strength for systemic risk.

Large interaction parameters lead to giant default clusters.

Abstract

We present a simple model of firm rating evolution. We consider two sources of defaults: individual dynamics of economic development and Potts-like interactions between firms. We show that such a defined model leads to phase transition, which results in collective defaults. The existence of the collective phase depends on the mean interaction strength. For small interaction strength parameters, there are many independent bankruptcies of individual companies. For large parameters, there are giant collective defaults of firm clusters. In the case when the individual firm dynamics favors dumping of rating changes, there is an optimal strength of the firm's interactions from the systemic risk point of view.