The Lehman Brothers Effect and Bankruptcy Cascades

TL;DR

This paper models the Lehman Brothers effect as a phase transition in a network of financial institutions, showing how initial defaults can trigger widespread cascades and how bailouts can mitigate systemic risk.

Contribution

It introduces a stylized model linking credit rating dynamics to phase transitions, providing insights into systemic risk and the limited effectiveness of early bailouts.

Findings

Systemic vulnerability arises from collective credit rating behaviors.

A phase transition explains the system's sensitivity to shocks.

Bailouts reduce the extent of defaults but do not prevent cascades.

Abstract

Inspired by the bankruptcy of Lehman Brothers and its consequences on the global financial system, we develop a simple model in which the Lehman default event is quantified as having an almost immediate effect in worsening the credit worthiness of all financial institutions in the economic network. In our stylized description, all properties of a given firm are captured by its effective credit rating, which follows a simple dynamics of co-evolution with the credit ratings of the other firms in our economic network. The dynamics resembles the evolution of Potts spin-glass with external global field corresponding to a panic effect in the economy. The existence of a global phase transition, between paramagnetic and ferromagnetic phases, explains the large susceptibility of the system to negative shocks. We show that bailing out the first few defaulting firms does not solve the problem, but does have the effect of alleviating considerably the global shock, as measured by the fraction of firms that are not defaulting as a consequence. This beneficial effect is the counterpart of the large vulnerability of the system of coupled firms, which are both the direct consequences of the collective self-organized endogenous behaviors of the credit ratings of the firms in our economic network.