A default system with overspilling contagion

TL;DR

This paper introduces an extended default contagion model that incorporates the impact of default events on the environment, allowing for both direct and spillover contagion effects to better capture systemic risk.

Contribution

It extends classical Markovian contagion models by enabling the default system to influence its environment, capturing indirect contagion effects and interactions with the broader economy.

Findings

Model captures both direct and spillover contagion effects.

Framework allows for analysis of systemic risk impacts.

Extends classical models to include environment influence.

Abstract

In classical contagion models, default systems are Markovian conditionally on the observation of their stochastic environment, with interacting intensities. This necessitates that the environment evolves autonomously and is not influenced by the history of the default events. We extend the classical literature and allow a default system to have a contagious impact on its environment. In our framework, contagion can either be contained within the default system (i.e., direct contagion from a counterparty to another) or spill from the default system over its environment (indirect contagion). This type of model is of interest whenever one wants to capture within a model possible impacts of the defaults of a class of debtors on the more global economy and vice versa.