An extension of Davis and Lo's contagion model

TL;DR

This paper develops a multi-period contagion model for credit risk, extending Davis and Lo's infectious default framework, incorporating dependencies, multiple contaminations, and providing computational algorithms and empirical calibration results.

Contribution

It introduces a multi-period contagion model with dependency structures and multiple contaminations, along with algorithms for distribution computation and empirical calibration.

Findings

The model captures the impact of contagion and dependencies on default probabilities.

Calibration shows the model's effectiveness during financial crises.

Dynamic features improve model performance during distressed periods.

Abstract

The present paper provides a multi-period contagion model in the credit risk field. Our model is an extension of Davis and Lo's infectious default model. We consider an economy of n firms which may default directly or may be infected by other defaulting firms (a domino effect being also possible). The spontaneous default without external influence and the infections are described by not necessarily independent Bernoulli-type random variables. Moreover, several contaminations could be required to infect another firm. In this paper we compute the probability distribution function of the total number of defaults in a dependency context. We also give a simple recursive algorithm to compute this distribution in an exchangeability context. Numerical applications illustrate the impact of exchangeability among direct defaults and among contaminations, on different indicators calculated from the law of the total number of defaults. We then examine the calibration of the model on iTraxx data before and during the crisis. The dynamic feature together with the contagion effect seem to have a significant impact on the model performance, especially during the recent distressed period.