An analysis of simultaneous company defaults using a shot noise process

Abstract

During subprime mortgage crisis, it became apparent that incumbent models had underestimated company default correlations. Complex models that attempt to incorporate default dependency are difficult to implement in practice. On the contrary, practical models, such as One-Factor Gaussian Copula model, greatly underestimated simultaneous default probabilities. In this article, we develop a model for a company asset process and based on this model, we calculate simultaneous default probabilities using option-theoretic approach. Our model focuses on one industry and includes a shot noise process in the asset model directly. The risk factor driving the shot noise process is common to all companies in the industry but the shot noise parameters are assumed to be company-specific; therefore, every company responds to this common risk factor differently. Apart from the shot noise process, the asset model includes company specific Brownian motion. Compared to commonly used geometric Brownian motion asset model in option-theoretic approach, our model predicted higher simultaneous default probabilities for Citigroup Inc. in 2008, and for all company combinations for the years of 2009 and 2010. Our model is easy to implement and can be extended to analyze any finite number of companies without greatly increasing computational difficulty.