An analysis of simultaneous company defaults using a shot noise process

Abstract

During the subprime mortgage crisis, it became apparent that practical models, such as the one-factor Gaussian copula, had underestimated company default correlations. Complex models that attempt to incorporate default dependency are difficult to implement in practice. In this study, we develop a model for a company asset process, based on which we calculate simultaneous default probabilities using an option-theoretic approach. In our model, a shot noise process serves as the key element for controlling correlations among companies' assets. The risk factor driving the shot noise process is common to all companies in an industry but the shot noise parameters are assumed company-specific; therefore, every company responds differently to this common risk factor. Our model gives earlier warning of financial distress and predicts higher simultaneous default probabilities than commonly used geometric Brownian motion asset model. It is also computationally simple and can be extended to analyze any finite number of companies. $