Advances in Common Shock Modeling

In this paper we rigorously investigate the common shock, or contagion, model, for correlating insurance losses. In addition, we develop additional theory which describes how the common shock model can be incorporated within a larger set of distributions. We also address the issue of calibrating contagion models to empirical data. To this end, we propose several procedures for calibrating contagion models using real-world industry data. Finally, we demonstrate the efficacy, and efficiency, of these calibration procedures by calibrating aggregate loss models, which incorporate contagion. Further, the case study illustrates the power of contagion modeling by demonstrating how the introduction of contagion can correct for the short-comings of traditional collective risk modeling.