Theoretical Analysis of Dependence Structures for Credit Risk+ Framework

The Credit Risk+ model is an influential method to evaluate the default risk level of a credit portfolio in the financial and insurance industry. As an essential modelling technique in the Credit Risk+ framework, dependence structure models relationship between default probability and risk factors using a variety of statistical methods. This research paper analyzes the dependence structure related to default correlation and sector dependence among classic and enhanced Credit Risk+ models. At first, the concepts of default event and default probability are discussed within classic models for explaining the connection between default correlation and risk factors. Then, given the limitations of classic models, two enhanced models are presented to incorporate sector dependence generated by additional Gamma-distributed variables. Based on previous literature and probability theory, this paper revisits methods of deriving the correlation coefficient for default dependence and the variance-covariance for sector dependence. The proof results show that default correlation is associated with default probability and sector characteristics. Also, the multi-system model, which develops sector dependence from a set of independent macro-economic variables via linear combination, provides a more flexible variance-covariance structure than the compound Gamma model.