Hidden Risks in Credit Risk Management

Consider a portfolio of n obligors such as loans, corporate bonds and other instruments subject to possible default. Tang and Yuan (2012, Submitted) introduced a new model for the loss given default and studied its tail behavior, Value at Risk, and Conditional Tail Expectation under the assumption that the losses jointly follow a multivariate regularly varying distribution. However, in the case that the loss variables are asymptotically independent, the asymptotic formulas obtained previously cannot capture the decaying speed of the tail probability of the loss given default and, therefore, fail to serve as asymptotic estimates. I address this issue in this paper under the framework of hidden regular variation and show that in this case there could be significant hidden risks.