An asymptotic characterization of hidden tail credit risk with actuarial applications

In this paper we study the tail risk of a properly diversified credit portfolio under a latent risk factor model. The usual perception is that if the diversification leads to asymptotic independence among the risk factors, then, because of the relatively low probability of simultaneous defaults, the tail risk of the entire portfolio is negligible. However, we point out that in fact there may be substantial tail risk hidden in this situation. We use a conditional tail probability of the portfolio loss to quantify the hidden tail risk, and then provide an asymptotic characterization for the risk under a hidden regular variation structure assumed for the risk factors. We also propose applications of the characterization to the determination and allocation of related insurance risk capital, based on the Conditional Tail Expectation risk measure. To understand the impact of dependence on the quantities of interest, we study two special cases where the risk factors have a Gaussian copula or an Archimedean copula. Numerical examples are provided to illustrate the results.