Stress Testing with Student's t Dependence

In this study we propose the use of the Student's t dependence function to model dependence between asset returns when conducting stress tests. To properly include stress testing in a risk management system, it is important to have accurate information about the (joint) probabilities of extreme outcomes. Consequently, a model for the behavior of risk factors is necessary, specifying the marginal distributions and their dependence. Traditionally, dependence is described by a correlation matrix, implying the use of the dependence function inherent in the multivariate normal (Gaussian) distribution. Recent studies have cast serious doubt on the appropriateness of the Gaussian dependence function to model dependence between extreme negative returns. The student's t dependence function provides an attractive alternative. In this paper, we introduce four tests to analyze the empirical fit of both dependence functions. The empirical results indicate that probabilities assigned to stress tests are largely influenced by the choice of dependence function. The statistical tests reject the Gaussian dependence function, but do not reject the Student's t dependence function.