Stress testing and systemic risk measures using multivariate conditional probability

The multivariate conditional probability distribution models the effects of a set of variables onto the statistical properties of another set of variables. In the study of systemic risk in a financial system, the multivariate conditional probability distribution can be used for stress-testing by quantifying the propagation of losses from a set of `stressing' variables to another set of `stressed' variables. In this paper I describe how to compute such conditional probability distributions for the vast family of multivariate elliptical distributions, and in particular for the multivariate Student-t and the multivariate Normal distributions. Measures of stress impact and systemic risk are proposed. An application to the US equity market illustrates the potentials of this approach.