The multivariate conditional probability distribution quantifies the effects of a set of variables onto the statistical properties of another set of variables. In the study of systemic risk in the 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. Here it is described how to compute such conditional probability distributions for the vast family of multivariate elliptical distributions, which includes the multivariate Student-t and the multivariate Normal distributions. Simple measures of stress impact and systemic risk are also proposed. An application to the US equity market illustrates the potentials of this approach.
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.
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