Cascade Sensitivity Measures

Relatore

Pietro Millossovich (Cass Business School, University of London e Università di Trieste)

Abstract

In risk analysis, sensitivity measures quantify the extent to which the probability distribution of a model output is affected by changes (stresses) in individual random input factors. For input factors that are statistically dependent, we argue that a stress on one input should also precipitate stresses in other input factors. We introduce a novel sensitivity measure, termed cascade sensitivity, defined as a derivative of a risk measure applied on the output, in the direction of an input factor. The derivative is taken after suitably transforming the random vector of inputs, thus enabling the cascade sensitivity measure to capture both the direct impact of the stressed input factor on the output, as well as indirect effects via other input factors that are dependent on the one being stressed. Alternative representations of the cascade sensitivity measure, which can be calculated from a single Monte Carlo sample, are provided for two types of stress: a) a perturbation of the distribution of an input factor such that the stressed input follows a mixture distribution, and b) an additive random shock applied to the input factor. The calculation of those representations does not require simulating under different model specifications or the explicit study of the properties of the model function, making the proposed method attractive for applications, as illustrated through numerical examples.