Before revision:  In this paper, we consider an underlying model which is popular in spatial extremes , the Smith max-stable random field. We study the sensitivity properties of risk or dependence measures based on the values of this field at a finite number of locations. Max-stable fields play a key role, e.g., in the modelling of natural disasters. As their multivariate density is generally not available for more than three locations, the likelihood ratio method cannot be used to estimate the derivatives of the risk measures with respect to the model parameters .
After revision:  In this paper, we consider an underlying model which is popular in spatial extremes , the Smith max-stable field to be explicit, and IPA necessitates the computation of the derivative with respect to the model parameters .