Within a loss distribution approach (LDA) framework, we propose to model catastrophic operational risk using a compound Neyman–Scott clustering model. The particularity of this compound model is that it relies on a Neyman–Scott process (the frequency component of the LDA) to model the occurrence behavior of catastrophic operational loss events. The motivation behind this is that catastrophic operational risk may be the manifestation of a two-level risk generation mechanism: on the first level, natural and human-made catastrophes (referred to as operational storms) occur and trigger, on the second level, clusters of catastrophic operational loss events. A graphical analysis based on a historical series of 334 extreme operational loss events supports the clustering structure of the event occurrences. The calibration of the Neyman–Scott process reveals a satisfactory model fitness and underlines the high vulnerability of financial organizations to eventual operational storms.