We determine the variability-luminosity relationship of quasars and Seyfert galaxies in the rest frame of the objects using IUE spectra. We find that the variability decreases with the luminosity. An important part of the scatter in the relationship may be explained if one tries to estimate the uncertainties on the variability due to the sampling. We discuss the variability using the concept of discrete events. The trend between variability and luminosity is described by a power-law with an index -0.08, which is incompatible with the power-law of index -1/2 predicted by the most general discrete-event models in which the change in average luminosity is due to differences in average event rates exclusively. We conclude that the -1/2 index is definitely inconsistent with the data. A flat relationship is however possible, if some bias has been underestimated. We propose different ways whereby discrete events may produce a different variability--luminosity relationship: by changing the luminosity or the life time of the events, or by introducing interdependence between the events. The latter possibility cannot produce a satisfactory relationship. Using the former possibilities, we do not find any natural explanation for the variability- luminosity relationship in the context of discrete-event models. This is possibly an indication that explanations in which variability is not expressed in terms of discrete events should be favoured.