To formalize the monitoring role of the media in corporate finance, we propose a new model of corporate catastrophic risk combining two disciplining forces: corporate self-regulation and media pressure. We assume that optimizing firms have a strong interest in hiding large operational loss events to avoid reputational losses. When a loss is revealed, the operation is immediately restored to its equilibrium, due to higher media attention. The model explains why public losses depend heavily on media attention but seem to be unrelated to the quality of internal governance. Internal governance has high impact on the hidden part of losses. Using the SAS Global Oprisk database, we test the model predictions for the period of 2011–2022 covering 4,547 loss events attributed to firms in the MSCI World index. The results of the empirical analysis are consistent with the theoretical model: higher media attention increases public losses but decreases total (the sum of public and hidden) losses in terms of both frequency and severity. We also find evidence that it may be easier to hide the actual size of large corporate losses than the occurrence of the loss event itself, especially within the financial sector. Promoting press freedom and market liquidity, prerequisites for media and investor attention, can be highly effective policies for improving corporate governance.