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Risk model hallucination happens when models are forced to forecast the likelihood of extreme events in cases where they have not been trained with such extreme outcomes. This is surprisingly common in applications such as financial regulations, pension funds, reinsurance, as well as the containment of market upheaval and financial crises. This column argues that measuring systemic financial risk needs to acknowledge the changing behaviour of agents and institutions during periods of market stress. This approach is more challenging and difficult to formalise, but crucial for learning how to develop financial resilience.