It has been shown that the price of catastrophe reinsurance varies considerably over time. In particular, prices tend to rise after catastrophes and drift down between catastrophes. We construct a dynamic model to explain these stylised features. The model has three sets of players; households, insurers and a reinsurer. As catastrophe losses are undiversifiable, insurers must set aside capital or buy reinsurance to cover losses in the eventuality of a catastrophe. This is costly because of alternative investment opportunities. We show that imperfections in the capital market are crucial for generating time variation in the price of catastrophe reinsurance.