We combine a global dataset of bilateral financial exposures with projections of changes in the distributions of river flooding and coastal impacts induced by climate change, in order to estimate potential impacts of climate change on global financial stability. We  model the propagation of climate impacts through financial interlinkages using the debtrank algorithm (Battiston et al. 2012). Impacts on global financial stability thus emerge from the combination of direct climate impacts on the one hand and from the leverage and network centrality of affected countries on the other hand. We find that the global value-at-risk, both from direct and indirect impacts, increase faster than the expected value of damage, hence backing up the arguments of Pyndick (2013) about the need to refocus climate impact assessment on the tail of the distribution of damages. Furthermore, we find that the shift in the distribution of direct damages induced by climate change can be amplified more than proportionally by financial interlinkages in scenarios where the relative exposure of developed countries, which are more financially leveraged, increases.