Recent studies on global warming have introduced the inherent uncertainties associated with the costs and benefits of climate policies and have often shown that abatement policies are likely to be less aggressive or postponed in comparison to those resulting from traditional cost-benefit analyses (CBA). Yet, those studies have failed to include the possibility of sudden climate catastrophes. The aim of this paper is to account simultaneously for possible continuous and discrete damages resulting from global warming, and to analyse their implications on the optimal path of abatement policies. Our approach is related to the new literature on investment under uncertainty, and relies on some recent developments of the real option in which we incorporated negative jumps (climate catastrophes) in the stochastic process corresponding to the net benefits associated with the abatement policies. The impacts of continuous and discrete climatic risks can therefore be considered separately. Our numerical applications lead to two main conclusions: (i) gradual, continuous uncertainty in the global warming process is likely to delay the adoption of abatement policies as found in previous studies, with respect to the standard CBA; however (ii) the possibility of climate catastrophes accelerates the implementation of these policies as their net discounted benefits increase significantly.