Anthropogenic climate change produces two conceptually distinct negative economic externalities. The first is an expected path of climate damage. The second, which is this paper's focus, is an expected path of economic risk. To isolate the climate-risk problem, we consider mean-zero, symmetric shocks in our 12-period, overlapping generations model. These shocks impact dirty energy usage (carbon emissions), the relationship between carbon concentration and temperature, and the connection between temperature and damages. Our model exhibits a de minimis climate problem absent its shocks. But due to non-linearities, symmetric shocks deliver negatively skewed impacts, including the potential for climate disasters. As we show, Pareto-improving carbon taxation can dramatically lower climate risk, in general, and disaster risk, in particular. The associated climate-risk tax, which is focused exclusively on limiting climate risk, can be as large or larger than the carbon average-damage tax, which is focused exclusively on limiting average damage.