This paper prices the risk of climate change by calculating a lower bound for the price of a virtual insurance policy against climate risks associated with the business as usual (BAU) emissions path. In analogy with ordinary insurance pricing, this price depends on the current risk to which society is exposed on the BAU emissions path and on a second emissions path reflecting risks that society is willing to take. The difference in expected damages on these two paths is the price which a risk neutral insurer would charge for the risk swap excluding transaction costs and profits, and it is also a lower bound on society’s willingness to pay for this swap. The price is computed by (1) identifying a probabilistic risk constraint that society accepts, (2) computing an optimal emissions path satisfying that constraint using an abatement cost function, (3) computing the extra expected damages from the business as usual path, above those of the risk constrained path, and (4) apportioning those excess damages over the emissions per ton in the various time periods. The calculations follow the 2010 US government social cost of carbon analysis, and are done with DICE2009.Paper submitted to the special issueThe Social Cost of Carbon