We analyze optimal climate financial regulation to address the question when capital requirements should be differentiated in order to encourage climate related investments. We distinguish between two key dimensions of climate policies: carbon emissions (mitigation) and investment in climate resilience (adaptation), and consider two scenarios according to the efficient and inefficient carbon policies. We show that for financial regulators, the prospect of extreme climate shocks creates a rationale for differential capital requirements even when carbon prices are efficient. When extreme climate-related events occur, monetary and fiscal policies and financial regulators will optimally react with accommodating policies. The anticipation of such regulatory accommodation leads to distortions in private investment incentives. The optimal ex ante policy of regulators will attempt to correct for such biases. We also show that regulators should differentiate capital requirements when private agents insufficiently internalize the effects of investments in resilience. Finally, regulators should differentiate capital requirements that encourage both abatement and resilience investments when carbon policies are inefficient.