Climate risk can have implications for financial stability. For Norway, a large oil sector entails a country-specific risk linked to a potential future decline in oil demand. Uncertainty about future climate regulation and technological developments make it demanding to estimate that risk. Empirical analyses of disruptive technologies (Nagy, et al, 2013) used in solar panels and electric car batteries indicate continued technological improvements. Cost analyses, regulations and car producers' plans suggest a potential reduction in oil demand growth by 2025. The European Systemic Risk Board (ESRB, 2016) posits that a gradual shift to lower climate emissions could reduce financial system risk. Insufficient early adaptation involves the risk of abrupt adaptation later. Abrupt effects of climate change, such as natural disasters, can lead to an unexpected and substantial tightening of climate measures and regulations. Available climate-friendly technology enables such measures to be taken. This could make oil-related industries vulnerable to risk. Actual and potential adaptation in the form of enhanced cost-efficiency, restructurings and lower debt raising influences the risk. As adaptation tends to be time-consuming, it would be an advantage to adapt before the changes are visible in the oil market. Banks can map and report on climate change in their own portfolios. Scenario analyses and stress tests can improve risk understanding and influence credit standards. Any increase in capital requirements relating to climate risk in the EU could help accelerate banks' adaptation.