Climate change may have a detrimental effect on a firm's financial performance. Using a forward-looking measure of climate risk exposure based on textual analysis of firms' 10-K reports, we assess whether climate risks---as disclosed to the regulator---are priced in the credit default swap (CDS) market. We construct this novel climate risk measure based on BERT, an advanced language understanding algorithm, and adapt it for our purpose. We differentiate between physical and transition risks and find that transition risk increases CDS spreads, especially after the Paris Climate Agreement of 2015. However, we do not find such an effect for physical risk.