The Portfolio Decarbonization Coalition (PDC) suggests that investors divest from carbon intensive companies. Meanwhile, many investors also recognize that financial support is crucial to the low-carbon transition of high emitters. As such, this paper investigates the cost of capital facing high emitters in the corporate green bond markets. Using a sample of 151 matched bond pairs, we find that high emitting green bond issuers face a discount in their green bond premium (Greenium). The relation between an issuer's emissions performance and its green bond pricing is moderated by external review. In fact, the marginal impact of second-party opinion (SPO) statement on Greenium is larger for issuers with higher emissions intensities. Our results suggest that green bond investors are ex-ante more cautious about investing in high emitters, and require more proof of the latter's credibility before conferring Greenium to support their green projects. As such, the positive signal conveyed by external review is more important to high emitting green bond issuers by distinguishing them from other high emitters who less likely to bring expected green impacts from executing the green projects.