The green bond market has increased rapidly in recent years amid growing concerns about climate change and wider environmental issues. However, whether green bonds provide cheaper funding to issuers by trading at a premium, so-called greenium, is still an open discussion. This paper provides evidence that a key factor explaining the greenium is the credibility of a green bond itself or that of its issuer. We define credible green bonds as those which have been under external review. Credible issuers are either firms in green sectors or banks signed up to UNEP FI. Another important factor is investors' demand as the greenium becomes more statistically and economically significant over time. This is potentially driven by increased climate concerns as the green bond market follows a similar trend to that observed in ESG/green equity and investment fund sectors. To run our analysis, we construct a database of daily pricing data on closely matched green and non-green bonds of the same issuer in the euro area from 2016 to 2021. We then use Securities Holdings Statistics by Sector (SHSS) to analyse investors' demand for green bonds.