Over the last decade, the green bond market experienced strong growth rates fueled by the need to combat climate change. However, the discourse on enhancing the effectiveness of green bonds primarily revolves around regulatory measures, often overlooking the possibility of designing inherent incentives. We show that a green bond with a coupon structure positively related to the carbon price development stimulates (early) investment in an emission-reducing project and creates higher net present values (NPVs) when applied in project financing. In our simulation-based framework, we model carbon prices using a geometric Brownian motion, and create a general optimal stopping time problem regarding the start of the project. The green bond in our setting carries the risk of default, also mitigated by its carbon price-linked coupon structure.