The United Nations Sustainable Development Goal 13 calls to "Take urgent action to combat climate change and its impacts" by 2030. This call to take action also reached central banks: A controversial debate of whether monetary policy shall target climate change mitigation is ongoing. This addresses also the use of titling the asset purchase programs towards green assets (green quantitative easing, green QE). GREENQE contributes to this discussion, by investigating how large of a carbon emission and temperature reduction could be achieved by tilting the corporate asset portfolio of central banks around the world towards green assets. Benefits from slowing down climate change are contrasted with costs from possible impediments to the monetary transmission channels. These costs and benefits are quantified using a rich integrated assessment model with incomplete markets and aggregate risk, featuring a green and brown sector of production, asset markets and fiscal and monetary authorities. This allows to evaluate the trade-offs of greening central banks' asset purchases (climate change mitigation vs. impeding monetary transmission mechanisms) as well as to investigate whether a monetary policy focused on the business cycle horizon can be used effectively to address a slow-moving climate change process. The results of GREENQE are of interest to various stakeholders, including foremost central banks as well as governments. If green QE is found to be an effective and not-costly tool it might be used to complement green fiscal policies of national governments and supranationals like the EU commission.