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Self-consistent GW calculations and the solution of the Bethe-Salpeter equation are to date the best available approaches to simulate electronic excitations in a vast class of materials, ranging from molecules to solids. However, up to now numerical instabilities made it impossible to use these techniques to calculate optical absorption spectra of the best-known thin-film absorbers for solar cells: Cu(In,Ga)(S,Se)2 chalcopyrites and Cu2ZnSn(S,Se)4 kesterites/stannites. We show here how to solve this problem using a finite-difference method in k space to evaluate the otherwise diverging dipole matrix elements, obtaining an excellent agreement with experiments. Having established the validity of this approach, we use it then to calculate the optical response of the less studied, but promising, Cu2ZnGe(S,Se)4 compounds, opening the way to predictive calculations of still unknown materials.