The optical properties of CuInSe2, CuGaSe2, Cu2ZnSnS4, and Cu2ZnSnSe4 are investigated using three different first-principles methods, namely the generalized gradient approximation by Perdew. Burke, and Ernzerhof (PBE), the hybrid Hartree-Fock-like functional by Heyd. Scuseria, and Emzerhof (HSE), and a Green's function approach (GW). The density-of-states, the complex dielectric function epsilon(omega) = epsilon(1)(omega) + i epsilon(2)(omega), and the optical absorption coefficient alpha(omega) are determined, providing fundamental understanding of these materials. We find that even though the PBE method generates fairly accurate effective crystal potentials, the HSE and GW methods improve considerably the band-gap energies E-g and also the localization of the semicore states, thereby describing the optical properties much better. Furthermore, we also present optimized convergence parameters for the self-consistent HSE calculation in order to reduce the computational time of this orbital-dependent method. (C) 2011 Elsevier B.V. All rights reserved.