The optical-absorption spectrum of a cationic Ag0 atom in a KCl crystal has been studied theoretically by means of a series of cluster models of increasing size. Excitation energies have been determined by means of a multiconfigurational self-consistent field procedure followed by a second-order perturbation correlation treatment. Moreover results obtained within the density-functional framework are also reported. The calculations confirm the assignment of bands I and IV to transitions of the Ag-5s electron into delocalized states with mainly K-4s,4p character. Bands II and III have been assigned to internal transitions on the Ag atom, which correspond to the atomic Ag-4d to Ag-5s transition. We also determine the lowest charge transfer (CT) excitation energy and confirm the assignment of band VI to such a transition. The study of the variation of the CT excitation energy with the Ag-Cl distance R gives additional support to a large displacement of the Cl ions due to the presence of the Ag0 impurity. Moreover, from the present results, it is predicted that on passing to NaCl:Ag0 the CT onset would be out of the optical range while the 5s-5p transition would undergo a redshift of 0.3 eV. These conclusions, which underline the different character of involved orbitals, are consistent with experimental findings. The existence of a CT transition in the optical range for an atom inside an ionic host is explained by a simple model, which also accounts for the differences with the more common 3d systems. The present study sheds also some light on the R dependence of the s2-sp transitions due to s2 ions like Tl+.