The spectral density of samarium sulfide is calculated using a multiband periodic Anderson model. The $s,$ $p,$ and $d$ states are treated as band states within the local-density approximation. Realistic, local many-electron states of the $4f$ shell are taken into account. Using projection techniques a $4f$ occupation of 5.94 is found in the semiconducting phase. The calculated spectral density is in fair agreement with the measured photoemission and inverse photoemission spectra. To simulate the mixed-valent phase, the global hybridization strength between $4f$ and band states is empirically enhanced. The limits of a valence change controlled by the hybridization strength are discussed.