Recent experiments motivated by solar light harvesting applications have brought a renewed interest in $\mathrm{AgBi}{\mathrm{S}}_{2}$ as an environmentally friendly material with appealing photovoltaic properties. The lack of detailed knowledge on its bulk structural and electronic structure however inhibits further development of this material. Here we have investigated by first-principles quantum mechanical methods models of the two most commonly reported $\mathrm{AgBi}{\mathrm{S}}_{2}$ crystal structures, the room temperature matildite structure, and the metastable schapbachite. Density functional theory (DFT) based calculations using the Perdew-Burke-Ernzerhof exchange-correlation (xc) functional reveal that matildite can be 0.37 eV per $\mathrm{AgBi}{\mathrm{S}}_{2}$ stoichiometry unit more stable than a schapbachite structure in bulk, and that the latter, in its ordered form, may display a metallic electronic structure, precluding its use for solar light harvesting. This points out the fact that $\mathrm{AgBi}{\mathrm{S}}_{2}$ nanocrystals used in solar cells should present a structure based on matildite. Matildite is found to be an indirect gap semiconductor, with an estimated band gap of $\ensuremath{\sim}1.5\phantom{\rule{4pt}{0ex}}\mathrm{eV}$ according to DFT based calculations using the more accurate hybrid xc functionals. These reveal that hole effective mass is twice that of electron effective mass, with concomitant consequences for the generated exciton. Hybrid DFT calculations also show that matildite has a high dielectric constant pertinent to that of an ionic semiconductor and slightly higher than that of PbS, a material that has been extensively used in solar cells in its nanocrystalline form. The calculated Bohr exciton radius of 4.6 nm and the estimated absorption coefficient of ${10}^{5}\phantom{\rule{4pt}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$ within the solar light spectrum are well in line with those experimentally reported in the literature.