Density-functional methods, as implemented in the Amsterdam Density Functional program, are used to calculate the electron paramagnetic resonance (EPR) and electron nuclear double resonance (ENDOR) parameters of the S2- defect in a halide monovacancy in various alkali halides (MZ:M=Na, K, Rb and Z=Cl, Br, I) lattices. The calculations were performed on cluster in vacuo models for the defect and its lattice surroundings, involving up to 88 atoms in order to limit boundary effects. For all MZ lattices, the calculated g and 33S hyperfine tensors of the S2- molecular ion are in very good agreement with the available EPR data, explicitly supporting the monovacancy model for the defect. In addition, computational results for the principal superhyperfine and quadrupole values and axes of the nearest shells of M+ and Z- ions are compared with experimental ENDOR data. The merits and shortcomings of the applied cluster in the vacuo method are critically evaluated.