The stability of the ground or excited state calcium atom in an argon-doped helium droplet has been investigated using an extension of the helium density functional method to treat clusters. This work was motivated by the experimental study presented in a companion paper, hereafter called Paper I [A. Masson, M. Briant, J. M. Mestdagh, M. A. Gaveau, A. Hernando, and N. Halberstadt, J. Chem. Phys. 137, 184310 (2012)10.1063/1.4762836], which investigated Ca2 photodissociation in an argon-doped helium droplet and the nature of the fluorescent species. It is found that one single argon atom is sufficient to bring the calcium atom inside the droplet, for droplets of over 200 helium atoms. The absorption and emission spectra of CaArM (M = 0-7) clusters have been simulated using the recently developed density sampling method to describe the influence of the helium environment. Absorption spectra exhibit broad, double bands that are significantly blueshifted with respect to the calcium atomic line. The emission spectra are less broad and redshifted with respect to the calcium resonance line. The shifts are found to be additive only for M ⩽ 2, because only the first two argon atoms are located in equivalent positions around the calcium p orbital. This finding gives a justification for the fit presented in the companion paper, which uses the observed shifts in the emission spectra as a function of argon pressure to deduce the shifts as a function of the number of argon atoms present in the cluster. An analysis of this fit is presented here, based on the calculated shifts. It is concluded that the emitting species following Ca2 photodissociation in an argon-doped droplet in Paper I could be Ca*ArM in a partly evaporated droplet where less than 200 helium atoms remain.