Recently we found strong evidence in favor of a BCS-like condensation of excitons in 1T-TiSe2 [Cercellier , Phys. Rev. Lett. 99, 146403 (2007)]. Theoretical photoemission intensity maps have been generated by the spectral function calculated within the exciton condensate phase model and set against experimental angle-resolved photoemission spectroscopy data. The scope of this paper is to present the detailed calculations in the framework of this model. They represent an extension of the original excitonic insulator phase model of Jerome [Phys. Rev. 158, 462 (1967)] to three dimensional and anisotropic band dispersions. A detailed analysis of its properties and comparison with experiment is presented. Finally, the disagreement with density-functional theory is discussed.