In this paper, a three-dimensional parametric spherical wave model is presented that constructs the multiple-input and multiple-output (MIMO) channel from a single single-input and single-output realization of a ray-based simulator. This model assumes that rays do not change in the vicinity of the arrays. It uses spherical propagation and image theory to construct the MIMO channel for any array configuration. The main novelty of this model is that it takes into account multiple reflections, diffraction, variations in the reflection coefficient for single-bounce rays, and variations in the diffraction coefficient. Reflection is shown to be sensitive for hard polarization at the Brewster angle, though these rays have very low energy. Diffraction must be considered at the shadow boundaries of the diffraction wedge and assuming a constant diffraction coefficient, leads to inaccurate results at these regions. It is shown that in outdoor environments and for long distances, this model and the planar wave model provide similar results. However, at short distances, the parametric spherical wave model yields more accurate MIMO channels. Finally, the model is compared to some measurements in an outdoor environment.