Complex magnetosphere-ionosphere coupling mechanisms result in high-latitude irregularities that are difficult to characterize using only Global Navigation Satellite System (GNSS) scintillation measurements. However, GNSS observations combined with physical parameters derived from modeling can be used to study the physics of these irregularities. We have developed a full three-dimensional electromagnetic wave propagation model called “Satellite-beacon Ionospheric-scintillation Global Model of the upper Atmosphere” (SIGMA), to simulate GNSS scintillations. This model eliminates the most significant approximation made by the previous simulation approaches about the correlation length of the irregularity. Thus, for the first time, using SIGMA, we can accomplish scintillation simulations of significantly high fidelity. While the model is global, it is particularly applicable at high latitudes as it accounts for the complicated geometry of the magnetic field lines in these regions. Using SIGMA, we simulate the spatial and temporal variations in the GNSS signal phase and amplitude on the ground. In this paper, we present the model and results from a study to determine the sensitivity of the SIGMA outputs to different input parameters. We have deduced from our sensitivity study that the peak to peak (P2P) power gets most affected by the spectral index and line of sight direction, while the P2P phase and standard deviation of the phase (σφ) are more sensitive to the anisotropy of the irregularity. The sensitivity study of SIGMA narrows the parametric space to investigate when comparing the modeled results to the observations.