The Grey wolf optimizer (GWO) is a recent swarm intelligence-based algorithm. The performance of GWO highly depends on the choice of the controlling parameters. Finding the most suitable values of these parameters becomes a challenging task due to the stochastic nature of the position update process. Mathematical analysis of the position update mechanism can guide in finding the most appropriate range of these parameters. This paper attempts to use von Neumann stability criteria to find the most suitable value of these parameters. The objective of this study is also to check whether the original parameter setting is in line with the recommendation of mathematical analysis. Recommendations are further examined using numerical experiments over 23 classical benchmark functions. It is found that the parameters of GWO are within the stable range. It is also verified that GWO performs poorly if the parameters are set beyond the stable range.