The convergence bound for Volterra series expansion of nonlinear systems is investigated with a novel parametric approach in this study. To this aim, two fundamental concepts --- parametric bound of convergence (PBoC) and parametric convergence margin (PCM) are proposed, which are related to the conditions, under which a given NARX model can be approximated by a convergent Volterra series, in terms of system characteristic parameters including model parameters (of interest), input magnitude, and frequency. The estimation of the PBoC and PCM is given in the frequency domain, which is expressed in terms of these characteristic parameters, and does not require iterative calculations. The results provide a fundamental basis for nonlinear analysis and design using Volterra series based methods, and also present a significant insight into understanding nonlinear influence (super/sub harmonics and modulation) with respect to model parameters and input magnitude. Several examples are given to illustrate the effectiveness of the results.