In this paper, we provide new parameter estimation methods for a stochastic process observed at some discrete times, that is a solution of a given class of stochastic differential equations driven by stable processes. Firstly, we consider the diffusion coefficients parameters estimation problem such as the scaling and the driving stable process parameters. Secondly, we address the question of the joint estimation with the drift coefficients for Stable driven Cox–Ingersoll–Ross and Ornstein-Uhlenbeck processes. Our methodology which is based on the use of Nadaraya-Watson estimator. Our approach is new, according to the literature dealing with this joint estimation problem. Indeed it is a combination of the sample characteristic function and regression methods ((linear or weighted) together with the Euler–Maruyama scheme. We discuss the validity and efficiency of the numerical implementation of the estimators using synthetic and real data in finance, such as exchange rates. As a forthcoming work, we intend to create a package on R software to handle this kind of problem.