Parametric optimization has been widely applied in game theory, control theory, economics and management, engineering technology, etc. Recently, the stability of solutions to parametric optimization has attracted increasing attention. This paper mainly studies the stability of solutions to parametric optimization problems under bounded rationality. By introducing an abstract rationality function, two rational models M are established with two types of perturbations: the perturbation of both objective functions and feasible sets, and the perturbation of objective functions, feasible sets and parameters simultaneously. For the two perturbations above, by the ``generic'' method, the rational model M is structurally stable and is robust to \varepsilon-equilibria (or solutions), respectively. That is, the solutions to most of parametric optimization problems are stable in the sense of Baire category. Finally, an example is illustrated.