Quantitative stability analysis for a deterministic parametric minimization problem with cone constraints are carried out. Under the Slater constraint qualification,we derive Holder continuity for the feasible solution set mapping and the optimal solution set mapping against variation of the parameter over Banach space. In comparison with the existing stability results for parametric programming, our results are established without any assumption on continuous differentiability of the underlying functions or reducibility of K. The results estblished are applied to stability analysis of a distributionally robust optimization、stability analysis of a stochastic quasi-variational inequality and convergence analysis of a global algorithm for a stochastic QCQP.