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In this paper, we assume the random variables are in the domain $\\mathcal{R}_{\\alpha}$ of normal attraction of a stable law of exponent $\\alpha$, then for $\\alpha\\in(1,2)$, we use the Stein's method developed in \\cite{CNX21} to give uniform and non uniform bounds on $\\alpha$-stable approximation for the call function without additional moment assumptions. 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