We obtain a solution of optical parametric amplification using self-phase modulation within the Kerr media in a nonlinear interferometer with two arms. We show that it is equivalent to the solution driven by four-wave mixing and that the solution of parametric amplification is suitable to generate a parametric gain. We obtain a derivative of power gain with respect to the propagation distance and show that gain-saturation can occur as the beam propagates along the nonlinear arms. We also show a bandwidth characteristic of the parametric amplification driven by nondegenerate four-wave mixing. Numerical examples are given to illustrate that the solution of the parametric amplification can be applied to design and analysis of all-optical devices such as all-optical amplifiers.