Most of all, this paper explains Option in financial market, and then describes Mellin transform method and apply it to the well-known several option pricing model. Also, we illustrate stochastic elasticity of variance model and study the solutions of the leading order term and correction order terms of the option price on the stochastic elasticity of variance (SEV) model using the Mellin transform technique. From the Mellin transform, we obtain the closed solutions of all order terms and they demonstrate that constructing these exact solutions have significant effects on the speed of the calibration of the model.