Although the reconstructed local volatility function can give an accurate approximation to the market volatility which leads to more efficient hedging, using the implied volatility calculated from a carefully chosen model is more ready to be accepted for the sake of easy implementation. We compare the dynamic hedging performance of the constant elasticity of variance model family with constant volatility Black-Scholes model. By assuming that the underlying stock follows a specific diffusion process, we use hypothetic examples to illustrate that Black-Scholes model yields the largest hedging parameter and the greater standard error of relative hedging error. Our observation shows that the constant volatility model can result in significant hedging error, and by allowing for varying volatility, the constant elasticity of variance model is more adaptive
