We compare the dynamic hedging performance of the deterministic local volatility function approach with the implied/constant volatility method. Using an example in which the underlying price follows an absolute diffusion process, we illustrate that hedge parameters computed from the implied/constant volatility method can have significant error even though the implied volatility method is able to calibrate the current option prices of different strikes and maturities. In particular the delta hedge parameter produced by the implied/constant volatility method is consistently significantly larger than that of the exact delta when the underlying price follows an absolute diffusion.