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Local volatility model is widely used in the fields of risk management, options pricing, etc. The model can not only describe the "smile" and the term structure of volatility, but can also ensure the completeness of the market. The core goal of local volatility research is to calculate the implied volatility. In this paper, the implied volatility surfaces arc built with both parametric and non-parametric methods to obtain smoother volatility surfaces. Parametric method can ensure the absence of arbitrage. Meanwhile, a closed form of solving the local volatility model with non-parametric method is proposed, which can eliminate the approximation error. In addition, the pricing of Shanghai 50ETF option in China based on the local volatility model is studied by comparing effects of the models from aspects of in-the-sample, out-of-the sample and hedging pricing errors. The empirical results show that the non-parametric method is better than the parametric method for errors in-the-samplc; the parametric method has better results for out-of-sample and hedging effects. Particularly, both the options pricing and hedging effects of the implied volatility modeling methods are better than nn-modeled method in the aspects that the pricing errors can be decreased by more than half and the mean square error can be reduced by 1~2 orders of magnitude. [ABSTRACT FROM AUTHOR]