关键词: 隐含波动率曲面,半参数模型,曲面拟合,BP神经网络

Abstract: Based on the term structure and the smile features of implied volatility, this paper presents a new semi-parametric model of implied volatility, which provides a new idea and method for the modeling of implied volatility surface. This model contains nine parameters with practical economic implications, corresponding to the level factors, slope factors, curvature factors and interaction factors of the two elements: the residual maturity and the on-value degree. By adopting the data of mini HSI option, this paper verifies the result that when the parameter is adjusted to be 0.6, this model can fit the implied volatility surface optimally. Then according to the daily cross-section data in the sample period, it estimates the time series of the nine parameters. The findings show that these time series have periodic characteristics that the peak value appears in the settlement days. By making use of the MATLAB programming, the extrapolation forecast on the periodic time series of the parameters is realized by adopting the chain-weighted mean method and the BP neural network method, the results show that the BP neural network method is obviously superior to the chain-weighted mean method.

Key words: implied volatility surface; semi-parametric model; surface fitting; BP neural network