隐含波动率曲面的建模与预测

Modeling and Forecasting of Implied Volatility Surface

根据隐含波动率期限结构与隐含波动率微笑特性提出的新的隐含波动率半参数模型,为隐含波动率曲面的建模提供了新的思路与方法。该模型包含九个具有现实经济含义的参数,分别对应剩余期限与在值程度两个因素的水平因子、斜率因子、曲度因子及其交互项因子。采用香港小型恒生指数期权数据,验证了在调整参数等于0.6时的模型能最优地拟合隐含波动率曲面。再根据样本期内日截面数据,估计出9个参数的时间序列,发现参数时间序列具有以交割日为峰值的周期性特征。利用MATLAB编程,分别实现了滚动加权平均法与BP神经网络法对参数的周期性时间序列进行外推预测,发现BP神经网络法明显优于滚动加权平均法。

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.