Functional Research On Volatility Of Stock Index Futures

In the financial field,volatility is of great important,for the reason that it can not only measure the variations of financial assets9 price,but also represent the risk of the financial asset in a sense.Nowadays,the exploration of the volatility's variations has become an important subject in the financial field.In the futures market,the trading system of "T+0" is implemented.That is to say,futures can be bought and sold on the same day.Hence,it is of great necessary to explore the volatility mode of stock index futures in a single day.In the empirical research on the volatility of SSE 50 stock index futures,Firstly,we estimate the volatility based on the derived formula.Then,the idea of functional data analysis is introduced,and the observation unit of volatility data is switched from single points to curves by B-spline basis function method.Secondly,four common factors are extracted from the smoothed volatility curve by principal component analysis,and four typical volatility modes in a day are depicted.Finally,on the basis of functional principal component analysis,the volatility is extrapolated and predicted,and we also compared the prediction accuracy with point prediction method.The empirical results shows that,the volatility's mean value curve of SSE 50 stock index future in 2017 presents a pattern of "high at both ends,low in the middle",which indicates that the common "overnight effect" in the stock market still exists in the stock index futures market;the extracted four main factors shows that the volatility is on the high level before and after the noon break.Relatively speaking,the fluctuation of the opening and closing time of the whole day is particularly obvious.Mean square error shows that the prediction effect based on cure volatility is better than that based on single point.