The Stock Volatility Forecasting Model Combing The GARCH Volatility With The Implied Volatility

With the rapid development of financial markets,the study of financial assets volatility gradually become one of the research focus.There are two main types of financial assets volatility estimation model:one is the Implied Volatility Model being with the appearance of the options.The implied volatility,which is calculated by the option prices from Black-Sholes model,is the expectations of the future volatility.the other one is the Historical Volatility Model,which used historical data of rate of return to predict the future volatility.The most common used models are Autoregressive Conditional Heteroscedasticity Model(ARCH Model),Generalized Autoregressive Conditional Heteroscedasticity Model(GARCH Model),Stochastic Volatility Model(SV Mode)and Realized Volatility Model(RV Model).In this paper,we first analyze the family of GARCH model and the Black-Scholes model.And taking Apple Inc's yields data as an example,the empirical analysis shows that the GARCH model has a good short-term forecasting performance for stock price.In the other hand,as the implied volatility can be seen as the market expectation of an underlying asset,we believed that the implied volatility impacts the stock volatility in a certain extent.Based on this,a new forecasting model combing the GARCH volatility with the implied volatility,GARCH-IMV model,is proposed.This new model considers the influence of implied volatility to the disturbance in the GARCH model and replace the GARCH volatility with a cubic interpolation function of GARCH volatility and implied volatility.The cubic interpolation function is fitted through sample data fitting.The sample points are the GARCH volatilities and the implied volatilities.And the real values of these sample points are the stocks' daily volatility that is the standard deviation of the stock's rate of return as the real value of volatility.We choose 77 stocks in the S&P500 index,and made GARCH models respectively to calculate the GARCH volatility of each stock at the last trading day.Then choose the option whose residual maturity are one day and strike price was the nearest to the close price of the last trading day,and calculated their implied volatility.Selected 70 of 77 stocks' real volatility,GARCH volatility and implied volatility to make up the sample data.The cubic interpolation function can be obtained by fitting these sample data and plugged it into GARCH-IMV model,which is used to predict the remaining 7 stock's volatility.The experimental result shows that the new model can acquire good prediction.Through the empirical analysis of using BP neural network and RBF neural network to predict stock price,we found that the neural network is also applicable to the nonlinear stock yield sequence,furthermore,RBF neural network is superior to the BP neural network on stock price prediction.In order to improve the prediction effect,in this paper the RBF-GARCH-IMV model based on the RBF neural network and GARCH-IMV model is proposed,in which the radial basis function is used to replace the autoregressive model of the mean equation of the GARCH model,to strengthen the description of stock's nonlinear characteristics.This model combined well with the nonlinear and volatility clustering features.The experimental results show that the RBF-GARCH-IMV model has a better performance than the GARCHmodel and GARCH-IMV model in prediction.