| The volatility of asset prices is the most attractive financial time series. In the financial engineering field, volatility has been given a pivotal position.Further more, it can not be directly observed.In recent years, scholars have been studying about estimating volatility with enough passion.Exactly, domestic options market has not started, so,it is difficult to estimate the volatility using implied volatility.At present,more and more models, which are very popular, estimate the volatility, such as the GARCH model and the realized volatility method,while the traditional and historical volatility as an old friend seems to be forgotten.In these few documents,most of them only use the closing price to study the volatility,so,it is a pity both in theory and in practice.In this paper, all of the assumptions in the geometric Brown motion that the stock price follows.A perfect explanation are firstly given to the model one from the angle of practical application,then replace the closing price usually with the opening price,closing price,the highest price,the lowest price to estimate the historical volatility,and then present five estimation models and introduce their calculation process.This research study on these five models and results by historical transaction price of Jiugui Liquor,maotai,Wuliangye Liquor,and twenty eight random stocks from three hundred stocks of the Shanghai and Shenzhen, which are recent transaction prices for one months,three months,six months,twelve months. To evaluate the five models, we use the rules of Estimated Mean Absolute Error and Estimated Mean Square Error,then the best model that is model one will be selected. Finally,we compare the best model with GARCH model using the price of Jiugui Liquor.We can draw five main conclusions by running the R software and eviews6.0.Firstly,in traditional historical volatility estimation models, the third model considering of the closing prices is better than anyoe else.To our surprise,the fifth model and model four with four kinds prices is not the best one.The reason may be that the stock market in not perfect as the western countries,therefore,extreme law is likely to represent certain error messages.It tells ous when the volatility is estimated,the price we considere is not the more the better,but the key is the right factor.Secondly, in all the models,the GARCH(1,1) model has the best effect when using the data of the one months.so,when using one month data to estimate the volatility parameters,we can consider the GARCH(1,1) model.Thirdly,in this study,model one uses the daily frequency data to approximate the high frequency data,and gains better results than the traditional historical volatility estimation method and more than the current popular GARCH(1,1) model,which is by using the closing price of alcoholic liquor.So,model one not only uses high frequency data of realized volatility model,but also uses daily data.fourthly,in this empirical study,the GARCH(1,1) model does not perform better than model three that only coniders the closing price.At the same time,the traditional historical volatility method can also have a good description about volatility parameters as long as the model is appropriate.Finally,after comparison of the empirical, we have promoted a kind of Realized Volatility that it is called model one. In theory, model one can be used to directly calculate the volatility of any period of time,and no longer need to transformate volatility into the required form. In this way,it is more perfect than that one that can only calculate a one day volatility, and its form is simple. |
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