Application Of Non-linear Theory In Volatility Of Stock Price

The non-linear theory has been playing an important role in describing volatility of financial time series. The class of ARCH models is a kind of typical creating models according to the non-linear theory. At present, they have already been applied to portraying volatility of the stock return extensively by scholars of foreign countries, but the domestic research in this field only begin in recent years, and a lot of scholars don't consider the impact on suitability of the models that due to the changes of stock exchange system of our country. So this thesis can further open-up domestic scholars' thought in studying volatility of stock price.on the basis of introducing non-linear theory, this paper discusses the methods of parameter estimating and ARCH test of the sample data. According to the characteristic of trade system change of the stock market of our country, this article analyses validity of Shanghai Stock market in three periods according to the sample block from May 21 ,1992 to May 31,2004 of Shanghai Stock Index. Then the paper verifies ARCH effect of the volatility of the daily yield of Shanghai Stock Index, and concludes EGARCH model is the most efficient model in describing volatility of Shanghai Stock Index with such software as Eviews, SPSS, etc. Furthermore, it provides the expression formula of EGARCH model.Classifying as index, this paper analyses ARCH effect of the volatility of the daily, weekly and monthly yield of thirty stocks from May 21, 1992 to May 31, 2004 in three periods. The sample stock also divides into three different kinds according to their size. This paper also applies GARCR model, EGARCH model, and TARCH model to portraying volatility of the stocks return. Finally, it concludes that there is no fitful model for describing the volatility of daily yield of big size stock at present, and ARCH effect does not exist in volatility of weekly yield. Moreover, it considers that GARCH model fits to most middle size stock relatively excellent, and there is no fitful model for weekly yield either. Furthermore, it concludes that volatility of daily yield of small size stock has ARCH effect in the whole sample period, and this kind of effect is being strengthened constantly, GARCH model is more suitable for most small size stocks, and there is no ARCH effect or faint ARCH effect in volatility of weekly yield.