The purpose of this study is to find out the characteristics of volatilities ofChinese stock markets, especially Sanghai, Shenzen and Hong Kong stock marketusing univariate and multivariate autoregressive conditional heteroscedasticity(ARCH)models.Recent empirical works on stock pricing have been focused on the timevarying volatilities in returns since Mandelbrot(1963) and Fama(1965). Theypointed out the volatility clustering phenomenon, that is, that the large changestend to be followed by large changes, of either sign, and small changes tend tobe followed by small changes, leading to contiguous periods of volatility andstability in stock market. This implies that stock prices may fluctuate evenwithout the change of fundamental economic sources affecting them, and thatthe fluctuation of stock prices is closely related to the time varying volatility.The common movements in volatility changes also are a nociceablephenomenon found in the stock markets. The arrival of new information tostock markets have common effects not only on all stock markets returns, butalso volatility changes. Black(1976) observed that there is a lot of commonalityin volatility changes across stocks, and stock volatilities tend to change in thesame direction. This indicates that we need multivariate models co-movementsin volatility changes as well as time varying phenomenon in volatilities of stockreturns of Sanghai, Shenzen and Hong Kong stock markets.Chinnese stock markets have been established for more than two decadeswith extremely rapid development. The market value of Chinese stock marketshave steadily ranked second in the world at current stage. But China's stockmarkets still in the stage of "emerging plus transition" period when comparedwith the developed markets and the typical performance is that the volatility ofstock price is too large. The stock market, the barometer of the economy willinevitably cause macroeconomic instability for its sharp fluctuations, especiallyin the China’s economic transformation and structural adjustment background.It is also necessary to choose a suitable mature capital market forcomparative research when studying the Chinese stock market volatility itself.Because we can reveal the volatility characteristics of the Chinese stock marketonly through a comparative analysis of the relatively effective stock marketvolatility, which can objectively judge the development level of China's currentcapital market, find the gap between the growing Chinese stock market andmature stock markets, and then propose targeted measures to eventuallyimprove the Chinese capital market. China Securities Regulatory Commissionand Hong Kong Securities &Futures Commission launched a strategiccooperation and issued a joint announcement that the mainland stock marketrepresented by the Shanghai Stock Exchange and China securities registrationand settlement and the Hong Kong stock market, represented by the HongKong Stock Exchange and the Hong Kong Central Clearing Co., Ltd., pilot theinterconnection of stock market transactions between this two places(hereinafter referred to as the "Shanghai Hong Kong stock connect") have beenspecially approved on 10th, April 2014. which is aim to promote mutual benefitbetween the mainland and Hong Kong capital markets and jointly achieveprosperity and development. The launch of the Shanghai-Hong Kong stockconnect is somehow equivalent to the gradually integrating the trading rulesand investment concepts of the mainland stock market with the Hong Kongstock market and It is an important step towards mature of our capital market.It has opened an effective channel for foreign investors to participate indomestic market investment, which marks China Stocks are beginning to trulyinternationalize. The comparative study of the Chinese mainland and HongKong stock markets volatility characteristics got the basis and significanceunder such circumstance.China-Hong Kong (hereinafter referred to as Hong Kong) has always playeda pivotal role in Asia and even the global capital markets as one of the world'sinternational financial centers, and any sign of trouble of the Hongkong capitalmarket will be enough to cause changes of the world market, the endowmentof geographical location also determines the close economic, political, andcultural connections between Hong Kong and the mainland, especially after thereunification, cross-strait economic exchanges have been more free comparedwith other mature international financial markets, Hong Kong stock market notonly has the characteristics of liberalization and internationalization of a matureinternational financial market, but also has the special economic, political andcultural relations with the mainland capital market. In the context of globalintegration, Hong Kong has naturally become an important link between Chinaand the international capital market and Hong Kong stock market has alsobecome an ideal reference for studying the mainland stock marketspontaneously.Therefore, the study of the characteristics of the volatility and interplayrelations of the stock market in mainland China and Hong Kong will help themajority of market participants to objectively and effectively judge thedevelopment of the stock market in mainland China, at the same time, it willhelp to further improve the capital market in China, which has importantpractical guiding significance in strengthening laws and regulations,implementing effective supervision and preventing systemic financial risks.This paper selects Shanghai, Shenzhen and Hong Kong stock markets asresearch samples to compare the volatility characteristics of emerging marketsand mature stock markets. Based on the daily closing price data of Shanghaiand Shenzhen 300 index and Hang Seng Index of Hong Kong from 27, April2005 to 5, March 2019, this paper establishes GARCH, EGARCH models andMultivariate GARCH model to make an empirical comparison on the volatilityrelationship between the stock market of mainland China and Hong Kong. Theresults show that: (1) there are obvious time-varying volatilities in theSanghai, Shenzen and Hong Kong stock markets; (2) there are no asymmetriceffects in Sanghai and Shenzen stock market, and there is obvious asymmetriceffect in Hong Kong stock market, however good news increase volatilities.(3) The Hong Kong and Sanghai stock markets has more significant relationin volatilities than that of Hong Kong and Shenzen stock market.