Abstract: In this paper, large volatility mutually exciting effects between the Chinese stock market and the U.S. stock market are discussed under the circumstances that the two markets are linked much more closely than ever before. Over the past ten years, there are more obvious coordinative price movements between the Chinese and the U.S. stock market, especially in large volatility price movements. For example, in October 27, 2008, CSI300 index fell 7.12%. Stimulated by the fall of A shares, the United States stock market S&P 500 index also fell 3.17% after the opening of the stock market. Large volatility mutually exciting effect is that a large price fluctuation in a certain market can be transmitted to other markets through various channels, and then trigger the sharp fluctuation of asset prices in other markets. The theory foundation of large volatility mutually exciting effect is the positive feedback mechanism and the contagion of the financial crisis. There are generally three traditional research methods on the volatility spill-over effect:Multivariate GARCH Model, Copula and VAR. However, there are some defects in these methods. Hawkes process is a special path dependent point stochastic process, which is compatible for modeling large volatility mutually exciting effect, the Hawkes process is use to model the mutually exciting effect of CSI300 and S&P500 large fluctuations from 2006-2017. It is found that (1) The large volatility mutually exciting effect between Chinese stock market and U.S. stock market is asymmetric, and U.S.stock market large volatility exciting effect towards Chinese stock market is stronger;(2) The amplitude of large volatility has no significant influence on the mutually exciting effect;(3) The duration of mutually exciting effect between the stock markets in China and U.S. is different. And the duration of mutually exciting effect from Chinese stock market to U.S. stock market is longer. The result has some implications for financial market regulators and investors.

Key words: Hawkes process, large volatility, mutually exciting effect