This paper employs ARJI model to examine jump frequency and volatility of the co-movements across stock markets and compares whether jump and diffusion induced volatilities are different during Asian Financial Crisis period. Financial utilize GIRF to analyze the relationship among U. S., Japan, Korea, Hong Kong, Singapore and Taiwan. The empirical results indicate that, firstly, jump intensity and frequency are time variant. Second. Asian Financial Crisis does not bring great impact to Taiwan. Volatility of US stock market during non-Asian Financial Crisis period is smaller than that during crisis period. Thirdly, the results of Pearson test indicate that the relationships of volatility among these countries are significant, and the coefficient correlation of volatility after Asian Financial Crisis is mostly higher than that before crisis. Fourthly, after Asian Financial Crisis, the volatility of US stock market relatively has independent character and impact to other countries, secondly is Taiwan. Therefore, while making the investment decision in oversea market, it is worthy to consider the stock market of U.S. or Taiwan.