The existence of jump exciting and volatility clustering in the stock market has become a common sense. However, whether there is mutual influence between random jumps and continuous volatility within a market is still a matter of debate, that is, there is no clear evidence showing that whether the changes of volatility may trigger random jumps. Motivated by this, in this paper, we regard the cumulative change of continuous volatility as the “quantitative change" of prices, the intermittent jumps as the "qualitative change”, and apply the two-factor cross feedback dynamic model of jump self-exciting and volatility clustering on international equity market indexes to capture the effects between them. Combined with the conditional characteristic function of the Lévy process, taking advantage of Generalized method of moments and Particle Filtering approaches (GMM-PF), and using international stock returns, we are able to capture and quantify the interactive transmission routes and degree of jump and diffusion. Research shows that there are co-evolution and cross-feedback effects between random jumps and continuous volatility, which means that jumps will lead to changes in the continuous volatility of the next period, the accumulation of volatility will also increase the jump arrival rate in the future as well, that is, the quantitative change of volatility causes the qualitative change of the jump. Besides, compared with Maximum Likelihood Estimation (MLE) and Sequential Bayesian Learning method (SBL), the combination of PF and GMM approaches that we develop is much more efficient, faster with high precision. Moreover, we also find that the transmission mechanism between jump and diffusion is quite different in different markets, that is, compared with developed markets overseas, most emerging markets are relatively weak in digesting, transferring and diversifying jump risk, thus making the persistence of jump components always remain at a high level. Regulatory authorities and investors need to pay more attention to it.