Abstract: A quantile regression model was built under the smooth transition mechanism with the market volatility index (VIX) as smooth transition variable to study the non-linear effects of the US stock market on most of the global stock markets. The transition position of the smoothing mechanism model can describe the sensitive point of global stock market to the US stock market, and the transition slope describes the conversion rate of interconnectedness. The empirical results show that there does exist nonlinear mechanism transformation in the correlation of international stock markets, and that almost all global stock markets are subject to the impact of the US stock market. Moreover, under different quantiles, the conversion rates between different mechanism are not identical. Evident difference is found under low quantiles, which suggests that the correlation between financial markets is mainly due to tail-risk conduction. Then the collected data was divided into three sub samples and were studied respectively using the proposed model. The results show that there is a significant difference between position parameters during and after the crisis. During the crisis the position parameters decreased, and the correlation improved significantly under low quantiles，indicating that the proposed model is feasible to study the dynamic correlation between financial markets and that the exogenous variable VIX has a considerable influence on the correlation between financial markets. This provides a new perspective for international investors and policy makers to consider the impact of the US economy on global equity markets with the help of the VIX.

Key words: quantile regression, smoothing mechanism transition, volatility index, value at risk