This paper examines the return links and volatility spillovers between US, Japan and European stock markets over the turbulent period 2005-2012. We use a recent generalized VARGARCH model which allows for transmission in return and volatility. The results show that American stock market is mostly influenced by past shocks and volatilities. Besides, for all markets under investigation, the past own volatilities is stronger driver in determining future volatility. This implies that a market’s fundamentals have more influence on volatility than shocks or news. Moreover, our results show the existence of shocks and volatility transmission between only US and EMU. For the Japanese market, only the past own conditional volatility and shocks are allowed to impact the future volatility. Our findings have important implications for the presence of diversification opportunities for portfolios investors.