This paper analyzes the asymmetric volatility spillovers across major financial markets. The good and bad volatility components are relative to positive and negative shocks, respectively. The proposed framework adds a great deal of information by separating the effects of good news and bad news on risk transmission, and by detecting the time variation in the asymmetric connectedness. Empirical evidence on the G7 stock market indices shows that the good and bad volatilities are transmitted with different time-varying intensities. Specifically, during the global financial crisis and the European sovereign debt crisis, the markets transmit, on average, more bad volatility than good volatility.