The study empirically examines correlation and volatility transmission across international stock markets by employing Bivariate GARCH model. The study uses weekly data for five major stock indices such as S&P 500(USA), BSE 30 sensex (India), FTSE 100(U.K), Nikkei 225(Japan) and Ordinary Share Price Index (Australia) from 30^th January, 1998 to 30^th July, 2011. Long run and short run integrations are investigated through Johansen cointegration and vector error correction models respectively. The results of Johansen test show that long run co-integration is found across international stock indices prices. Further, results suggest that the arrival of external news is simultaneously received by US and Japan stock markets and then transmitted to other Asian and European stock markets. The results of bivariate GARCH model reveal that there is a bidirectional volatility spillover between US and Indian stock markets. This is due to fact that these two economies are strongly integrated through international trade and investment. Finally, results show that a unidirectional volatility spillover from Japan and United Kingdom to India.