Volatility exchanges between equity markets and oil markets are vital for portfolio designing and risk management. This study empirically analyses the interdependence of stock and oil market for G7 countries. For econometric estimations, we used the data of G7 countries� stock markets for the period of 2000-2016. Dynamic conditional correlation and corrected dynamic conditional correlation are employed for symmetric estimation. We find differences in the magnitudes of negative and positive oil price shocks of G7 countries. The study also uses the asymmetric estimations to examine the response of different shocks, and the variance and covariance series of these estimations are used for portfolio optimization and hedging of stock and oil assets. The findings of symmetric and asymmetric estimations depict that past news and lagged volatility have a significant impact on the current conditional volatility of G7 stock markets. On the contrary, the current conditional volatility in the oil market is less dependent on past news and lagged volatility in the oil market. Our results portray that G7 stock markets are more sensitive to past news and lagged volatility than oil markets. FIGARCH and FIEGARCH provide evidence of an intermediate range of persistence of volatility. Finally, portfolio estimations report the importance of oil assets to form an optimal portfolio that can minimize the portfolio risk without changing the expected return. Based on our findings, we suggest that investors and portfolio managers of G7 countries should formulate a portfolio of stock and oil assets to manage their portfolio risk. © The Author(s) 2019.