Abstract This study attempts to contribute to the literature on stock markets and energy prices by examining the dynamic volatility and volatility transmission between oil and Ghanaian stock market returns in a multivariate setting using the recently developed VAR–GARCH, VAR–AGARCH and DCC–GARCH frameworks. In turn, the models' results are used to compute and analyze the optimal weights and hedge ratios for oil-stock portfolio holdings. For comparison purposes and to put the paper more in the perspective of West Africa, the Nigerian stock market is also included in the analysis. Our findings point to the existence of significant volatility spillover and interdependence between oil and the two stock market returns. While spillover effects are stronger for Nigeria, the transmission of volatility is much more apparent from oil to stock than from stock to oil in the case of Ghana. Also, the study demonstrates evidence of short-term predictability in oil and stock price changes through time and reveals that conditional volatility changes more rapidly as result of substantial effects of past volatility rather than past news/shocks for all market returns. Moreover, we show that there is a slightly more effective hedge in the two stock markets under the DCC–GARCH framework (our preferred model) compared to the other two models, although hedging effectiveness is much greater for Ghana. On the whole, our findings for optimal hedge ratios are consistent with other studies and particularly the view that oil assets should be an integral part of a diversified portfolio of stocks and suggest that a better understanding of volatility links is crucial for portfolio management in the presence of oil price risk. Finally, the existence of multivariate asymmetric effects and dynamic conditional correlations as revealed by the VAR–AGARCH and DCC–GARCH models make it clear that the assumptions of symmetric effects and constant conditional correlations are not supported empirically.