Abstract This paper studies the comovement between volatility of the equity market and the oil market, both for implied and realized volatilities. The wavelet methodology enables us to study this relationship on various time scales. We find that there is a strong comovement between the volatilities of the two markets. However, this comovement is time-varying and depends on the time scale. It is strong at yearly horizon, but much weaker at horizons of a few days. Moreover, implied volatility of the stock market leads the implied volatility of the oil market, whereas no such relationship is observed for realized volatilities.