In this paper, we examine whether jumps matter in both equity market returns and integrated volatility. For this purpose, we use the swap variance (SwV) approach to identify monthly jumps and estimated realized volatility in prices for both developed and emerging markets from February 2001 to February 2020. We find that jumps arise in all equity markets; however, emerging markets have more jumps relative to developed markets, and positive jumps are more frequent than negative jumps. In emerging markets, the markets with average volatility earn higher returns during jump periods; however, highly volatile markets earn higher returns during jump periods in developed markets. Furthermore, markets with low continuous returns and high volatility are more adversely affected during periods of negative jumps. The average ratio of jump variations to total variation shows considerable variations due to jumps. Integrated volatility is high during periods of negative jumps, and this pattern is consistent in both developed and emerging markets. Moreover, the peak volatility of stock markets is observed during periods of crises. The implication of this study is useful in the asset pricing model, risk management, and for individual investors and portfolio managers for both developed and emerging markets.