This study investigates the impacts of asymmetry on the modeling and forecasting of realized volatility in the Japanese futures and spot stock markets. We employ heterogeneous autoregressive (HAR) models allowing for three types of asymmetry: positive and negative realized semivariance (RSV), asymmetric jumps, and leverage effects. The estimation results show that leverage effects clearly influence the modeling of realized volatility models. Leverage effects exist for both the spot and futures markets in the Nikkei 225. Although realized semivariance aids better modeling, the estimations of RSV models depend on whether these models have leverage effects. Asymmetric jump components do not have a clear influence on realized volatility models. While leverage effects and realized semivariance also improve the out-of-sample forecast performance of volatility models, asymmetric jumps are not useful for predictive ability. The empirical results of this study indicate that asymmetric information, in particular, leverage effects and realized semivariance, yield better modeling and more accurate forecast performance. Accordingly, asymmetric information should be included when we model and forecast the realized volatility of Japanese stock markets.