This article extends the HAR‐CJN model proposed by Andersen, Bollerslev, and Huang (Journal of Econometrics, 2011, 160, 176–189) and explores the role of overnight information and leverage effects in improving volatility forecasting. To explore the interaction between different components of daily volatility, this paper attempts to separately model the dynamics of continuous variation, the discontinuous jump, and the overnight return variance by including leverage effects. The findings show that lagged continuous and discontinuous jump variations generate significant impacts on future continuous segments, discontinuous jump segments, and the overnight return variance. Furthermore, in addition to the usual leverage effects, additional leverage effects with respect to overnight returns are found to play a significant role in volatility forecasting. Finally, out‐of‐sample forecasts are investigated; the results show that the new HAR‐CJN model can describe and predict daily volatility more accurately than other HAR models.