This paper explores if the crossproduct of return and realized volatility measure contributes to volatility forecasting. We find there is an asymmetric crossproduct effect in volatility and propose a realized asymmetric GARCH (henceforth RealAGARCH) model. The RealAGARCH model is a generalization to the absolute GARCH and the asymmetric GARCH. Moreover, the RealAGARCH model has a news impact surface instead of a news impact curve, which makes it different from other GARCH-like models. Empirical performance of the RealAGARCH model is evaluated on a variety of stock indices, and the results show dominance of RealAGARCH over the benchmark RealGARCH judging by either in-sample or out-of-sample forecasting performance. A battery of checks confirm the robustness of our findings and thus the importance of incorporating crossproduct effect into volatility forecasting.