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Global warming and rare weather caused by climate change continue to affect ecosystems, human health, and economic systems, which pose serious climate risk challenges for humanity. To address and adapt to climate change risks and to facilitate the process of achieving carbon peaking and carbon-neutral targets, the financial industry has become more concerned about the information spillover effects of extreme climate events on green financial products. Therefore, this paper adopts the Southern Oscillation Index (SOI) to describe climate change and investigates the influence of the SOI on the volatility of the NASDAQ OMX Green Economy Index (OMX-GEI) under a variant of the Double Asymmetric GARCH-MIDAS (DA-GM-X) model. The results show that the SOI provides relevant information for OMX-GEI volatility forecasting and the DA-GM-X model yields outstanding forecasting performance in statistical and economic terms. This conclusion indicates that considering SOI and its asymmetry changes can significantly improve the prediction accuracy of econometric models. Also, several robustness tests confirm our findings. Overall, the findings of this paper suggest that to achieve the two-carbon goal and combat climate change, governments should pay more attention to policy formulation that combines environment, climate, health, energy, and economy, and actively promote green, low-carbon, and sustainable energy development globally.