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Earnings conference calls are significant information events for volatility forecasting, which is essential for financial risk management and asset pricing. Although some recent volatility forecasting models have utilized the textual content of conference calls, the dialogue structures of conference calls and company relationships are almost ignored in extant literature. To bridge this gap, we propose a new model called Temporal Virtual Graph Neural Network (TVGNN) for volatility forecasting by jointly modeling conference call dialogues and company networks. Our model differs from existing models in several important ways. First, we propose to exploit more dialogue structures by encoding position, utterance, speaker role, and Q\&A segments. Second, we propose to encode the market states for volatility forecasting by extending the Gated Recurrent Units (GRU). Third, we propose a new method for constructing temporal company networks in which the messages can only flow from temporally preceding to successive nodes, and extend the Graph Attention Networks (GAT) for modeling company relationships. We collect conference call transcripts of S\&P500 companies from 2008 to 2019, and construct a dataset of conference call dialogues with additional information on dialogue structures and company networks. Empirical results on our dataset demonstrate the superiority of our model over competitive baselines for volatility forecasting. We also conduct supplementary analyses to examine the effectiveness of our model's key components and interpretability.