Given the exponential growth in the number of documents on the web in recent years, there is an increasing demand for accurate models to extract keyphrases from such documents. Keyphrase extraction is the task of automatically identifying representative keyphrases from the source document. Typically, candidate keyphrases exhibit latent hierarchical structures embedded with intricate syntactic and semantic information. Moreover, the relationships between candidate keyphrases and the document also form hierarchical structures. Therefore, it is essential to consider these latent hierarchical structures when extracting keyphrases. However, many recent unsupervised keyphrase extraction models overlook this aspect, resulting in incorrect keyphrase extraction. In this paper, we address this issue by proposing a new hyperbolic ranking model (HyperRank). HyperRank is designed to jointly model global and local context information for estimating the importance of each candidate keyphrase within the hyperbolic space, enabling accurate keyphrase extraction. Experimental results demonstrate that HyperRank significantly outperforms recent state-of-the-art baselines.