Document-level event argument extraction (EAE) aims to extract structured event information from a document. In this paper, we first identify the issue of the long-tail distribution of argument roles in document-level event extraction datasets. This makes it challenging to extract low-frequency argument roles, despite their potential inclusion of crucial semantic information that enriches event descriptions. However, the manual annotation for these rare argument roles is costly. In contrast, generating synthetic data with Large Language Models (LLMs) is cost-effective and has demonstrated the ability to produce fluent and coherent text. Current research only conducts augmentation at the sample level, overlooking these rare argument roles, and is limited to sentence-level data augmentation, struggling to ensure the integrity of event arguments. Context-level augmentation enables more precise and fine-grained supplementation of arguments, and it poses greater challenges in quality control. In our work, we propose FineCSDA, a method integrating fine-grained data augmentation at both sample and context levels, which contains two novel and effective modules. The Sample-level Data Augmentation Module (SDAM) generates document-level samples of rare event types using the LLMs to increase the number of rare argument roles belonging to these rare event types. The Context-level Data Augmentation Module (CDAM) supplements argument roles that are inherently rare within common event types by utilizing LLMs to generate missing arguments and their corresponding contexts. Experimental results demonstrate that FineCSDA is capable of generating high-quality textual data and effectively improving the extraction performance of rare arguments.