Parameter descriptions are essential for improving developers' understanding of the source code and its functionality. An effective approach for generating descriptions for each parameter individually requires appropriate contextual information, typically represented as code or abstract syntax tree (AST). Prior research lacks a systematic investigation into how different granularities of context, their combinations, and parameter characteristics affect the effectiveness of parameter description generation. This study aims to address the gap by investigating the effectiveness of different types of contextual information, function-level context, parameter-related context and the integration of semantic and structural context, in generating parameter descriptions. Additionally, we analyze the impact of parameter characteristics, such as the number of parameters and naming conventions, on the quality of generated descriptions. The study revealed several key findings for parameter description generation: (1) trained-from-scratch deep learning models perform better with parameter-related code than with full code, whereas pre-trained models show no significant difference. (2) Full AST outperforms parameter-related AST across all models. (3) Combining semantic and structural information does not generally improve performance. (4) Models perform better with fewer function parameters (1 or 2), and performance decreases as the number of parameters increases. (5) Models perform best when parameter names are single dictionary words, and pre-trained models are more effective at handling combination names. These findings provide practical guidance for selecting appropriate contextual information and designing more effective parameter description generation approaches for future research in this domain.