Algebraic Combinatorics in Financial Data Analysis: Modeling Sovereign Credit Ratings for Greece and the Athens Stock Exchange General Index

This study investigates the relationship between sovereign credit rating transitions and domestic equity market performance, focusing on Greece from 2004 to 2024. Although credit ratings are central to sovereign risk assessment, their immediate influence on financial markets remains contested. This research adopts a multi-method analytical framework combining algebraic combinatorics and time-series econometrics. The methodology incorporates the construction of a directed credit rating transition graph, the partially ordered set representation of rating hierarchies, rolling-window correlation analysis, Granger causality testing, event study evaluation, and the formulation of a reward matrix with optimal rating path optimization. Empirical results indicate that credit rating announcements in Greece exert only modest short-term effects on the Athens Stock Exchange General Index, implying that markets often anticipate these changes. In contrast, sequential downgrade trajectories elicit more pronounced and persistent market responses. The reward matrix and path optimization approach reveal structured investor behavior that is sensitive to the cumulative pattern of rating changes. These findings offer a more nuanced interpretation of how sovereign credit risk is processed and priced in transparent and fiscally disciplined environments. By bridging network-based algebraic structures and economic data science, the study contributes a novel methodology for understanding systemic financial signals within sovereign credit systems.