The intricacy of the financial systems reflected in bilateral ties has piqued the interest of many specialists. In this research, we introduce network-induced soft sets, a novel mathematical model for studying the dynamics of a financial stock market with several orders of interaction. To achieve its intelligent parameterization, this model relies on the bilateral connections between economic actors, who are agents in a financial network, rather than relying on any other single feature of the network itself. Our study also introduces recently developed statistical measures for network-induced soft sets and provides an analysis of their application to the study of financial markets. Findings validate the efficacy of this novel method in assessing the effects of various economic stress periods registered in Borsa Istanbul.