In the rapidly maturing financial landscape of India, understanding the exogenous and endogenous drivers of market stability is critical for ensuring institutional resilience and maintaining retail investor confidence. Between 2015 and 2025, the Indian capital markets underwent a structural metamorphosis, primarily shaped by the shifting interplay between Foreign Institutional Investors (FIIs) and Domestic Institutional Investors (DIIs). This research addresses a vital gap in current literature by quantifying how these institutional flows induce volatility at the sectoral level, moving beyond aggregate index analysis to provide a granular decomposition of market dynamics.Utilizing a rigorous quantitative framework—incorporating the Augmented Dickey-Fuller (ADF) test for stationarity, the ARCH-LM test for heteroskedasticity, and GARCH (1,1) modeling—this study evaluates four key BSE sectoral indices: IT, Oil & Gas, Power, and Healthcare. Our longitudinal analysis reveals a distinct "dual-engine" dynamic: while FIIs function as "volatility igniters" sensitive to global macroeconomic shifts, DIIs have emerged as "economic anchors," providing critical counter-cyclical stability during foreign capital reversals. The findings establish a strategic roadmap for market resilience, demonstrating that the maturity of domestic institutions serves as the ultimate guardian against systemic shocks in a globally integrated economy.