A generalization of the Topological Tail Dependence theory: From indices to individual stocks

This study investigates the Topological Tail Dependence (TTD) theory's applicability to individual stock volatility and high dimensions. Utilizing a comprehensive dataset from the S&P 100, the research employs various methodologies to test the predictions and implications of the TTD theory. The theory's main prediction of Wasserstein Distance's predictive utility, particularly in nonlinear models during volatile periods, is confirmed. The research suggests extending the TTD theory's application to various financial instruments and incorporating dynamic topological features to enhance understanding market dynamics. This study validates the TTD theory for individual stocks and highlights the necessity of topological considerations in financial modeling, promising advancements in financial econometrics and risk management strategies.