Statistical Methods in Finance 2024

Decoding Market Disorder: A Data Science Perspective

By: Anirban Chakraborti
Jawaharlal Nehru University, New Delhi.

Financial markets are prime examples of "complex systems", characterized by dynamic correlations among asset price returns. These correlation patterns can change dramatically during significant market events, such as bubbles and crashes, resembling "critical phenomena" in physics. Our study employs eigenvalue decomposition and eigen-entropy, derived from eigenvector centralities in the cross-correlation matrix, to quantify "market disorder". A "phase space" is constructed to map different market events, revealing order-disorder transitions and phase separations. Also, financial markets have been modelled as inferential networks, where stocks are nodes and their pairwise correlations form edges. However, recent approaches focus on uncovering higher-order structures beyond simple pairwise relationships. Geometry-inspired tools, such as discrete Ricci curvatures, and topological data analysis (TDA) methods, like persistent homology, offer deeper insights into these intricate network structures. We present a comprehensive understanding of financial systems, capturing complex interactions that influence market dynamics, by integrating these data science approaches.