Emergence of Statistical Financial Factors by a Diffusion Process
This study addresses the limitation of traditional factor models, which rely on exogenously specified factors and fail to capture endogenous interaction mechanisms among assets. The authors propose a network-coupled map-based model of financial markets that generates statistical factors endogenously through dynamic asset interactions. By applying an orthogonal transformation of the graph Laplacian matrix and employing center manifold dimensionality reduction, the model reveals an intrinsic link between initial asset clustering structures and the emergent number of factors. Furthermore, it integrates coupled iterative maps with network diffusion dynamics to simulate the impact of irrational trading behavior on asset prices. Empirical experiments demonstrate that, within an optimal parameter regime, the endogenously generated factors effectively explain cross-sectional variance in asset returns, thereby validating both the feasibility and explanatory power of the proposed interaction-driven factor mechanism.