Emergence of Statistical Financial Factors by a Diffusion Process

Factor models characterize the joint behavior of large sets of financial assets through a smaller number of underlying drivers. We develop a network-based framework in which factors emerge naturally from the structure of interactions among assets rather than being imposed statistically. The market is modeled as a system of coupled iterated maps, where assets' return depends on its own past returns and those of related assets. Effectively modeling the influence of irrational traders whose decisions are based on the past movements of a collection of stocks. The interaction structure between stock returns is defined by a coupling matrix derived from an orthogonal transformation of a Laplacian matrix that gradually links initially isolated clusters into a fully connected network. Within this structure, stable patterns of co-movement arise and can be interpreted as financial factors. The relationship between the initial clustering and the number of observed factors is consistent with a center manifold reduction. We identify an optimal regime in which assets' variance is effectively explained by the set of factors produced by the network. Our framework offers a structural perspective based on interaction-based factor formation and dimension reduction in financial markets.