  Atoms and molecules are important conceptual entities we invented to
understand the physical world around us. The key to their usefulness lies in
the organization of nuclear and electronic degrees of freedom into a single
dynamical variable whose time evolution we can better imagine. The use of such
effective variables in place of the true microscopic variables is possible
because of the separation between nuclear/electronic and atomic/molecular time
scales. Where separation of time scales occurs, identification of analogous
objects in financial markets can help advance our understanding of their
dynamics. To detect separated time scales and identify their associated
effective degrees of freedom in financial markets, we devised a two-stage
statistical clustering scheme to analyze the price movements of stocks in
several equity markets. Through this two-time-scale clustering analysis, we
discovered a hierarchy of levels of self-organization in real financial
markets. We call these statistically robust self-organized dynamical structures
financial atoms, financial molecules, and financial supermolecules. In general,
the detailed compositions of these dynamical structures cannot be deduced based
on raw financial intuition alone, and must be explained in terms of the
underlying portfolios, and investment strategies of market players. More
interestingly, we find that major market events such as the Chinese Correction
and the Subprime Crisis leave many tell-tale signs within the correlational
structures of financial molecules.
