Spin-glass like network model for stock market

Summary

A statistical physics model for the collective price changes of stock portfolios is proposed. That is an analogue to spin glass model (Mezard et al. 1987) for disordered magnetic system. In this model the time series of price changes are coded into the sequences of up and down spins. The Hamiltonian of the system is expressed by long-range spin-spin interactions as in SherringtonKirtpatrick (S-K) model (Sherrington et al. 1975) of spin glass. The interaction coefficients between two stocks are determined by empirical using fluctuationresponse theorem.

Our theory is applied to price changes of stocks sampled at two time intervals, i.e., 1, 10-minutes, in Dow-Jones (D-J) industrial portfolio. Monte Carlo simulations are performed based on the model. The resultant probability densities of the system energy and magnetization show the remarkable fit of the equilibrium curve to empirical data in the study of 1-minute price changes. This result clarify that the concept of energy fully works even in economical systems such as financial markets. A small deviation is observed for 10-minutes price changes. The reason for this deviation of data from the theoretical prediction is briefly mentioned.