Hamiltonian in Financial Markets

Abstract

A statistical physics model for the time evolutions of stock portfolios is proposed. 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 introduced and is expressed by spin-spin interactions as in spin glass models of disordered magnetic systems. The interaction coefficients between two stocks are determined by empirical data coded into up and down spin sequences using fluctuation-response theorem. Monte Carlo simulations are performed and the resultant probability densities of the system energy and magnetization show good agreement with empirical data.