Effect of boundary conditions on stochastic Ising-like financial market price model

Price formation in financial markets based on the 2D stochastic Ising-like spin model is proposed, with a randomized inverse temperature of each trading day. The statistical behaviors of returns of this financial model are investigated for zero boundary condition and five different classes of mixed boundary conditions. For comparison with actual financial markets, we also analyze the statistical properties of Shanghai Stock Exchange (SSE) composite Index, Shenzhen Stock Exchange (SZSE) component Index and Hushen 300 Index. Fluctuation properties, fat-tail phenomena, power-law distributions and fractal behaviors of returns for these indexes and the simulative data are studied. With the plus boundary condition, for example the boundary condition A (6), the value of market depth parameter A is smaller than those of the corresponding market depth parameters A with zero boundary condition A (1) and weak mixed boundary conditions A (2) and A (3). And the changing range of tails exponents of boundary condition A (6) is much smaller than those of the other five boundary conditions.