Structurally dynamic spin market networks

The agent-based model of stock price dynamics on a directed evolving complex network is suggested and studied by direct simulation. The stationary regime is maintained as a result of the balance between the extremal dynamics, adaptivity of strategic variables and reconnection rules. The inherent structure of node agent "brain" is modeled by a recursive neural network with local and global inputs and feedback connections. For specific parametric combination the complex network displays small-world phenomenon combined with scale-free behavior. The identification of a local leader (network hub, agent whose strategies are frequently adapted by its neighbors) is carried out by repeated random walk process through network. The simulations show empirically relevant dynamics of price returns and volatility clustering. The additional emerging aspects of stylized market statistics are Zipfian distributions of fitness.Comment: 13 pages, 5 figures, accepted in IJMPC, references added, minor changes in model, new results and modified figure

The co-evolutionary dynamics of directed network of spin market agents

The spin market model [S. Bornholdt, Int.J.Mod.Phys. C 12 (2001) 667] is extended into co-evolutionary version, where strategies of interacting and competitive traders are represented by local and global couplings between the nodes of dynamic directed stochastic network. The co-evolutionary principles are applied in the frame of Bak - Sneppen self-organized dynamics [P. Bak, K. Sneppen, Phys. Rev. Letter 71 (1993) 4083] that includes the processes of selection and extinction actuated by the local (node) fitness. The local fitness is related to orientation of spin agent with respect to instant magnetization. The stationary regime characterized by a fat tailed distribution of the log-price returns with index $\alpha\simeq 3.6$ (out of the Levy range) is identified numerically. The non-trivial consequence of the extremal dynamics is the partially power-law decay (an effective exponent varies between -0.3 and -0.6) of the autocorrelation function of volatility. Broad-scale network topology with node degree distribution characterized by the exponent $\gamma=1.8$ from the range of social networks is obtained.Comment: 10 pages, 4 figures. accepted for publication in Physica

A self-adjusted Monte Carlo simulation as model of financial markets with central regulation

Properties of the self-adjusted Monte Carlo algorithm applied to 2d Ising ferromagnet are studied numerically. The endogenous feedback form expressed in terms of the instant running averages is suggested in order to generate a biased random walk of the temperature that converges to criticality without an external tuning. The robustness of a stationary regime with respect to partial accessibility of the information is demonstrated. Several statistical and scaling aspects have been identified which allow to establish an alternative spin lattice model of the financial market. It turns out that our model alike model suggested by S. Bornholdt, Int. J. Mod. Phys. C {\bf 12} (2001) 667, may be described by L\'evy-type stationary distribution of feedback variations with unique exponent $\alpha_1 \sim 3.3$. However, the differences reflected by Hurst exponents suggest that resemblances between the studied models seem to be nontrivial.Comment: 19 pages, 9 figures, 30 reference