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

TL;DR

This paper introduces a self-adjusted Monte Carlo algorithm that autonomously tunes to criticality and models financial markets, revealing complex statistical behaviors similar to Levy distributions and highlighting nontrivial differences from existing models.

Contribution

The paper presents a novel self-adjusted Monte Carlo method that converges to criticality without external tuning and proposes a new spin lattice model for financial markets.

Findings

The model exhibits Levy-type stationary distributions with exponent ~3.3.

Robustness of the stationary regime despite partial information access.

Differences in Hurst exponents indicate complex dynamics distinct from previous models.

Abstract

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.