Nonlinear fluctuation behaviors of complex voter financial price dynamics on small-world network

To simulate the price fluctuation dynamics of financial markets, a novel financial price model is developed by the voter dynamic system on the Watts-Strogtz small-world network and the random jump process. The voter system is a classical statistical physics system, which describes the dynamics of voters' attitudes towards a certain topic in the mutual influence. The Watts-Strogtz small-world network is a special kind of complex networks, which can be used to study the transmission dynamics of different things in complex and real-world systems. The paper first attempts to use the voter dynamic system on the small-world network to reproduce the micro-mechanism of price fluctuations caused by the interaction among different investors in financial markets, where investors can potentially disseminate information and interact via additional long-distance contacts. Moreover, considering that external macro environments have the impact on price fluctuations in financial markets, this paper introduces the random jump process in the price model. The effectiveness of the proposed model can be verified by comparing price returns generated by the model with returns of several important stock indexes in terms of nonlinear fluctuation behaviors. First, some statistical behaviors of the fluctuation dynamics are explored, including distribution characteristics and autocorrelation. Moreover, based on the ensemble empirical mode decomposition method, multifractal behaviors and complexity behaviors of returns and the first three intrinsic mode functions are investigated. The empirical results show that the dynamical model can well simulate these nonlinear fluctuation behaviors of real markets.

Automated summary

This study develops a novel financial price model by utilizing the voter dynamic system on the Watts-Strogtz small-world network and the random jump process to simulate the price fluctuation dynamics of financial markets. The effectiveness of the model is verified through comparing price returns with returns of important stock indexes, showing that the model can well simulate nonlinear fluctuation behaviors of real markets. Additionally, statistical behaviors, multifractal behaviors, and complexity behaviors of returns are explored through empirical methods.