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.

为了模拟金融市场的价格波动动态，由Watts-Strogtz小世界网络上的投票者动态系统和随机跳跃过程开发了一种新颖的金融价格模型。选民系统是一个经典的统计物理系统，它描述了选民在相互影响中对某个主题的态度的动态变化。Watts-Strogtz小世界网络是一种特殊的复杂网络，可用于研究复杂和现实系统中不同事物的传输动力学。本文首先尝试使用小世界网络上的投票者动态系统来再现由金融市场中不同投资者之间的互动所引起的价格波动的微观机制，投资者可以在其中传播信息并通过其他长途联系进行互动。此外，考虑到外部宏观环境对金融市场价格波动的影响，本文介绍了价格模型中的随机跳跃过程。可以通过将模型产生的价格收益与几种重要股指的收益在非线性波动行为方面进行比较来验证所提出模型的有效性。首先，探讨了波动动力学的一些统计行为，包括分布特征和自相关。此外，基于整体经验模式分解方法，研究了收益的多重分形行为和复杂性行为以及前三个内在模式函数。