Complex and composite entropy fluctuation behaviors of statistical physics interacting financial model

Abstract

In an attempt to investigate and reproduce the fluctuation dynamics of price changes in financial markets, a novel complex random interacting financial price model is developed by combining voter interacting system with compound Poisson process. In this model, the dissemination of investors’ investment attitudes can simulate normal and frequent small price fluctuations of financial markets, while the random drastic jumps can capture undue and rare large price fluctuations as results of sudden economic events and political events in the markets. In order to verify the rationality of the model, some statistical characteristics of the model returns including fat-tail, power-law scaling, complexity and multifractal are compared with real returns by probability density functions, composite distance fuzzy entropy (C-FuzzyEn), matching energy and multifractal detrended fluctuation analysis. The C-FuzzyEn is a new entropy-based approach, based on fuzzy entropy and complexity-invariant, to measure the complexity behaviors of return series. The effectiveness analysis of C-FuzzyEn indicates that it has a higher estimation accuracy and stronger robustness than fuzzy entropy. The empirical results show that the price model is able to reproduce some important statistical properties of financial markets to a certain extent, and the complexity of returns for the proposed model increases when infection intensity or jump intensity increases.