Statistical volatility duration and complexity of financial dynamics on Sierpinski gasket lattice percolation

Abstract

A novel agent-based financial dynamics is established based on the percolation system on Sierpinski gasket lattice to reproduce the statistical characteristics of financial markets. Sierpinski gasket lattice is a fractal-like graph which corresponds to the fractal well-known Sierpinski gasket. Modeling a financial dynamics on Sierpinski gasket lattice is a new approach in financial micro-mechanism construction. In an attempt to investigate the statistical properties of returns and prove the feasibility of the proposed model, two new nonlinear statistics maximum and average monotonous volatility duration are introduced in this work for the first time, which describe the trend of volatility of return time series in financial markets. Furthermore, a new method CMCID is proposed to measure the synchronization and similarity behaviors of return volatility duration in multiscale, the results show that the pairs of real data and simulated data have synchronization, and the synchronization becomes stronger when the scale increases And the power-law distribution is employed to investigate the corresponding statistical properties, which shows that the proposed model shares a common power-law distribution with regard to monotonous volatility duration. The empirical results show that the simulated series from the financial model and the historical data share common statistical properties, which indicate that the proposed model is reasonable in terms of volatility behavior.