COMPLEXITY AND MULTIFRACTAL OF VOLATILITY DURATION FOR AGENT-BASED FINANCIAL DYNAMICS AND REAL MARKETS

Abstract

A random agent-based financial model is developed and investigated by the finite-range multitype contact dynamic system, in an attempt to reproduce and study the dynamics of financial markets. And an analysis method of detecting duration and intensity relationship in volatility series is introduced, called the volatility duration analysis. Then the auto-correlation analysis suggests that there exists evident volatility clustering feature in absolute volatility durations for the simulation data and the real data. Besides, the Lempel–Ziv complexity analysis is applied to study the complexity of the returns, the corresponding absolute returns and the volatility duration returns, which can reflect the fluctuation behaviors, the volatility behaviors and the volatility duration behaviors. At last, the multifractal phenomena of volatility durations of returns are comparatively studied for Shanghai Composite Index and the proposed model by multifractal detrended fluctuation analysis.