Nonlinear Scaling Behavior of Visible Volatility Duration for Financial Statistical Physics Dynamics

The visibility graph algorithm is applied to convert the financial volatility duration series into the assortative complex network, in an attempt to investigate nonlinear scaling behaviors of volatility duration. The visibility graph maps a time series into a network, and the volatility duration describes the volatility consistently above or below a given data point in the volatility series. In order to comprehensively study the visible volatility duration series, a financial Potts market dynamics model is developed, where the Potts model is an extension of the Ising model with the integer q-state interacting spins on a two-dimensional lattice, and depicts the interaction strength among the agents. For the proposed model, we make an approach focusing on the scaling exponent analysis, including vertex degree distribution, fractal scaling and hierarchical property. The validity of the price model is verified through the comparatively empirical research with the real market data.