Volatility cascade and market dynamics

Price fluctuations in speculative market dynamics have interesting statistical properties. Temporal properties include: (i) vanishing autocorrelation of return, (ii) intermittency and long-memory in the magnitude of return called volatility, (iii) self-similarity of volatilities for different time-scales ("volatility cascade"). These properties in a strongly correlated regime from minutes to months are crucial for understanding markets and to control risk. The author briefly reviews how one can characterize the statistical properties of such a non-equilibrium nature. Next, adaptive agent models with opinion-epidemics and speculative bubbles are considered, including T. Lux's (1998) stochastic model. The origin of volatility clustering and cascade might be understood as aggregate behavior of human speculations, and the dynamics might be regarded as a kind of on-off intermittency.