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