Power-Law Behaviour, Heterogeneity, and Trend Chasing

Long-range dependence in volatility is one of the most prominent examples in financialmarket research involving universal power laws. Its characterization has recently spurredattempts to provide some explanations of the underlying mechanism. This paper contributesto this recent line of research by analyzing a simple market fraction asset pricing model withtwo types of traders ? fundamentalists who trade on the price deviation from estimatedfundamental value and trend followers whose conditional mean and variance of the trend areupdated through a geometric learning process. Our analysis shows that agent heterogeneity,risk-adjusted trend chasing through the geometric learning process, and the interplay of noisyfundamental and demand processes and the underlying deterministic dynamics can be thesource of power-law distributed fluctuations. In particular, the noisy demand plays animportant role in the generation of insignificant autocorrelations (ACs) on returns, while thesignificant decaying AC patterns of the absolute returns and squared returns are moreinfluenced by the noisy fundamental process. A statistical analysis based on Monte Carlo simulations is conducted to characterize the decay rate. Realistic estimates of the power-lawdecay indices and the (FI)GARCH parameters are presented.