Abstract:
Long-range dependence in volatility is one of the most prominent examples in financial
market research involving universal power laws. Its characterization has recently spurred
attempts to provide some explanations of the underlying mechanism. This paper contributes
to this recent line of research by analyzing a simple market fraction asset pricing model with
two types of traders – fundamentalists who trade on the price deviation from estimated
fundamental value and trend followers whose conditional mean and variance of the trend are
updated through a geometric learning process. Our analysis shows that agent heterogeneity,
risk-adjusted trend chasing through the geometric learning process, and the interplay of noisy
fundamental and demand processes and the underlying deterministic dynamics can be the
source of power-law distributed fluctuations. In particular, the noisy demand plays an
important role in the generation of insignificant autocorrelations (ACs) on returns, while the
significant decaying AC patterns of the absolute returns and squared returns are more
influenced 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-law
decay indices and the (FI)GARCH parameters are presented.
