A nonlinear structural model for volatility clustering

A simple nonlinear structural model of endogenous belief heterogeneity is proposed. News about fundamentals is an IID random process, but nevertheless volatility clustering occurs as an endogenous phenomenon caused by the interaction between different types of traders, fundamentalists and technical analysts. The belief types are driven by adaptive, evolutionary dynamics according to the success of the prediction strategies as measured by accumulated realized profits, conditioned upon price deviations from the rational expectations fundamental price. Asset prices switch irregularly between two different regimes --periods of small price fluctuations and periods of large price changes triggered by random news and reinforced by technical trading -- thus, creating time varying volatility similar to that observed in real financial data.

Nonlocal onset of instability in an asset pricing model with heterogeneous agents

Empirical time series of financial market data, like day-to-day stock returns, exhibit the phenomenon that although usually tomorrow's price is unpredictable, the absolute value of the price change is correlated with the magnitude of past price changes; though the corresponding correlation coefficients are not very large, they are significantly different from zero. This phenomenon is known as `volatility clustering' in the financial liturature. In this note a micro-economic model of volatility clustering, introduced by Gaunersdorfer and Hommes, will be analysed. The deterministic skeleton of the model has a Chenciner bifurcation, and hence periodic points and invariant quasi-periodic circles coexisting with the `fundamental' equilibrium. Adding noise in form of stochastic supply shocks, volatility clustering is generated by the system jumping between the bases of attraction of the fundamental equilibrium (low volatility), and that of the non-fundamental attractor (high volatility).

Bifurcation Routes to Volatility Clustering under Evolutionary Learning

A simple asset pricing model with two types of adaptively learning traders, fundamentalists and technical analysts, is studied. Fractions of these trader types, which are both boundedly rational, change over time according to evolutionary learning, with technical analysts conditioning their forecasting rule upon deviations from a benchmark fundamental. Volatility clustering arises endogenously in this model. Two mechanisms are proposed as an explanation. The first is coexistence of a stable steady state and a stable limit cycle, which arise as a consequence of a so-called Chenciner bifurcation of the system. The second is intermittency and associated bifurcation routes to strange attractors. Both phenomena are persistent and occur generically. Simple economic intuition why these phenomena arise in nonlinear multi-agent evolutionary systems is provided.

Time Averages for Heteroclinic Attractors

In the neighborhoods of attracting heteroclinic cycles, the time averages fail to converge for almost all initial conditions, but spiral closer and closer to the boundary of a polygon. This is shown by using a Poincare-section argument

The Dynamics of Asymmetric Games

A game dynamical analysis of a simple asymmetric game (two roles with two alternatives each) shows that an interesting class of "semi-stable" heteroclinic cycles leading to a highly unpredictable behavior can occur in a robust way. Biological examples related to conflicts over ownership and parental investment are analyzed

Heterogeneous Agent Models: Two Simple Case Studies

These notes review two simple heterogeneous agent models in economics and finance. The first is a cobweb model with rational versus naive agents introduced in Brock and Hommes (1997). The second is an asset pricing model with fundamentalists versus technical traders introduced in Brock and Hommes (1998). Agents are boundedly rational and switch between different trading strategies, based upon an evolutionary fitness measure given by realized past profits. Evolutionary switching creates a nonlinearity in the dynamics. Rational routes to randomness, that is, bifurcation routes to complicated dynamical behaviour occur when agents become more sensitive to differences in evolutionary fitness

The adaptiveness in stock markets: testing the stylized facts in the DAX 30

© 2017, Springer-Verlag Berlin Heidelberg. By testing a simple asset pricing model of heterogeneous agents to characterize the power-law behavior of the DAX 30 from 1975 to 2007, we provide supporting evidence on empirical findings that investors and fund managers use combinations of fixed and switching strategies based on fundamental and technical analysis when making investment decisions. A mechanism analysis based on the calibrated model provides a behavioral insight into the explanatory power of rational switching behavior of investors on the volatility clustering and long range dependence in return volatility