Why a simple herding model may generate the stylized facts of daily returns: explanation and estimation

• DOI: 10.1007/s11403-014-0140-6
• Publication Date: 2014-08-19T11:52:58Z
• Authors: Reiner Franke; Frank Westerhoff
• Keywords: autocorrelation pattern; 330; jel:D84; ddc:330; Structural stochastic volatility; G14; G15; 05 social sciences; jel:G12; structural stochastic volatility; method of simulated moments; jel:G14; jel:G15; D84; bootstrapped p-values; fat tails; 0502 economics and business; G12; structural stochastic volatility,method of simulated moments,autocorrelation pattern,fat tails,bootstrapped p-values

The paper proposes an elementary agent-based asset pricing model that, invoking the two trader types of fundamentalists and chartists, comprises four features: (i) price determination by excess demand; (ii) a herding mechanism that gives rise to a macroscopic adjustment equation for the market fractions of the two groups; (iii) a rush towards fundamentalism when the price misalignment becomes too large; and (iv) a stronger noise component in the demand per chartist trader than in the demand per fundamentalist trader, which implies a structural stochastic volatility in the returns. Combining analytical and numerical methods, the interaction between these elements is studied in the phase plane of the price and a majority index. In addition, the model is estimated by the method of simulated moments, where the choice of the moments reflects the basic stylized facts of the daily returns of a stock market index. A (parametric) bootstrap procedure serves to set up an econometric test to evaluate the model’s goodness-of-fit, which proves to be highly satisfactory. The bootstrap also makes sure that the estimated structural parameters are well identified.