Estimation of sentiment effects in financial markets : a simulated method of moments approach

We take the model of Alfarano et al. (Journal of Economic Dynamics & Control 32, 2008, 101-136) as a prototype agent-based model that allows reproducing the main stylized facts of financial returns. The model does so by combining fundamental news driven by Brownian motion with a minimalistic mechanism for generating boundedly rational sentiment dynamics. Since we can approximate the herding component among an ensemble of agents in the aggregate by a Langevin equation, we can either simulate the model in full at the micro level, or investigate the impact of sentiment formation in an aggregate asset pricing equation. In the simplest version of our model, only three parameters need to be estimated. We estimate this model using a simulated method of moments (SMM) approach. As it turns out, sensible parameter estimates can only be obtained if one first provides a rough "mapping" of the objective function via an extensive grid search. Due to the high correlations of the estimated parameters, uninformed choices will often lead to a convergence to any one of a large number of local minima. We also find that even for large data sets and simulated samples, the efficiency of SMM remains distinctly inferior to that of GMM based on the same set of moments. We believe that this feature is due to the limited range of moments available in univariate asset pricing models, and that the sensitivity of the present model to the specification of the SMM estimator could carry over to many related agent-based models of financial markets as well as to similar diffusion processes in mathematical finance.