Structural stochastic volatility in asset pricing dynamics: Estimation and model contest

Abstract

In the framework of small-scale agent-based financial market models, the paper starts out from the concept of structural stochastic volatility, which derives from different noise levels in the demand of fundamentalists and chartists and the time-varying market shares of the two groups. It advances several different specifications of the endogenous switching between the trading strategies and then estimates these models by the method of simulated moments (MSM), where the choice of the moments reflects the basic stylized facts of the daily returns of a stock market index. In addition to the standard version of MSM with a quadratic loss function, we also take into account how often a great number of Monte Carlo simulation runs happen to yield moments that are all contained within their empirical confidence intervals. The model contest along these lines reveals a strong role for a (tamed) herding component. The quantitative performance of the winner model is so good that it may provide a standard for future research.JEL classification: D84; G12; G14; G15.

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

“…We believe that the aforementioned figures can be considered a success, and present a challenge to other models of similar complexity. Regarding the analytical underpinnings of the present model's dynamic properties, the switching mechanism of which is based on the transition probability approach, it may be worthwhile to attempt a similar analysis for its "twin" model, which is based on the discrete choice approach and fared so well in the model contest discussed in Franke and Westerhoff (2011b). In this sense, the paper is more of a stimulus for further research than a final once-and-for-all result.…”

Heterogeneity, spontaneous coordination and extreme events within large-scale and small-scale agent-based financial market models

“…These ten summary statistics are presented together with the lower and upper boundaries of their 95% conficence intervals in Table 1. The computation of the confidence intervals follows also Franke and Westerhoff (2012); see their Appendix A and To evaluate how well their model is able to match the moments, Franke and Westerhoff (2012) used the concept of a joint moment coverage ratio, which measures the fraction of simulation runs for which all nine simulated moments jointly are contained in the 95 percent confidence intervals of their empirical counterparts. For instance, with their estimated parameter setting they obtained a JMCR(09) score, i.e.…”

“…Taking the original nine moments of Franke and Westerhoff (2012) into account, the model produces a JMCR(09) score of about 27 percent. Also the matching of the individual nine moments is quite satisfactory.…”

“…To be more precise, Franke and Westerhoff (2012) quantify the stylized facts of financial markets with the help of nine moments (summary statistics). Moreover, they define a so-called joint moment coverage ratio, which measures the fraction of simulation runs for which all nine simulated moments jointly drop into the 95 percent confidence intervals of their empirical counterparts.…”

“…For our setup, we obtain a JMCR score of about 30 percent. However, we modify the JMCR score of Franke and Westerhoff (2012) by adding a tenth summary statistic. Besides the tail index at the 5 percent level, we also take the tail index at the 2.5 percent level into account.…”