Following Alfarano et al. [Estimation of agent-based models: the case of an asymmetric herding model, Comput. Econ. 26 (2005) 19–49; Excess volatility and herding in an artificial financial market: analytical approach and estimation, in: W. Franz, H. Ramser, M. Stadler (Eds.), Funktionsfähigkeit und Stabilität von Finanzmärkten, Mohr Siebeck, Tübingen, 2005, pp. 241–254], we consider a simple agent-based model of a highly stylized financial market. The model takes Kirman’s ant process [A. Kirman, Epidemics of opinion and speculative bubbles in financial markets, in: M.P. Taylor (Ed.), Money and Financial Markets, Blackwell, Cambridge, 1991, pp. 354–368; A. Kirman, Ants, rationality, and recruitment, Q. J. Econ. 108 (1993) 137–156] of mimetic contagion as its starting point, but allows for asymmetry in the attractiveness of both groups. Embedding the contagion process into a standard asset-pricing framework, and identifying the abstract groups of the herding model as chartists and fundamentalist traders, a market with periodic bubbles and bursts is obtained. Taking stock of the availability of a closed-form solution for the stationary distribution of returns for this model, we can estimate its parameters via maximum likelihood. Expanding our earlier work, this paper presents pertinent estimates for the Australian dollar/US dollar exchange rate and the Australian stock market index. As it turns out, our model indicates dominance of fundamentalist behavior in both the stock and foreign exchange market.