||This thesis proposes computational framework for empirical estimation of Financial Agent-Based Models (FABMs) that does not rely upon restrictive theoretical assumptions. First, we develop a two-step estimation methodology for one of the historically first FABMs—the stochastic cusp catastrophe model. Our method allows us to apply catastrophe theory to stock market returns with time-varying volatility and to model stock market crashes. The methodology is empirically tested on nearly 27 years of U.S. stock market returns. We find that the U.S. stock market’s downturns were more likely to be driven by the endogenous market forces during the first half of the studied period, while during the second half of the period, the exogenous forces seem to be driving the market’s instability. The results suggest that the proposed methodology provides an important shift in the application of catastrophe theory to stock markets. Second, we customise a recent methodology of the Non-Parametric Simulated Maximum Likelihood Estimator (NPSMLE) based on kernel methods by Kristensen & Shin (2012) and elaborate its capability for FABMs estimation purposes. To start with, we apply the methodology to the most famous and widely analysed model of Brock & Hommes (1998). We extensively test finite sample properties of the estimator via Monte Carlo simulations and show that important theoretical features of the estimator, the consistency and asymptotic efficiency, also hold in small samples for the model. We also verify smoothness of the simulated log-likelihood function and identification of parameters. Main empirical results of our analysis are the statistical insignificance of the switching coefficient β but markedly significant belief parameters defining heterogeneous trading regimes with an absolute superiority of trend-following over contrarian strategies and a slight proportional dominance of fundamentalists over trend following chartists. Finally, we apply the NPSMLE to a stylised herding FABM developed by Alfarano et al. (2008). Empirical estimates of parameters governing opinion switching indicate unimodal distribution of the market sentiment variable. Model behaviour is thus characterised by a general tendency to gradually revert back to a balanced sentiment and theoretically expected performance of the estimator. Rolling window estimation reveals interesting model dynamics and clearly captures jumps in the ‘herding-based’ opinion switching parameter and elevated fundamental volatility in turbulent times.