Bayesian estimation and likelihood-based comparison of agent-based volatility models

The statistical description and modeling of volatility plays a prominent role in econometrics, risk management and finance. GARCH and stochastic volatility models have been extensively studied and are routinely fitted to market data, albeit providing a phenomenological description only. In contrast, agent-based modeling starts from the premise that modern economies consist of a vast number of individual actors with heterogeneous expectations and incentives. Observed market statistics then emerge from the collective dynamics of many actors following heterogeneous, yet simple rules. On the one hand, such models generate volatility dynamics, qualitatively matching several stylized facts. On the other hand, they illustrate the possible role of different mechanisms, such as chartist trading and herding behavior. Yet, rigorous and quantitative statistical fits are still mostly lacking. Here, we propose Hamiltonian Monte Carlo, an efficient and scalable Markov chain Monte Carlo algorithm, as a general method for Bayesian inference of agent-based models. In particular, we implement several models by Vikram and Sinha, Franke and Westerhoff and Alfarano, Lux and Wagner in Stan, an accessible probabilistic programming language for Bayesian modeling. We also compare the performance of these models with standard econometric models of the GARCH and stochastic volatility families. We find that the best agent-based models are on par with stochastic volatility models in terms of predictive likelihood, yet exhibit challenging posterior geometries requiring care in model comparison and sophisticated sampling algorithms.