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The statistical description and modeling of volatility plays a prominent rolein econometrics, risk management and finance. GARCH and stochastic volatilitymodels have been extensively studied and are routinely fitted to market data,albeit providing a phenomenological description only.  In contrast, the field of econophysics starts from the premise that moderneconomies consist of a vast number of individual actors with heterogeneousexpectations and incentives. In turn explaining observed market statistics asemerging from the collective dynamics of many actors following heterogeneous,yet simple, rather mechanistic rules. While such models generate volatilitydynamics qualitatively matching several stylized facts and thus illustrate thepossible role of different mechanisms, such as chartist trading, herdingbehavior etc., rigorous and quantitative statistical fits are still mostlylacking.  Here, we show how Stan, a modern probabilistic programming language forBayesian modeling, can be used to fit several models from econophysics. Incontrast to the method of moment matching, which is currently popular, our fitsare purely likelihood based with many advantages, including systematic modelcomparison and principled generation of model predictions conditional on theobserved price history. In particular, we investigate models by Vikram & Sinhaand Franke & Westerhoff, and provide a quantitative comparison with standardeconometric models.

Reality-check for Econophysics: Likelihood-based fitting of physics-inspired market models to empirical data