Revisiting the Excess Volatility Puzzle Through the Lens of the Chiarella Model

TL;DR

This work extends the Chiarella heterogeneous-agents framework to handle arbitrary long-term drift in fundamental value and calibrates it on monthly data across four asset classes, using an EM–Kalman scheme on de-drifted prices. It shows that price volatility is largely amplified relative to fundamentals due to noise-trader activity, with an average amplification around $4\times$ for stocks and even higher for some classes, providing quantitative support for the excess volatility puzzle. The non-linear (cubic) fundamentalist demand is essential to reproduce bimodal mispricing distributions observed empirically and numerically, challenging the Efficient Market Hypothesis. A Fisher-information-based sloppiness analysis reveals a clear hierarchy in parameter sensitivity, identifying stiff directions that govern variance and bifurcation behavior across asset classes, and suggesting robust qualitative features of trend-versus-value dynamics across heterogeneous markets.

Abstract

We amend and extend the Chiarella model of financial markets to deal with arbitrary long-term value drifts in a consistent way. This allows us to improve upon existing calibration schemes, opening the possibility of calibrating individual monthly time series instead of classes of time series. The technique is employed on spot prices of four asset classes from ca. 1800 onward (stock indices, bonds, commodities, currencies). The so-called fundamental value is a direct output of the calibration, which allows us to (a) quantify the amount of excess volatility in these markets, which we find to be large (e.g. a factor $\approx$ 4 for stock indices) and consistent with previous estimates; and (b) determine the distribution of mispricings (i.e. the difference between market price and value), which we find in many cases to be bimodal. Both findings are strongly at odds with the Efficient Market Hypothesis. We also study in detail the 'sloppiness' of the calibration, that is, the directions in parameter space that are weakly constrained by data. The main conclusions of our study are remarkably consistent across different asset classes, and reinforce the hypothesis that the medium-term fate of financial markets is determined by a tug-of-war between trend followers and fundamentalists.

Figures (23)

• Figure 1: Typical dynamics of system \ref{['eq: ModifiedChiarella']} in the case where its limit set is a spiral, $\kappa > \alpha (\beta\gamma -1)$, and without noise ($\sigma_N=\sigma_V=0$). The parameters are $(\kappa, \, \alpha, \, \beta, \, \gamma) = (0.01,\, 1/7, \, 0.5, \, 2)$, and the system is initialised with $(P_0, \, V_0, \, M_0) = (26,\, 20,\, 1)$; the drift $g$ is constant. Left: Phase portrait of the mispricing $\delta$ and the trend signal $M$ together with its nullclines and a sample trajectory. The streamlines' (blue) width and density encode the magnitude of the velocity field. Right: evolution of the price $P$, value $V$ and trend signal $M$.
• Figure 2: Same as Fig. \ref{['fig:spiral_determ']} but in the case where the limit set is a limit cycle, $\kappa < \alpha (\beta\gamma -1)$. The parameters are $(\kappa, \, \alpha, \, \beta, \, \gamma) = (0.05,\, 1/7, \, 0.65, \, 10)$, and the system is initialised with $(P_0, \, V_0, \, M_0) = (16,\, 12,\, 0.1)$.
• Figure 3: Same as Fig. \ref{['fig:spiral_determ']} but in the presence of noise ($\sigma_N=0.35$ and $\sigma_V=0.2$).
• Figure 4: Same as Fig. \ref{['fig:limitcycle_determ']} but in the presence of noise ($\sigma_N=0.6$ and $\sigma_V=0.2$). The parameters are $(\kappa, \, \alpha, \, \beta, \, \gamma) = (0.01,\, 1/7, \, 0.35, \, 10)$, and the system is initialised with $(P_0, \, V_0, \, M_0) = (26.5,\, 26,\, 0.1)$.
• Figure 5: Evolution of the log-price $p$, the integrated drift $G$, and the de-drifted log-'price' $\tilde{p}$ of the US index. $G$ is estimated as a polynomial with one order per decade of data, i.e. a $22^\textup{nd}$ order polynomial here for data ranging from 1791-12 to 2014-12.