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

ArXiv ID: 2505.07820 “View on arXiv”

Authors: Jutta G. Kurth, Adam A. Majewski, Jean-Philippe Bouchaud

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.

Keywords: Chiarella Model, Fundamental Value, Excess Volatility, Mispricing Distribution, Trend Followers vs. Fundamentalists, Multi-Asset Class (Equities, Bonds, Commodities, Currencies)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper uses advanced SDEs, Bayesian filtering, and sloppiness analysis, indicating high math complexity, while it also performs rigorous empirical calibration on multiple asset classes spanning centuries, showing substantial data and implementation effort.

  flowchart TD
    A["Research Goal:<br>Re-examine Excess Volatility<br>using Chiarella Model"] --> B["Methodology:<br>Amend Model for Arbitrary Drifts<br>Develop Calibration Scheme"]
    B --> C["Input Data:<br>Historical Prices (ca. 1800+)<br>Stocks, Bonds, Commodities, Currencies"]
    C --> D["Process:<br>Calibrate individual monthly time series<br>Compute Fundamental Values & Mispricing"]
    D --> E["Outcome 1:<br>Quantified Excess Volatility<br>(Factor ≈ 4 for Equities)"]
    D --> F["Outcome 2:<br>Bimodal Mispricing Distribution<br>(Violates EMH)"]
    E & F --> G["Conclusion:<br>Market Dynamics =<br>Trend Followers vs. Fundamentalists"]