Paper: arXiv 2505.07820

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

Cited References (78)

  1. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields (2013)
  2. Nonlinear dynamical economics and chaotic motion (1993)
  3. Can heterogeneous agent models explain the alleged mispricing of the S&P 500? (2021)
  4. Market force, ecology and evolution (2002)
  5. Bayesian filtering and smoothing (2023)
  6. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains (1970)
  7. Maximum likelihood from incomplete data via the EM algorithm (1977)
  8. The EM approach to the multiple indicators and multiple causes model via the estimation of the latent variable (1981)
and 70 more
  1. On The Dynamic Behavior of Prices in Disequilibrium (1980) — link
  2. Efficient capital markets (1970)
  3. Efficient capital markets: II (1991)
  4. Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends? (1981)
  5. On the behaviour of commodity prices (1992)
  6. Empirical exchange rate models of the seventies: Do they fit out of sample? (1983)
  7. Yield spreads and interest rate movements: A bird’s eye view (1991)
  8. Chapter 15 Anomalies and market efficiency (2003) — link
  9. Value and momentum everywhere (2013)
  10. Some anomalous evidence regarding market efficiency (1978)
  11. Security Analysis. New York: Whittlesey House (1934)
  12. Does the stock market overreact? (1985)
  13. Persuasive evidence of market inefficiency (1985)
  14. Does the stock market rationally reflect fundamental values? (1986)
  15. Stock prices, earnings, and expected dividends (1988)
  16. The cross-section of expected stock returns (1992)
  17. Size, value, and momentum in international stock returns (2012)
  18. Contrarian investment, extrapolation, and risk (1994)
  19. Black was right: Price is within a factor 2 of Value (2017) — link
  20. Evidence of predictable behavior of security returns (1990)
  21. Returns to buying winners and selling losers: Implications for stock market efficiency (1993)
  22. Fads, martingales, and market efficiency (1990)
  23. On persistence in mutual fund performance (1997)
  24. Time series momentum (2012)
  25. The excess volatility puzzle explained by financial noise amplification from endogenous feedbacks (2022)
  26. Two centuries of trend following (2014) — link
  27. Investor behavior in the October 1987 stock market crash: Survey evidence (1987)
  28. Irrational Exuberance, Princeton Univ (2000)
  29. Excess volatility (2006)
  30. Advances in Behavioral Finance (Russell Sage Foundation, New York) (1993)
  31. Advances in behavioral finance, Volume II (2005)
  32. Scaling and criticality in a stochastic multi-agent model of a financial market (1999)
  33. Exploration of the Parameter Space in Macroeconomic Models (2024)
  34. How market ecology explains market malfunction (2021)
  35. Information geometry for multiparameter models: New perspectives on the origin of simplicity (2022)
  36. A century of evidence on trend-following investing (2017) — link
  37. The inelastic market hypothesis: a microstructural interpretation (2022)
  38. Noise (1986)
  39. Ponzi funds — → 2405.12768
  40. In Search of the Origins of Financial Fluctuations: The Inelastic Markets Hypothesis (2021)
  41. Trades, quotes and prices: financial markets under the microscope (2018)
  42. Investor psychology and security market under-and overreactions (1998)
  43. Fast and slow thinking (2011)
  44. New experimental evidence on expectations formation (2017)
  45. Heterogeneous agent models in economics and finance (2006)
  46. Agent-based computational finance (2006)
  47. Heterogeneity, market mechanisms, and asset price dynamics (2009)
  48. Heterogeneous agent models in finance (2018)
  49. The dynamics of speculative behaviour (1992)
  50. An analysis of the effect of noise in a heterogeneous agent financial market model (2011)
  51. Co-existence of trend and value in financial markets: Estimating an extended Chiarella model (2020) — link
  52. Universally sloppy parameter sensitivities in systems biology models (2007)
  53. Quadratic Hawkes processes for financial prices (2017)
  54. Zooming in on equity factor crowding (2020) — link
  55. The Footprint of Trend-Following: Can CTAs really move the market? (2022) — link
  56. Continuous auctions and insider trading (1985)
  57. Behavioral heterogeneity in stock prices (2007)
  58. The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions (1998)
  59. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering (2018)
  60. How market ecology explains market malfunction (2021)
  61. On the calibration of Silverman’s test for multimodality (2001)
  62. Dynamic portfolio choice with frictions (2016)
  63. On the bimodality of the distribution of the S&P 500’s distortion: Empirical evidence and theoretical explanations (2017)
  64. Using kernel density estimates to investigate multimodality (1981)
  65. Trends, reversion, and critical phenomena in financial markets (2021)
  66. Trends’ signal strength and the performance of CTAs (2019)
  67. The stochastic bifurcation behaviour of speculative financial markets (2008)
  68. CRSP US Stock Database: Daily Stock Prices (2025)
  69. A new metric for probability distributions (2003)
  70. Some asymptotics for multimodality tests based on kernel density estimates (1992)

1 of 78 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.