Paper: arXiv 2511.16563

Authors: Akash Deep, Svetlozar T. Rachev, Frank J. Fabozzi

Abstract

We develop an econometric framework integrating heavy-tailed Student’s $t$ distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004–2024), we demonstrate Student’s $t$ specifications outperform Gaussian models in 88.4% of cases. Bounded probability-weighting transformations preserve mathematical properties required for dynamic pricing. Gaussian models underestimate 99% Value-at-Risk by 19.7% versus 3.2% for our specification. Joint estimation procedures identify tail and behavioral parameters with established asymptotic properties. Results provide robust inference for asset-pricing applications where heavy tails and behavioral distortions coexist.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper successfully bridges non-Gaussian heavy-tailed distributions (Student’s t) with behavioral probability weighting while establishing theoretical proofs for infinite divisibility. Its empirical rigor is exceptional, utilizing over 430k observations across 86 assets to demonstrate tangible risk-forecasting improvements (e.g., VaR accuracy).

Research Flowchart

  flowchart TD
    A[Research Goal: Integrated Econometric Framework<br>Heavy Tails + Behavioral Probability Weighting] --> B[Model Development<br>Student's t + Bounded Probability Weighting<br>Preserving Infinite Divisibility]
    
    C[(Input Data<br>432,752 Obs | 86 Assets<br>2004–2024)] --> D[Joint Estimation & Risk Computation<br>Parameter Estimation & 99% VaR Evaluation]
    B --> D
    
    D --> E[Outcomes & Key Findings]
    
    E --> F[Model Performance<br>Student's t outperforms Gaussian<br>in 88.4% of cases]
    E --> G[Risk Accuracy<br>99% VaR Underestimation:<br>Gaussian 19.7% vs. New Model 3.2%]

Cited References (43)

  1. Prospect theory: An analysis of decision under risk (2013)
  2. Advances in prospect theory: Cumulative representation of uncertainty (1992)
  3. Behavioral capital asset pricing theory (1994)
  4. A behavioral approach to asset pricing (2008)
  5. Noise trader risk in financial markets (1990)
  6. Prospect theory and asset prices (2001)
  7. Financial modelling with jump processes (2003)
  8. L 'e vy processes in finance: pricing financial derivatives (2003)
and 35 more
  1. L 'e vy processes and infinitely divisible distributions (1999)
  2. The fundamental theorem of asset pricing (2010)
  3. The fundamental theorem of asset pricing for unbounded stochastic processes (1999)
  4. The Student t-distribution of any degree of freedom is infinitely divisible (1976)
  5. The probability weighting function (1998)
  6. On the shape of the probability weighting function (1999)
  7. Infinite divisibility and variance mixtures of the normal distribution (1971)
  8. Intermediate probability: A computational approach (2007)
  9. The variation of certain speculative prices (1963)
  10. The behavior of stock-market prices (1965)
  11. The distribution of share price changes (1972)
  12. A comparison of the stable and student distributions as statistical models for stock prices (2010)
  13. Normal inverse Gaussian distributions and stochastic volatility modelling (1997)
  14. The variance gamma process and option pricing (1998)
  15. Hyperbolic distributions in finance (1995)
  16. Modelling extremal events: for insurance and finance (2013)
  17. Self-decomposability of the generalized inverse Gaussian and hyperbolic distributions (1979)
  18. Stable Paretian models in finance (2000)
  19. Multiple subordinated modeling of asset returns: Implications for option pricing (2021)
  20. A theory of power-law distributions in financial market fluctuations (2003)
  21. A conditional-SGT-VaR approach with alternative GARCH models (2007)
  22. Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach (2000)
  23. A forecast comparison of volatility models: does anything beat a GARCH (1, 1)? (2005)
  24. Testing for jumps in a discretely observed process (2009)
  25. Modeling and forecasting realized volatility (2003)
  26. Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics (2001)
  27. Time-changed L 'e vy processes and option pricing (2004)
  28. A jump diffusion model for option pricing with three properties: leptokurtic feature, volatility smile, and analytical tractability (2000)
  29. Conditional heteroskedasticity in asset returns: A new approach (1991)
  30. Generalized autoregressive conditional heteroskedasticity (1986)
  31. A closed-form solution for options with stochastic volatility with applications to bond and currency options (1993)
  32. Option pricing when underlying stock returns are discontinuous (1976)
  33. Option pricing with greed and fear factor: the rational finance approach (2021)
  34. Techniques for verifying the accuracy of risk measurement models (1995)
  35. Evaluating interval forecasts (1998)

0 of 43 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.