Probability Weighting Meets Heavy Tails: An Econometric Framework for Behavioral Asset Pricing

2025-11-20

AI Summary

Gaussian models severely underestimate risk when heavy-tailed return distributions coexist with behavioral probability weighting biases. Method: This paper develops an econometric framework that jointly incorporates infinite divisibility and behavioral probability weighting. It innovatively couples a bounded probability weighting function with the Student’s *t* distribution—a heavy-tailed, infinitely divisible distribution—and proposes a joint estimation method for parameter inference. Contribution/Results: The framework simultaneously captures extreme asset return risks (via heavy tails) and nonlinear investor probability distortions (via behavioral weighting). Empirical analysis across 86 assets and over 430,000 daily observations shows that the model significantly outperforms the Gaussian benchmark in 88.4% of samples. At the 99% quantile, Value-at-Risk (VaR) underestimation declines sharply from 19.7% to 3.2%. Moreover, the estimator exhibits strong statistical properties, including consistency and asymptotic normality.

Technology Category

• Game Theory and Economic Paradigms: Behavioral Game Theory
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

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.

Problem

• Integrating heavy-tailed distributions with behavioral probability weighting for asset pricing
• Addressing Gaussian models' underestimation of extreme risks in financial data
• Providing robust inference for assets with heavy tails and behavioral distortions

Innovation

• Integrates heavy-tailed distributions with behavioral probability weighting
• Uses Student's t specifications outperforming Gaussian models
• Preserves mathematical properties for dynamic pricing applications