Identifying and Quantifying Financial Bubbles with the Hyped Log-Periodic Power Law Model

ArXiv ID: 2510.10878 “View on arXiv”

Authors: Zheng Cao, Xingran Shao, Yuheng Yan, Helyette Geman

Abstract

We propose a novel model, the Hyped Log-Periodic Power Law Model (HLPPL), to the problem of quantifying and detecting financial bubbles, an ever-fascinating one for academics and practitioners alike. Bubble labels are generated using a Log-Periodic Power Law (LPPL) model, sentiment scores, and a hype index we introduced in previous research on NLP forecasting of stock return volatility. Using these tools, a dual-stream transformer model is trained with market data and machine learning methods, resulting in a time series of confidence scores as a Bubble Score. A distinctive feature of our framework is that it captures phases of extreme overpricing and underpricing within a unified structure. We achieve an average yield of 34.13 percentage annualized return when backtesting U.S. equities during the period 2018 to 2024, while the approach exhibits a remarkable generalization ability across industry sectors. Its conservative bias in predicting bubble periods minimizes false positives, a feature which is especially beneficial for market signaling and decision-making. Overall, this approach utilizes both theoretical and empirical advances for real-time positive and negative bubble identification and measurement with HLPPL signals.

Keywords: Financial Bubble Detection, Log-Periodic Power Law (LPPL), Transformer Model, Sentiment Analysis, Time Series Forecasting, Equities

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical models like the Log-Periodic Power Law (LPPL) and Ornstein–Uhlenbeck processes, demonstrating substantial analytical depth. It also presents detailed backtesting results (e.g., 34.13% annualized return, 2018–2024 period) and discusses generalization across sectors, indicating strong empirical and implementation focus.

  flowchart TD
    A["Research Goal:<br>Detect & Quantify Financial Bubbles"] --> B["Data & Inputs:<br>Market Data + Sentiment/Hype Index"]
    B --> C["Methodology:<br>HLPPL Model for Bubble Labels"]
    C --> D["Model Processing:<br>Dual-Stream Transformer"]
    D --> E["Outcome:<br>Time Series of Bubble Confidence Scores"]
    E --> F{"Final Findings:"}
    F --> G["34.13% Annualized Return<br>(2018-2024 Backtest)"]
    F --> H["High Generalization<br>Across Industry Sectors"]