Riding Wavelets: A Method to Discover New Classes of Price Jumps

ArXiv ID: 2404.16467 “View on arXiv”

Authors: Unknown

Abstract

Cascades of events and extreme occurrences have garnered significant attention across diverse domains such as financial markets, seismology, and social physics. Such events can stem either from the internal dynamics inherent to the system (endogenous), or from external shocks (exogenous). The possibility of separating these two classes of events has critical implications for professionals in those fields. We introduce an unsupervised framework leveraging a representation of jump time-series based on wavelet coefficients and apply it to stock price jumps. In line with previous work, we recover the fact that the time-asymmetry of volatility is a major feature. Mean-reversion and trend are found to be two additional key features, allowing us to identify new classes of jumps. Furthermore, thanks to our wavelet-based representation, we investigate the reflexive properties of co-jumps, which occur when multiple stocks experience price jumps within the same minute. We argue that a significant fraction of co-jumps results from an endogenous contagion mechanism.

Keywords: Jump Analysis, Wavelet Coefficients, Endogenous Dynamics, Co-jumps, Volatility, Equities

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced wavelet-based representation and PCA for classification, involving moderate mathematical density, while the empirical work is highly data-driven with a large, specific dataset (301 US stocks over 8 years) and detailed methodology for jump detection and co-jump analysis.

  flowchart TD
    A["Research Goal<br>Distinguish Endogenous vs Exogenous Price Jumps"] --> B["Methodology<br>Unsupervised Wavelet-Based Representation"]
    B --> C["Input Data<br>High-Frequency Stock Price Data"]
    C --> D["Compute Wavelet Coefficients<br>(Capture Multi-scale Dynamics)"]
    D --> E["Feature Extraction<br>Time-Asymmetry, Mean-Reversion, Trend"]
    E --> F["Clustering Analysis<br>Identify Distinct Jump Classes"]
    F --> G["Key Findings<br>1. New Jump Classes Discovered<br>2. Endogenous Contagion in Co-jumps"]
    style G fill:#d4edda,stroke:#155724