Research Report on Identifying New Classes of Financial Price Jumps Using Wavelets

Academic Background

Price jumps in financial markets refer to significant price fluctuations occurring within an extremely short period, typically caused by exogenous factors (such as sudden news) or endogenous factors (internal market feedback mechanisms). Distinguishing between these two types of price jumps is crucial for understanding market dynamics, predicting extreme events, and developing effective regulatory strategies. However, existing research methods often rely on supervised learning, requiring explicit labels (such as news events) to classify jumps, which can be limiting in practical applications because many price jumps lack clear news triggers.

To better identify and classify price jumps, especially those without obvious exogenous triggers, researchers have proposed an unsupervised classification framework that leverages multiscale wavelet representation to analyze time-series data. This framework not only captures the time-asymmetry of price jumps but also identifies new classes of jumps, such as mean-reversion and trend-related jumps.

Paper Source

This paper was co-authored by Cecilia Aubrun, Rudy Morel, Michael Benzaquen, and Jean-Philippe Bouchaud from institutions including École Polytechnique, Flatiron Institute, LadHyX, and Capital Fund Management. It was published in the journal Proceedings of the National Academy of Sciences (PNAS) on February 7, 2025, titled “Identifying New Classes of Financial Price Jumps with Wavelets.”

Research Process and Methods

1. Detection of Price Jumps and Dataset Construction

The study first employed a detection method based on “jump-score” to extract 43,628 price jumps from 301 US stocks between 2015 and 2022. This included 18,802 “cojumps,” where multiple stocks experienced jumps within the same minute. The researchers excluded high-frequency trading data during market opening and closing hours and cojumps involving more than 250 stocks to ensure data stability and representativeness.

2. Unsupervised Classification Framework

The researchers introduced an unsupervised classification method based on wavelet scattering coefficients. Wavelet coefficients capture multi-scale features of price jumps, particularly the time-asymmetry of volatility. Principal component analysis (PCA) was used to extract three key features: volatility asymmetry, mean-reversion, and trend. These features were then used to embed each price jump into a low-dimensional space for clustering analysis.

3. Classification Results

Three main types of jumps were identified: - Exogenous Jumps: Volatility significantly increases after the jump, typically triggered by sudden news. - Endogenous Jumps: Volatility shows symmetry before and after the jump, usually due to internal market feedback mechanisms. - Anticipatory Jumps: Volatility increases significantly before the jump, possibly due to market anticipation of upcoming news.

Additionally, three new classes of jumps were identified: - Mean-Reverting Jumps: Price changes direction before and after the jump. - Trend-Aligned Jumps: Price changes consistently before and after the jump. - Trend-Anti-Aligned Jumps: Price changes direction before and after the jump.

4. Endogeneity Analysis of Cojumps

Further analysis of cojumps revealed that many large-scale cojumps are not triggered by common news events but rather by an endogenous contagion mechanism. This finding supports the notion of endogenous synchronization in financial markets and provides new insights into market fragility.

Main Conclusions and Research Significance

Conclusions

Using an unsupervised wavelet analysis approach, the study successfully identified various classes of price jumps and revealed the endogenous nature of cojumps. Many large-scale cojumps are found to result from endogenous contagion mechanisms rather than exogenous news, indicating that financial market extremes often have self-exciting characteristics.

Scientific and Practical Value

This research offers a new unsupervised framework for classifying price jumps in financial markets, providing more accurate identification of endogenous jumps. It introduces new tools for market risk management and extreme event prediction. The findings also suggest that endogenous dynamics play a crucial role in extreme events, offering valuable insights for regulators and investors.

Research Highlights

1. Methodological Innovation: First application of wavelet scattering coefficients to unsupervised classification of price jumps, overcoming limitations of traditional supervised learning.
2. Discovery of New Jump Classes: Identification of mean-reverting, trend-aligned, and trend-anti-aligned jumps, enriching the classification system for price jumps.
3. Revelation of Endogeneity in Cojumps: Analysis of cojump dynamics reveals internal contagion mechanisms, providing new perspectives on financial market fragility.

Additional Valuable Information

The study provides publicly available code and data for replication and extension by other researchers. The code can be accessed on GitHub (https://github.com/rudymorel/scattering_spectra), while some data require access through standard financial data providers due to licensing restrictions.

This paper not only advances the methodology for studying price jumps in financial markets but also provides important theoretical support for understanding the origins of extreme events and the endogenous dynamics of markets.