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Transformer-based CoVaR: Systemic Risk in Textual Information

Junyu Chen, Tom Boot, Lingwei Kong, Weining Wang

TL;DR

A Transformer-based methodology is developed that integrates financial news articles directly with market data to improve CoVaR estimates and proves explicit error bounds for the Transformer CoVaR estimator, showing that accurate CoVaR learning is possible even with small datasets.

Abstract

Conditional Value-at-Risk (CoVaR) quantifies systemic financial risk by measuring the loss quantile of one asset, conditional on another asset experiencing distress. We develop a Transformer-based methodology that integrates financial news articles directly with market data to improve CoVaR estimates. Unlike approaches that use predefined sentiment scores, our method incorporates raw text embeddings generated by a large language model (LLM). We prove explicit error bounds for our Transformer CoVaR estimator, showing that accurate CoVaR learning is possible even with small datasets. Using U.S. market returns and Reuters news items from 2006--2013, our out-of-sample results show that textual information impacts the CoVaR forecasts. With better predictive performance, we identify a pronounced negative dip during market stress periods across several equity assets when comparing the Transformer-based CoVaR to both the CoVaR without text and the CoVaR using traditional sentiment measures. Our results show that textual data can be used to effectively model systemic risk without requiring prohibitively large data sets.

Transformer-based CoVaR: Systemic Risk in Textual Information

TL;DR

A Transformer-based methodology is developed that integrates financial news articles directly with market data to improve CoVaR estimates and proves explicit error bounds for the Transformer CoVaR estimator, showing that accurate CoVaR learning is possible even with small datasets.

Abstract

Conditional Value-at-Risk (CoVaR) quantifies systemic financial risk by measuring the loss quantile of one asset, conditional on another asset experiencing distress. We develop a Transformer-based methodology that integrates financial news articles directly with market data to improve CoVaR estimates. Unlike approaches that use predefined sentiment scores, our method incorporates raw text embeddings generated by a large language model (LLM). We prove explicit error bounds for our Transformer CoVaR estimator, showing that accurate CoVaR learning is possible even with small datasets. Using U.S. market returns and Reuters news items from 2006--2013, our out-of-sample results show that textual information impacts the CoVaR forecasts. With better predictive performance, we identify a pronounced negative dip during market stress periods across several equity assets when comparing the Transformer-based CoVaR to both the CoVaR without text and the CoVaR using traditional sentiment measures. Our results show that textual data can be used to effectively model systemic risk without requiring prohibitively large data sets.
Paper Structure (32 sections, 15 theorems, 185 equations, 15 figures, 4 tables)

This paper contains 32 sections, 15 theorems, 185 equations, 15 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Methodology
  4. Systemic Risk Modeling
  5. Transformer Architecture
  6. Self-Attention Sublayer
  7. Feed-Forward Network Sublayer
  8. Transformer-based Estimator
  9. Theoretical Results
  10. Empirical Study
  11. Data
  12. Data Preprocessing
  13. CoVaR Prediction
  14. Average Quantile Loss
  15. Comparison with Sentiment-Based Measures
  16. ...and 17 more sections

Key Result

Theorem 1

Suppose that Assumptions assp:cdf--assp:var and conditions in Lemma lem:theo1 hold, then the CoVaR prediction satisfies: where $\widetilde{R}_{j,\delta_T,T} =\; \inf_{f \in \mathcal{F}} \Bigl\|f - f_{j,\tau}^*\Bigl\|_{\infty}^2 + \Biggl( \delta_T + \sqrt{\frac{V_{\left(\mathcal{F},\|\cdot\|_{\infty}\right)}(\delta_T)}{T}} \Biggl)$ with $\delta_T>0, \delta_T \rightarrow 0, \delta_T^2 T \right

Figures (15)

  • Figure 1: Example illustration of self-attention scores
  • Figure 2: Illustration of the Transformer-based CoVaR prediction model
  • Figure 3: Daily news article frequency and stock market index
  • Figure 4: Distribution of article lengths
  • Figure 5: t-SNE visualization of Goldman Sachs–related news articles
  • ...and 10 more figures

Theorems & Definitions (33)

  • Theorem 1: Out-of-Sample CoVaR Estimator Consistency
  • proof
  • Corollary 1: Convergence Rate
  • proof
  • Lemma D.1
  • proof
  • proof
  • proof
  • Lemma F.1
  • proof
  • ...and 23 more