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Unveiling Nonlinear Dynamics in Catastrophe Bond Pricing: A Machine Learning Perspective

Xiaowei Chen, Hong Li, Yufan Lu, Rui Zhou

TL;DR

This paper tackles CAT bond pricing by leveraging a machine-learning framework that uncovers nonlinear relationships and interactions among risk factors. It introduces XGBoost as a powerful nonlinear estimator and Conformal Prediction to deliver valid probabilistic intervals around point forecasts, evaluated on a primary-market CAT bond dataset spanning 1999–2021. The study finds that EL is the dominant predictor in linear models, while XGBoost reveals substantial nonlinear effects and important interactions, particularly with market-cycle indices like ROLX and GC. The combination of XGBoost and Jackknife+ Conformal Prediction yields more accurate forecasts and narrower, well-calibrated prediction intervals, offering practical benefits to investors, issuers, and risk managers facing complex catastrophe risk structures. Overall, the work advances CAT bond pricing by integrating probabilistic ML with interpretable tools, enabling better risk transfer decision-making and budgeted risk premiums under nonlinear dynamics.

Abstract

This paper explores the implications of using machine learning models in the pricing of catastrophe (CAT) bonds. By integrating advanced machine learning techniques, our approach uncovers nonlinear relationships and complex interactions between key risk factors and CAT bond spreads -- dynamics that are often overlooked by traditional linear regression models. Using primary market CAT bond transaction records between January 1999 and March 2021, our findings demonstrate that machine learning models not only enhance the accuracy of CAT bond pricing but also provide a deeper understanding of how various risk factors interact and influence bond prices in a nonlinear way. These findings suggest that investors and issuers can benefit from incorporating machine learning to better capture the intricate interplay between risk factors when pricing CAT bonds. The results also highlight the potential for machine learning models to refine our understanding of asset pricing in markets characterized by complex risk structures.

Unveiling Nonlinear Dynamics in Catastrophe Bond Pricing: A Machine Learning Perspective

TL;DR

This paper tackles CAT bond pricing by leveraging a machine-learning framework that uncovers nonlinear relationships and interactions among risk factors. It introduces XGBoost as a powerful nonlinear estimator and Conformal Prediction to deliver valid probabilistic intervals around point forecasts, evaluated on a primary-market CAT bond dataset spanning 1999–2021. The study finds that EL is the dominant predictor in linear models, while XGBoost reveals substantial nonlinear effects and important interactions, particularly with market-cycle indices like ROLX and GC. The combination of XGBoost and Jackknife+ Conformal Prediction yields more accurate forecasts and narrower, well-calibrated prediction intervals, offering practical benefits to investors, issuers, and risk managers facing complex catastrophe risk structures. Overall, the work advances CAT bond pricing by integrating probabilistic ML with interpretable tools, enabling better risk transfer decision-making and budgeted risk premiums under nonlinear dynamics.

Abstract

This paper explores the implications of using machine learning models in the pricing of catastrophe (CAT) bonds. By integrating advanced machine learning techniques, our approach uncovers nonlinear relationships and complex interactions between key risk factors and CAT bond spreads -- dynamics that are often overlooked by traditional linear regression models. Using primary market CAT bond transaction records between January 1999 and March 2021, our findings demonstrate that machine learning models not only enhance the accuracy of CAT bond pricing but also provide a deeper understanding of how various risk factors interact and influence bond prices in a nonlinear way. These findings suggest that investors and issuers can benefit from incorporating machine learning to better capture the intricate interplay between risk factors when pricing CAT bonds. The results also highlight the potential for machine learning models to refine our understanding of asset pricing in markets characterized by complex risk structures.
Paper Structure (23 sections, 9 equations, 11 figures, 7 tables)

This paper contains 23 sections, 9 equations, 11 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Catastrophe Bond Data
  3. Methodology
  4. Problem Formulation
  5. Linear Regression
  6. Ensemble Learning
  7. Overview
  8. XGBoost
  9. Conformal Prediction
  10. Prediction Interval
  11. Overview of Conformal Prediction
  12. Jackknife+ Conformal Prediction Interval
  13. Linear Regression: Model Estimation and Implications
  14. XGBoost: Model Estimation and Implications
  15. Relative Importance of Risk Factors
  16. ...and 8 more sections

Figures (11)

  • Figure 2.1: Scatter plots of bond spread against expected loss (left) and probability of first loss (right) using the 765 bonds in the data set. The horizontal axes are percentage points.
  • Figure 2.2: The number of CAT bonds issued and the issue volume per year (left) and per calendar month (right).
  • Figure 2.3: Lane Financial LLC Synthetic Rate on Line Index (left) and the US High Yield BB Option-Adjusted Spread (right) between January 1999 and March 2021.
  • Figure 2.4: The Guy Carpenter Rate on Line Index for the Global, European, US, and Asia Pacific markets, respectively, between January 1999 and March 2021.
  • Figure 5.1: Feature importance plot for the XGBoost model.
  • ...and 6 more figures