Optimal Catastrophe Bond Design and its Applications to Climate Change Risk
Abstract
Catastrophe bonds have become a central instrument for transferring catastrophic risk to capital markets, yet their payout structures are typically specified exogenously rather than optimized. In this paper, we treat the indemnity function as the decision variable and study the optimal design of CAT bonds from the sponsor's perspective. We establish the optimality of a piecewise linear indemnity function under both expected-disutility and spectral-risk-measure frameworks and thereby reduce an infinite-dimensional design problem to a one-dimensional optimization over the attachment point. The optimal design also eliminates the potential moral hazard associated with the discontinuity of threshold payout structures. We characterize the optimal attachment point under six risk criteria and obtain explicit or semi-explicit solutions. We further derive bounds for the optimal attachment point and develop comparative statics that provide practical design insights. Using U.S. severe storm losses from NOAA's Billion-Dollar Weather and Climate Disasters database for calibration, we show that the optimal CAT bond designs achieve substantial risk reductions across most risk criteria.
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BibTeX
@misc{medina2026optimal,
title = {{Optimal Catastrophe Bond Design and its Applications to Climate Change Risk}},
author = {Andres Medina and Wei Wei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03793},
eprint = {2610.03793},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03793},
}
RIS
TY - UNPB
TI - Optimal Catastrophe Bond Design and its Applications to Climate Change Risk
AU - Andres Medina
AU - Wei Wei
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.03793
UR - https://arxiv.org/abs/2610.03793
AB - Catastrophe bonds have become a central instrument for transferring catastrophic risk to capital markets, yet their payout structures are typically specified exogenously rather than optimized. In this paper, we treat the indemnity function as the decision variable and study the optimal design of CAT bonds from the sponsor's perspective. We establish the optimality of a piecewise linear indemnity function under both expected-disutility and spectral-risk-measure frameworks and thereby reduce an infinite-dimensional design problem to a one-dimensional optimization over the attachment point. The optimal design also eliminates the potential moral hazard associated with the discontinuity of threshold payout structures. We characterize the optimal attachment point under six risk criteria and obtain explicit or semi-explicit solutions. We further derive bounds for the optimal attachment point and develop comparative statics that provide practical design insights. Using U.S. severe storm losses from NOAA's Billion-Dollar Weather and Climate Disasters database for calibration, we show that the optimal CAT bond designs achieve substantial risk reductions across most risk criteria.
ER -