最优巨灾债券设计及其在气候变化风险中的应用

中文摘要 AI 辅助

巨灾债券已成为将巨灾风险转移至资本市场的重要工具，然而其赔付结构通常是外生给定的，而非经过优化。本文中，我们将赔付函数视为决策变量，从发起人的角度研究巨灾债券的最优设计。我们在期望负效用和谱风险度量两种框架下建立了分段线性赔付函数的最优性，从而将无限维设计问题简化为关于附着点的一维优化。最优设计还消除了与阈值赔付结构不连续性相关的潜在道德风险。我们在六种风险准则下刻画了最优附着点，并获得了显式或半显式解。我们进一步推导了最优附着点的界限，并发展了比较静态分析，为实际设计提供了洞见。利用NOAA的“十亿美元天气与气候灾害”数据库中美国强风暴损失进行校准，我们表明最优巨灾债券设计在大多数风险准则下实现了显著的风险降低。

英文摘要

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.

发表机构

• University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）

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