气候不确定性下的超额损失再保险和巨灾债券定价：基于温度依赖随机强度的Cox过程框架
Pricing Excess-of-Loss Reinsurance and CAT Bonds under Climate Uncertainty: A Cox Process Framework with Temperature-Dependent Stochastic Intensity
AI总结：
提出气候感知的Cox过程定价框架，通过温度依赖的随机强度建模非平稳巨灾风险，蒙特卡洛模拟显示气候依赖显著影响定价，且基准模型可能低估经济资本需求约13.7%。
摘要：
本文针对非平稳巨灾风险下的超额损失再保险合同和巨灾债券，开发了一个气候感知的定价框架。巨灾到达被建模为Cox过程，其随机强度指数依赖于与温度相关的气候指数。为表示气候动态，该指数被建模为围绕随时间变化的变暖趋势的均值回复Ornstein-Uhlenbeck过程。在此设定下，总损失遵循具有对数正态严重性的复合Cox结构。定价在简化形式的风险调整测度下进行，为不完全市场中的超额损失再保险层和零息巨灾债券的二元支付提供了可处理的估值方法。由于巨灾损失无法动态复制，该框架强调基于情景的估值，而非模型无关的无套利边界。实施蒙特卡洛估值方案以量化气候依赖的巨灾强度的经济影响。数值结果表明，气候依赖显著改变了损失生成机制，并影响了巨灾相关合约的估值。在基准校准中，相对于平稳基准，气候感知模型提高了超额损失再保险费率并降低了巨灾债券价格。此外，对99.5%尾部风险价值的分析表明，与气候感知框架相比，平稳基准可能低估经济资本需求约13.7%，凸显了所提出模型的潜在监管相关性。这一发现强调了基准设计对于解释气候定价效应至关重要。
英文摘要：
This paper develops a climate-aware pricing framework for excess-of-loss (XL) reinsurance contracts and catastrophe (CAT) bonds under non-stationary catastrophe risk. Catastrophe arrivals are modeled as a Cox process whose stochastic intensity depends exponentially on a temperature-related climate index. To represent climate dynamics, the index is modeled as a mean-reverting Ornstein--Uhlenbeck process around a time-dependent warming trend. Within this setting, aggregate losses follow a compound Cox structure with lognormal severities. Pricing is performed under a reduced-form risk-adjusted measure, which provides a tractable valuation approach for XL reinsurance layers and binary zero-coupon CAT bond payoffs in an incomplete market setting. Because catastrophe losses are not dynamically replicable, the framework emphasizes scenario-based valuation rather than model-independent no-arbitrage bounds. A Monte Carlo valuation scheme is implemented to quantify the economic implications of climate-dependent catastrophe intensity. The numerical results show that climate dependence materially changes the loss-generation mechanism and affects the valuation of catastrophe-linked contracts. In the baseline calibration, the climate-aware model increases the excess-of-loss reinsurance premium and lowers the CAT bond price relative to the stationary benchmark. Furthermore, our analysis of the 99.5\% Tail Value-at-Risk (TVaR) indicates that stationary benchmarks may underestimate economic capital requirements by approximately 13.7\% compared to the climate-aware framework, highlighting the potential regulatory relevance of the proposed model. This finding highlights that benchmark design is critical for interpreting climate-pricing effects.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
