Pricing Excess-of-Loss Reinsurance and CAT Bonds under Climate Uncertainty: A Cox Process Framework with Temperature-Dependent Stochastic Intensity

2026-06-12

AI Summary

This study addresses the critical limitation of traditional catastrophe risk pricing models, which ignore the non-stationarity in disaster frequency induced by climate change, leading to biased reinsurance and catastrophe bond valuations and a systematic underestimation of capital reserves. To rectify this, the authors propose a climate-aware pricing framework that, for the first time, incorporates a temperature-driven stochastic intensity into a Cox process: the catastrophe arrival intensity depends on a temperature index modeled by an Ornstein–Uhlenbeck process with a time trend, coupled with a compound Poisson loss structure. Valuation is performed under a risk-adjusted measure via Monte Carlo simulation. Empirical results demonstrate that the model significantly increases excess-of-loss reinsurance premiums and reduces catastrophe bond prices; compared to a stationary benchmark, the 99.5% TVaR reveals that economic capital requirements are underestimated by approximately 13.7%, underscoring the essential role of integrating climate dynamics into risk management.

Abstract

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.

Problem

• climate uncertainty
• catastrophe risk
• excess-of-loss reinsurance
• CAT bonds
• non-stationary risk

Innovation

• Cox process
• climate-aware pricing
• stochastic intensity
• non-stationary catastrophe risk
• Tail Value-at-Risk