Document Type : Original Research Paper

Authors

• Ali Zinsaz ¹
• Omid Fathi ²

¹ Director of Reinsurance and International Affairs at Razi Insurance Company

² Reinsurance Manager at Arman Insurance Company - Certified Actuary of the Central Insurance of the Islamic Republic of Iran

Abstract

Background and Objectives: The increasing frequency and severity of floods in Iran, coupled with accelerating climate change, has become a serious challenge to the stability of insurance and reinsurance markets. Iran, due to its geographical location and climatic diversity, has historically been exposed to natural disasters, with floods accounting for over 60% of total economic losses from natural catastrophes between 1990 and 2023. Major recent events, such as the devastating floods of March 2019, which caused more than $8 billion in economic damage, have starkly revealed the country's high vulnerability and the urgent need for efficient risk transfer mechanisms. Under such circumstances, sole reliance on traditional actuarial pricing models based on stationary historical data—an approach that assumes the past is a reliable guide to the future—can lead to systematic underestimation of future risks. This limitation is particularly critical for the upper layers of catastrophe excess-of-loss (Cat XL) reinsurance, which are inherently exposed to extreme tail risks where data is scarce but potential losses are catastrophic. The scientific consensus confirms that the climate system is undergoing fundamental changes due to anthropogenic activities, rendering the stationarity assumption increasingly untenable for weather-related risks. This study aims to design and apply a novel climate-informed actuarial pricing framework to quantify the impact of climate change on the technical pricing of flood reinsurance in Iran. The main focus is on estimating and analyzing the "climate risk premium" across different reinsurance layers, thereby providing a quantitative basis for incorporating climate projections into actuarial practice.
METHODS: To model annual flood losses over the period 1990–2023, a composite Lognormal–Generalized Pareto Distribution (GPD) was employed to adequately capture the heavy-tailed behavior of the data. To incorporate climate change effects, projected changes in the extreme precipitation index (RX5day) from regional climate models under SSP2-4.5 and SSP5-8.5 scenarios were extracted and used to adjust the scale parameter of the GPD. This transformation shifted the loss distribution from a stationary to a non-stationary framework. Subsequently, a Monte Carlo simulation with 100,000 iterations was conducted to price a four-layer catastrophe excess-of-loss reinsurance program.
FINDINGS: The results demonstrate that the composite Lognormal-GPD distribution provides a statistically superior fit to the tail of historical loss data compared to conventional single-distribution approaches, as confirmed by Kolmogorov-Smirnov tests (p-value > 0.05) and Q-Q plot analysis. Analysis of the regional climate model outputs revealed mean relative increases in the RX5day index for Iran of approximately +12% under SSP2-4.5 and +24% under SSP5-8.5. These projected changes translated into corresponding adjustments to the GPD scale parameter, shifting the loss distributions toward larger values. Under the high-emission scenario (SSP5-8.5), the "climate risk premium"—defined as the percentage increase in the technical rate relative to the stationary historical baseline—exhibited a pronounced and systematic upward gradient across reinsurance layers. Specifically, the climate risk premium was calculated at 8% for the lowest layer ($5 million excess of $5 million), increasing to 11.1% for the second layer, 19.9% for the third layer, and reaching 38% for the highest layer ($90 million excess of $60 million). Furthermore, the exhaustion probability of the top layer more than doubled, increasing from 0.00094 in the historical baseline to 0.00201 under SSP5-8.5. These findings clearly indicate that the impact of climate change is disproportionately more severe on higher and riskier layers, creating a distinct "premium gradient" that traditional stationary models cannot capture.
Conclusion: Ignoring the non-stationary nature of climate risks leads to systematic and layer-dependent underpricing in catastrophe reinsurance, with the magnitude of underpricing increasing dramatically for upper layers. The proposed climate-informed actuarial framework provides a practical, transparent, and replicable methodology for primary insurers and reinsurers to directly integrate climate projections into their technical rate calculations. By quantifying the climate risk premium explicitly, this approach enables more accurate pricing, improved capital allocation, and enhanced risk management. For Iranian insurers, the findings imply an 8–38% increase in technical rates for flood catastrophe layers, with corresponding implications for pricing and reinsurance purchasing decisions. For international reinsurers, the framework offers a robust basis for evaluating flood risk in Iran under different climate scenarios and informing portfolio strategy. More broadly, this approach can enhance market resilience, support evidence-based regulatory decisions, and inform optimal risk transfer strategies in Iran and other vulnerable regions facing similar climate challenges. The transition from stationary to dynamic paradigms in catastrophe risk management is an unavoidable necessity in an era of accelerating climate change.

Keywords

• Climate Risk
• Composite Models
• Extreme Value Theory
• Non-Stationary Risk
• Reinsurance Pricing

Main Subjects

• Insurance pricing