Catastrophe risk and climate change

Catastrophe risk has two features that break the assumptions of ordinary pricing. First, low frequency: the history of an insurer, or even of a country, does not contain enough events to estimate the tail of the distribution. Second, accumulation: a single event affects thousands of policies at the same time, so the law of large numbers does not diversify the risk within the portfolio. The industry's answer was catastrophe models, which combine earth sciences, structural engineering and actuarial mathematics.

Mexico is one of the most exposed countries in the world: subduction of the Cocos and Rivera plates generates large earthquakes along the Pacific coast, the Valley of Mexico amplifies seismic waves because of its lakebed soils, and the country is hit by hurricanes from both the Atlantic and the Pacific. That is why the CNSF (National Insurance and Surety Commission) regulates earthquake and hurricane insurance specifically, and the federal government has been a pioneer in transferring sovereign risk through catastrophe bonds.

Climate change adds another layer of difficulty: models are calibrated on the past, but the frequency and severity of some hydrometeorological perils are shifting. This guide connects the metrics with regulation and with risk transfer practice, with links to reinsurance and solvency.

A catastrophe model has four components. The exposure module describes each insured property: geocoded location, structural type, number of stories, year built, occupancy, and insured values for building, contents and consequential losses.

The hazard module generates a stochastic catalog of thousands of possible events, each with its annual rate of occurrence. For earthquake, it starts from seismogenic sources, magnitude-frequency recurrence relationships and attenuation laws that give the intensity (spectral acceleration) at each site, with site effects such as soft soil amplification. For hurricane, historical tracks are perturbed or synthetic storms are simulated with their wind field, storm surge and rainfall. The CNSF technical bases for hurricane describe exactly this procedure: perturbing historical tracks and simulating hail, flood, storm surge and non-hurricane wind events.

The vulnerability module translates intensity into damage through functions that give the mean damage ratio (between 0 and 1) and its dispersion, typically with a beta distribution. The financial module applies the policy terms (deductibles, coinsurance, limits and sublimits) and then the reinsurance (quota share, surplus and excess of loss layers) to obtain the gross, retained and ceded loss per event.

The model output is an event loss table (ELT): for each event, its annual rate λ_i and its loss L_i (or a loss distribution). If events occur as independent Poisson processes, the average annual loss (AAL) is the sum of rates times losses, and it is the basis of the pure premium. Expenses and a load for the capital required by the tail are added to obtain the technical premium.

The occurrence exceedance probability (OEP) curve gives the probability that in a year the most severe event exceeds a given amount; it is the relevant curve for per-event excess of loss layers. The aggregate curve (AEP) gives the probability that the sum of losses in the year exceeds the amount; it is the relevant curve for capital, annual aggregates and stop loss covers. Because the sum of several events can exceed a threshold that none exceeds on its own, AEP(x) ≥ OEP(x) always holds, and the difference grows at low thresholds and for frequent perils such as hydrometeorological ones.

The return period is the inverse of the exceedance rate: a loss with a 250-year return period is exceeded on average once every 250 years, which does not mean it occurs with that regularity. The PML is the loss associated with a chosen return period: 200 years in Solvency II, 1,500 years in the CNSF technical bases. As a complement, TVaR averages the losses beyond that point and captures the size of the tail.

Mexico's seismic hazard is concentrated along the Pacific coast, from Jalisco to Chiapas, because of subduction, and in intermediate-depth intraplate earthquakes, such as the one on September 19, 2017, which cause damage far from the coast. Mexico City is a case study worldwide: the lakebed zone amplifies long-period waves, and damage depends critically on the structural period of the building. The earthquakes of September 19, 1985 and of September 7 and 19, 2017 shaped the building code, reserve regulation and modeling practice.

For hurricanes, both coastlines are exposed. Wilma (2005), in the Mexican Caribbean, remains the costliest hydrometeorological event for the insurance industry according to AMIS (Mexican Association of Insurance Institutions). Otis (2023), which intensified within hours to category 5 before making landfall in Acapulco, generated payments of 39,343 million pesos according to AMIS: the second costliest hurricane and the third most expensive loss in the history of Mexican insurance, after the COVID-19 pandemic and Wilma. Its intensification, which forecasts did not anticipate, is an example of why catalogs must be reviewed in light of a changing climate.

Earthquake insurance and hurricane and other hydrometeorological insurance make up the catastrophe risk line of business (article 27, section XV of the LISF, Insurance and Surety Institutions Law). For these, the CNSF provides institutions with mandatory software to calculate the risk premium and the PML: Sistema R for earthquake and volcanic eruption, updated in 2012, and Sistema RH-Mex for hurricane, from 2006. In August 2024 the CNSF presented their 2.0 versions, which keep the same technical bases with marginal differences and modernize the platform. The technical bases are in Annexes 5.1.5-a (earthquake) and 5.1.6-a (hurricane) of the CUSF (Single Insurance and Surety Circular), which cite work by the UNAM Institute of Engineering and define the PML as the loss with a 1,500-year return period.

These results are used to value three things: the unearned premium reserve (with the risk premium), the catastrophe risk reserve and the capital requirement for risks based on the PML. The purpose of the catastrophe reserve is to cover the value of the PML (article 217, section VI of the LISF). Under Chapters 5.6.5 and 5.6.6 of the CUSF, it is cumulative, increases monthly with the earned portion of retained risk premiums, earns investment income and may only be drawn down in defined circumstances, such as catastrophe losses not covered by excess of loss reinsurance or reinstatement costs. It has a ceiling tied to the retained PML; for hurricane, 90% of the greater of the average PML over the last five years and the PML at year-end.

In the RCS (solvency capital requirement), the RC_PML component starts from the retained PML and recognizes as deductions the catastrophe risk reserve and the protection from catastrophe excess of loss contracts, whose reinsurer default risk is measured separately. An insurer can therefore substitute reinsurance or accumulated reserves for capital, and the actuary must optimize that mix.

Mexico was the first government to issue a catastrophe bond, in 2006, and by 2024 it had sponsored 20 bonds through the World Bank program. They are parametric instruments: they pay if an event meets predefined parameters (magnitude, depth and location for earthquake; central pressure and track for hurricane), not according to the measured loss. This allows payment within weeks. After the September 7, 2017 earthquake in Chiapas, the earthquake class of the 2017 bond paid 100% of its 150 million dollars; after Otis, the Pacific hurricane class of the 2020 bond lost about half of its principal.

In 2024 the World Bank placed bonds for Mexico totaling 420 million dollars in April (two earthquake classes of 225 and 70 million, and an Atlantic storm class of 125 million) and 175 million in May for Pacific hurricanes: 595 million in total, maturing in April 2028. They are complemented by an annual parametric insurance policy placed through Agroasemex, which for the June 2026 to May 2027 policy period covers 10,000 million pesos.

The price of parametric cover is basis risk: the difference between the payout and the actual loss. In July 2026 a magnitude 7.3 earthquake off the coast of Chiapas occurred within a trigger box of the 2024 bond, but class B required at least 7.4 for a first payout of 25%, so nothing was paid. Designing boxes, thresholds and tiered payouts is an actuarial problem of minimizing basis risk with a verifiable trigger.

Parametric insurance is not limited to governments. In 2019, the trust for the integrated management of the Quintana Roo coastal zone, with support from The Nature Conservancy and participation from the hotel sector, purchased the first parametric insurance policy for a coral reef, covering a stretch of the Mesoamerican Reef System. The trigger is hurricane wind speed within a predefined area; after Hurricane Delta in 2020, the policy paid about 17 million pesos, which funded brigades to assess damage, remove debris and repair the reef.

The economic logic is that the reef is infrastructure: it dissipates wave energy and protects beaches and hotels, so its rapid restoration reduces future losses to the tourism economy. The actuary designs the payout function from a hazard model (the distribution of maximum wind in the area) and from the need for post-event liquidity, not from a damage appraisal.

Event catalogs assume stationarity: that the frequency and severity observed in the past represent next year. For hydrometeorological perils that assumption is weakening: ocean warming favors rapid intensification, sea level rise worsens storm surge and patterns of extreme rainfall are changing. In practice, one-year models are adjusted with catalogs conditioned on sea surface temperature, while long-term analysis uses scenarios.

The scenarios of the Network for Greening the Financial System (NGFS), which brings together central banks and supervisors, are the benchmark: orderly (early transition to net zero), disorderly (late and abrupt transition) and hot house world (current policies, greater physical risk). They combine physical risk and transition risk, which affects the value of assets in carbon-intensive sectors. In Europe, EIOPA published guidance on using climate scenarios in the ORSA, and the Solvency II review strengthens the integration of these risks.

In Mexico, CINIF issued the Sustainability Reporting Standards NIS A-1 and NIS B-1, effective from 2025, with basic indicators that include emissions and energy, and the IAA's ISAP 8 guides actuarial work related to climate disclosures under IFRS S2. For an insurer, integrating climate into the ARSI (own risk and solvency assessment) means quantifying how the AAL and the PML change under frequency and intensity scenarios, and what that implies for pricing, reinsurance and capital.

The Mexican market operates under catastrophe regulation that is more prescriptive than in other countries: institutions do not freely choose their model for regulatory purposes but use the CNSF systems for risk premium, PML, reserve and capital. This standardizes the calculation and protects the market against underestimation, at the cost of making improvements in exposure data quality, such as precise geocoding and structural classification, the main lever available to each insurer. In parallel, international reinsurers apply their own commercial models to price excess of loss programs.

On the public side, Mexico combines World Bank catastrophe bonds, a parametric insurance policy renewed annually through Agroasemex and budget resources. Before it was dissolved, FONDEN (Natural Disaster Fund) promoted tools such as R-FONDEN, developed with the participation of the UNAM Institute of Engineering to identify exposed public assets and estimate probable losses, and it supported prevention programs. The Mexican experience is cited internationally as a case study in disaster risk financing.

The outstanding agenda is the protection gap: a significant share of homes and small businesses have no earthquake or hurricane insurance. Simple parametric products, insurance linked to mortgage lending and schemes with state governments are avenues where actuarial work in pricing, trigger design and reinsurance has a direct impact.