Return Periods & Exceedance Probability

The Exceedance Probability Curve

The most fundamental output of a catastrophe model is the Exceedance Probability (EP) curve. For a given portfolio of insured properties, an EP curve is a graphical representation of the probability that a certain level of loss will be surpassed in a given time period — typically one year. The EP curve is the primary communication tool for conveying cat model results to underwriters, executives, regulators, and capital market investors.

Return Periods

A return period is the average number of years between events of a given severity or greater. A 1-in-100 year event has a 1% annual probability of occurring. A 1-in-250 year event has a 0.4% annual probability.

OEP vs. AEP

There are two types of EP curve, reflecting different questions:

• Occurrence Exceedance Probability (OEP): The probability that the single largest event in a year will exceed a given loss level. Used when the concern is a single catastrophic event devastating the portfolio.
• Aggregate Exceedance Probability (AEP): The probability that the total of all events in a year will exceed a given loss level. Relevant for assessing aggregate annual cat exposure, especially where multiple moderate events could combine into a significant annual loss.

Distributing Losses Among Stakeholders

The EP curve can be used to allocate losses among different stakeholders — homeowners bearing a deductible, an insurer covering mid-layer losses, and a reinsurer covering extreme losses. For example, suppose a portfolio has a total value of $100 million and potential losses are divided: the first $5 million (L1) is borne by policyholders through deductibles, losses between $5M and $30M (L2) are covered by the insurer, and losses above $30M (L3) are covered by reinsurance. This structure directly maps onto an EP curve — each stakeholder's exposure can be read off at the relevant attachment and exhaustion points.

The Role of Uncertainty

EP curves carry significant uncertainty, particularly in the tail. When loss uncertainty is introduced (modelled by the coefficient of variation, or CV, of event losses), events that appear unable to penetrate a high reinsurance layer may now carry a small probability of doing so. For example, with CV = 1.0 on event losses, there may be a 0.28% annual probability of loss reaching a reinsurance layer that the mean estimates suggest would never be touched. Understanding and communicating this uncertainty is a core skill of the professional cat modeller.