Occurrence exceedance probability curve

An occurrence exceedance probability curve associates with each loss amount the probability that at least one event in the year exceeds it. It is the catastrophe model output most used to size a non-proportional reinsurance program, since per occurrence layers respond to exactly that quantity. The loss at a given return period reads directly off it: the amount exceeded one year in two hundred corresponds to the 0.5 percent quantile. To size the top of a program you need to know how far protection must reach, and only an exceedance curve answers that. The cost of an average year does not. The curve differs from the aggregate curve, which covers the annual accumulation rather than the single worst event. The two must never be confused: on a frequency-exposed portfolio the aggregate curve gives amounts far above the occurrence curve at the same return period.