Temporal clustering of events
The tendency of catastrophes, European windstorms first among them, to arrive in runs within a season more often than a Poisson model predicts, which fattens the tail of annual losses.
Temporal clustering of events is the tendency of some catastrophes to arrive in runs, several in the same season, more often than independent draws would predict. In late December 1999, Lothar swept across northern France, Switzerland and southern Germany on the 26th; Martin crossed southwestern France overnight from the 27th to the 28th. Nine years earlier, from late January to early March 1990, Daria, Herta, Vivian and Wiebke hit Western Europe one after another. In 2004, four hurricanes struck Florida in six weeks. For winter storms the mechanism is well understood: a strong, stable jet stream pointed at Europe turns out low after low for weeks on end. A catastrophe model that draws the annual event count from a Poisson distribution assumes the opposite, that each storm knows nothing of the one before. The usual fix is a negative binomial distribution, or a Poisson mixture whose rate changes from year to year: same mean, higher variance. Average annual loss does not move. The AEP curve (aggregate exceedance probability of annual losses) gets a fatter tail, while the OEP curve (largest single event loss) barely shifts and even drops a little, since years with no storm also become more common. So the impact lands on anything that looks at the full year: stop-loss, aggregate excess of loss, annual aggregate cat bonds, and the number of reinstatements on a per-event cover. A second limit that looked almost free under Poisson now carries a price. The main European windstorm models build clustering in today, with parameters the data pin down poorly: a few decades of well-observed winters cannot measure overdispersion with any precision.
Textbook case, made-up figures: a European windstorm layer is hit 0.5 times a year on average, with one reinstatement. Under Poisson, the probability of at least two hits in a year is 9.0%, and of a third, uncovered, 1.4%. With a negative binomial of the same mean and a variance of 1, those probabilities rise to 11.6% and 5.0%. Average loss has not moved; the risk of being left bare by a third storm has more than tripled, and the cedant carries it.
event clustering, storm clustering, serial clustering, windstorm clustering
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