Secondary uncertainty
The spread of the damage a property suffers once the event has occurred: two identical houses on the same street, under the same wind, do not suffer the same loss.
A catastrophe model separates two sources of uncertainty. Primary uncertainty concerns the event itself: whether it occurs, where, and with what intensity, and the stochastic event set represents it. Secondary uncertainty concerns the damage once the intensity is known: for the same wind speed, the same construction type and the same flood depth, the observed damage ratio spreads widely around its mean, and the model represents it with a probability distribution attached to each location. It does not change the mean loss of a property insured without deductible or limit, but it matters as soon as the contract stops being linear. A deductible, a limit or a reinsurance layer transform the damage nonlinearly, and the mean insured loss then depends on the whole distribution rather than on its mean alone. Ignoring secondary uncertainty therefore misprices precisely the contract features the underwriter negotiates.
Hypothetical case: a 300,000 euro house carries a 30,000 euro deductible. For the simulated windstorm, the mean damage ratio is 8 percent, or 24,000 euros: computed on the mean alone, the insured loss is zero. If one house in ten actually suffers more than 20 percent damage, over 60,000 euros, the insurer pays at least 30,000 euros in those cases, and the mean insured loss is no longer zero.
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