Claim frequency

Claim frequency is the number of claims divided by the matching exposure, in policy-years, vehicle-years or sums insured: frequency = claim count ÷ exposure. March 17, 2020, first lockdown in France: cars stay in the garage and motor claim frequency drops sharply within weeks, while the number of policies barely moves. Together with severity, the average cost per claim, it makes up the pure premium in a priori rating: pure premium = frequency × severity. A frequency of 0.12 means 12 claims per 100 policy-years of exposure. The standard model treats the two drivers as independent, which remains an assumption. Claim counts are first modeled with a Poisson distribution whose parameter is frequency times exposure; when the observed variance exceeds the mean, a sign of a heterogeneous book, actuaries move to the negative binomial. In pricing, a Poisson generalized linear model with a log link and log exposure as an offset does the same calculation rating factor by rating factor. It gets confused with two related measures. The loss ratio divides claim amounts by premium, not counts by exposure. The share of insureds with a claim counts a policyholder who reports three claims in a year only once, and so understates frequency. Exposure has to be counted on the same basis as claims, and frequency moves with the claim definition used (before or after deductible), with seasonality and with behavior. In non-proportional reinsurance, people talk about excess frequency, the expected number of losses that reach the layer. Tracked over time, it flags a loss trend before severity shows how big it is.