Frequency and severity

The frequency and severity decomposition is one of the most fundamental lenses of actuarial science. It consists of analyzing separately two dimensions of risk, frequency, which measures the number of losses expected over a period, and severity, which measures the average cost of a loss when it occurs. The product of these two quantities gives the expected burden, which is the core of the pure premium, the one that covers the expected loss before any loading for expenses and margin. This approach allows each component to be modeled with the appropriate statistical laws, for example a Poisson or negative binomial law for frequency, and a lognormal or Pareto law for severity, and then combined. It also illuminates the nature of a risk and the available levers, since two portfolios with the same premium can conceal opposite profiles, one with high frequency and low severity, the other the reverse. Cyber risk presents in this respect a formidable combination, a frequency rising under the effect of the professionalization of attacks, and a fat-tailed severity in which extreme events dominate, which makes its pricing particularly unstable.

To price a cover, the actuary estimates that a company will suffer on average two incidents per year at an average cost of fifty thousand euros, giving a pure premium of one hundred thousand euros, before adding loadings and accounting for the fat tail specific to cyber.

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