Fat-tailed distribution

A fat-tailed distribution is a probability law in which extreme events, far from the mean, have a markedly higher probability of occurrence than a normal, Gaussian, law would predict. In concrete terms, very large losses are rare but far less improbable than intuition based on the bell curve suggests. This property is crucial in insurance and finance, because many real risks, natural catastrophes, financial crashes, systemic cyberattacks, follow fat-tailed rather than normal laws. Ignoring the thickness of the tail leads to a dramatic underestimation of the probability and cost of catastrophic events, and therefore to under-pricing and under-reserving. On these distributions, measures such as the mean and the standard deviation become unreliable, even misleading, because they are dominated by extreme values; tail-focused risk measures such as Value at Risk or Tail Value at Risk are preferred. Nassim Taleb popularized the idea that many fields belong to Extremistan, where a single event can dominate the entire series. Cyber risk and algorithmic risk are precisely suspected of belonging to these fat-tailed laws, which complicates their insurability.

Assuming a normal law, an insurer deems a loss beyond five standard deviations negligible; under a fat-tailed law, such a loss, for example a systemic cyberattack, is in fact plausible and must be priced.

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