Normal-distribution assumptions understate crisis risk

Most financial risk models assume returns follow a normal distribution: small moves common, large moves rare, extreme moves negligible. The assumption is convenient and analytically tractable.

Real markets have heavy tails. Extreme events occur far more often than the normal distribution allows. Under standard models the 2008 crisis was characterised as so improbable it should occur roughly once in 100,000 years, yet events of comparable magnitude have happened several times within one lifetime.

When a model assigns a probability that low to something that then happens, the failure is in the founding assumption, not in the implementation.

The alternative is to start from the opposite premise: treat extreme events as a normal feature of complex systems, and measure the structural stress that precedes them rather than patching a distribution that does not fit.

That is the route we took: a derivation of our own rather than a fit to observed data, and an instrument built on it, calibrated on one half of the history and checked on the other. The literature agreeing corroborates the derivation; it does not replace it.