Evaluating probabilities without model risk

This article presents methods for estimating extreme probabilities, beyond the range of the observations. These methods are model-free and applicable to almost any sample size. They are grounded in order statistics theory and have a wide range of applications, as they simply require the assumption of a finite expectation. Even in cases when a particular risk model exists, the new methods provide clarity, security and simplicity. The methodology is applicable to the behavior of financial markets, and the results may be compared to those provided by extreme value theory.