Although the most commonly employed risk measures are based upon the entire distribution of asset prices, many financial events are related to extreme risks located at the tails of the distribution. This article appliesthe extreme value theory to the computation of the capital requirement for a financial institution. Statistical theory allows us to quantify the behavior of extreme price variations observed in financial markets. Extremes selected over a long period of time obey the so-called extreme value distribution, which can either be a Weibull, a Gumbel or a Fréchet distribution according to the shape of the distribution tail. The specified extreme value distribution is then used to compute the position-risk requirement of a portfolio. An example is presented for a US equity portfolio.
LONGIN, F. (2000). Capital Requirement: A New Method Based on Extreme Price Variations. Journal of Risk Finance, pp. 42-50.