This article presents extreme value theory and its application to the computation of the value at risk of a position. This statistical theory allows to quantify the behavior of extreme movements in prices and rates. Empirically, it is shown that the Fréchet distribution is an accurate model for this type of movement. Extreme movements are associated with shocks like market adjustments or corrections during normal periods and also with "earthquakes" such as stock market crashes or foreign exchange crises observed during extraordinary periods.
LONGIN, F. (1997). Value at Risk : une nouvelle méthode fondée sur la théorie des valeurs extrêmes. ESSEC Business School.