This paper presents extreme value theory and its application to the computation of the value at risk of a position. The statistical theory allows us to quantify the behavior of extreme movements in prices and rates. Empirically, it is shown that the Fréchet distribution models this type of movement well. Extreme movements are associated with both little tremors like market adjustments or corrections during ordinary periods, and also earthquake-like stock market crashes or foreign exchange crises observed during extraordinary periods. An approach based on extreme values to compute value at risk then reconciles the existing VaR methods which consider usual market conditions, and stress testing methods which focus on crises.
LONGIN, F. (1997). From Value at Risk to Stress Testing: The Extreme Value Approach. ESSEC Business School.