Extreme value theory allows us to quantify the statistical behavior of the largest shocks in financial markets. First, it is applied to different financial markets (equity and interest rates). The behavior of the extremes of these financial variables seems to be modelled well by the Fréchet distribution. We apply the results about the extremes to the regulation on market risks for financial institutions. We compute the capital requirement for a given probability, and inversely, the probability associated with a given level of capital requirement.
BOULIER, J.F., DALAUD, R. and LONGIN, F. (1997). Application de la théorie des valeurs extrêmes aux marchés financiers. ESSEC Business School.