The generalized extreme value distribution

This paper determines the type of asymptotic distribution for the extreme changes in stock prices, foreign exchange rates and interest rates. To find the correct limiting distribution for the maximal and minimal changes in market variables, a more general extreme value distribution is introduced using the Box-Cox transformation. Both the generalized Pareto distribution of Pickands [Ann. Stat. 3 (1975) 119] and the generalized extreme value distribution of Jenkinson [Q. J. R. Meteorol. Soc. 87 (1955) 145] are strongly rejected in favor of the newly proposed Box-Cox-GEV distribution. (C) 2003 Elsevier Science B.V. All rights reserved.