Abstract
In the class of bivariate extreme value copulas, an upper bound is calculated for the measure of non-exchangeability $\mu_{\infty}$ based on the $L^{\infty}$-norm distance between a copula $C$ and its transpose $C^t(x,y)=C(y,x)$. Copulas that are maximally non-exchangeable with respect to $\mu_{\infty}$ are also determined.
Moreover, similar upper bounds are given, respectively, for the
class of all EV copulas having a fixed upper tail dependence coefficient and for the larger
class of Archimax copulas.