Symmetrization of bivariate copulas preserves Spearman's rho while setting non-exchangeability measures to zero, and a sharp bound shows the Schweizer-Wolff measure is at least six times any non-exchangeability measure.
and Fernández-Sánchez, J
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Concordance, symmetrization and non-exchangeability for bivariate copulas
Symmetrization of bivariate copulas preserves Spearman's rho while setting non-exchangeability measures to zero, and a sharp bound shows the Schweizer-Wolff measure is at least six times any non-exchangeability measure.