We study the international interbank market through a geometric analysis of empirical data. The geometric analysis of the time series of cross-country liabilities shows that the systematic information of the interbank international market is contained in a space of small dimension. Geometric spaces of financial relations across countries are developed, for which the space volume, multivariate skewness and multivariate kurtosis are computed. The behavior of these coefficients reveals an important modification acting in the financial linkages since 1997 and allows to relate the shape of the geometric space that emerges in the last years to the globally turbulent period that has characterized financial systems since the latest Nineties. Here we show that, besides a persistent decrease in the volume of the geometric space since 1997, the observation of a generalized increase in the values of the multivariate skewness and kurtosis sheds some light on the behavior of cross-border interdependencies during periods of financial crises. This was found to occur in such a systematic fashion, that these coefficients may be used as a proxy for systemic risk.