  Based on data from the European banking stress tests of 2014, 2016 and the
transparency exercise of 2018 we demonstrate for the first time that the latent
geometry of financial networks can be well-represented by geometry of negative
curvature, i.e., by hyperbolic geometry. This allows us to connect the network
structure to the popularity-vs-similarity model of Papdopoulos et al., which is
based on the Poincar\'e disc model of hyperbolic geometry. We show that the
latent dimensions of `popularity' and `similarity' in this model are strongly
associated to systemic importance and to geographic subdivisions of the banking
system. In a longitudinal analysis over the time span from 2014 to 2018 we find
that the systemic importance of individual banks has remained rather stable,
while the peripheral community structure exhibits more (but still moderate)
variability.
