  One of the most challenging aspects in the analysis and modelling of
financial markets, including Credit Default Swap (CDS) markets, is the presence
of an emergent, intermediate level of structure standing in between the
microscopic dynamics of individual financial entities and the macroscopic
dynamics of the market as a whole. This elusive, mesoscopic level of
organisation is often sought for via factor models that ultimately decompose
the market according to geographic regions and economic industries. However, at
a more general level the presence of mesoscopic structure might be revealed in
an entirely data-driven approach, looking for a modular and possibly
hierarchical organisation of the empirical correlation matrix between financial
time series. The crucial ingredient in such an approach is the definition of an
appropriate null model for the correlation matrix. Recent research showed that
community detection techniques developed for networks become intrinsically
biased when applied to correlation matrices. For this reason, a method based on
Random Matrix Theory has been developed, which identifies the optimal
hierarchical decomposition of the system into internally correlated and
mutually anti-correlated communities. Building upon this technique, here we
resolve the mesoscopic structure of the CDS market and identify groups of
issuers that cannot be traced back to standard industry/region taxonomies,
thereby being inaccessible to standard factor models. We use this decomposition
to introduce a novel default risk model that is shown to outperform more
traditional alternatives.
