Mutual Excitation in Eurozone Sovereign CDS

We study self- and cross-excitation of shocks in the sovereign CDS market, on the basis of a
large database of Eurozone sovereign CDS spreads. We adopt a multivariate setting with credit
default intensities driven by mutually exciting jump processes, to capture the salient features
observed in the data, in particular, the clustering of high default probabilities both in time (over
days) and in space (across countries). We develop and implement an estimation methodology
for our model, by deriving closed-form formulae for CDS prices using the conditional character-
istic function, and matching those prices to their empirical counterparts. We …nd evidence for
self-excitation and asymmetric cross-excitation. Our analysis has important …nancial economic
applications, such as to assess the impact of a capital injection not just on a single country under
scrutiny but also, through reduction of cross-excitation risk — the essence of systemic sovereign
risk— , on other interconnected countries.