  We extend the common Poisson shock framework reviewed for example in Lindskog
and McNeil (2003) to a formulation avoiding repeated defaults, thus obtaining a
model that can account consistently for single name default dynamics, cluster
default dynamics and default counting process. This approach allows one to
introduce significant dynamics, improving on the standard "bottom-up"
approaches, and to achieve true consistency with single names, improving on
most "top-down" loss models. Furthermore, the resulting GPCL model has
important links with the previous GPL dynamical loss model in Brigo,
Pallavicini and Torresetti (2006a,b), which we point out. Model extensions
allowing for more articulated spread and recovery dynamics are hinted at.
Calibration to both DJi-TRAXX and CDX index and tranche data across attachments
and maturities shows that the GPCL model has the same calibration power as the
GPL model while allowing for consistency with single names
