Narrow Results

We analyze the impact of the network structure, the default probability and the loss given default (LGD) on the loss distribution of systemic defaults in the interbank market, where network structures analyzed include random networks, small-world networks and scale-free networks. We find that the network structure has little effect on the shape of the loss distribution, whereas the opposite is true to the default probability; the LGD changes the shape of the loss distribution significantly when default probabilities are high; the maximum of the possible loss is sensitive to the network structure and the LGD.

We extend the common Poisson shock framework reviewed for example in Lindskog and McNeil [15] 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 et al. [6], 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.

We extend the common Poisson shock framework reviewed for example in Lindskog and McNeil [15] 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 et al. [6], which we point out. Model extensions allowing for more articulated spread and recovery dynamics are hinted at. Calibration to both D Ji-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.