Default correlation, cluster dynamics and single names: The GPCL dynamical loss model

TL;DR

The paper introduces the GPCL dynamical loss model, extending Poisson shock frameworks to better capture default dynamics at both single name and cluster levels, with strong calibration performance.

Contribution

It presents a novel formulation that avoids repeated defaults, enabling consistent modeling of individual and cluster default dynamics, improving on existing top-down and bottom-up approaches.

Findings

Achieves comparable calibration to the GPL model.

Ensures consistency with single name default dynamics.

Provides a flexible framework for spread and recovery dynamics.

Abstract

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