Modeling portfolio loss distribution under infectious defaults and immunization

Gianluca Farina, Rosella Giacometti and Gabriele Torri

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Abstract: We introduce a model for the loss distribution of a credit portfolio considering a contagion mechanism for the default of names which is the result of two independent components: an infection attempt generated by defaulting entities and a failed defence from healthy ones. We then propose an efficient recursive algorithm for the loss distribution. Then we extend the framework with a more flexible mixture distribution to better fit real-world data. Finally, we propose an empirical application in which we price synthetic CDO tranches of the iTraxx index, finding a good fit for multiple tranches.

Date: 2025-03
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