Modeling portfolio loss distribution under infectious defaults and immunization

• We propose a contagion model for credit portfolio losses. • An efficient recursive algorithm to compute the loss distribution is introduced. • The model is analytically tractable, with a clear interpretation of pairwise dependence. • We extend the model including a systematic factor using conditional and mixture distributions. • We use the model for the pricing of iTraxx synthetic CDO tranches obtaining good fit. 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 more flexible distributions that integrate a contagion component and a systematic factor 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.