Modeling portfolio loss distribution under infectious defaults and immunization

2025-03-05

AI Summary

This paper addresses the inadequate modeling of default contagion in credit portfolio loss distribution. We propose a novel two-factor stochastic contagion model wherein defaulted entities initiate “infection attempts,” and solvent entities become infected only upon defense failure—formalizing, for the first time, an immunization mechanism. Crucially, the model decouples and integrates contagion dynamics with systemic risk factors. Methodologically, we develop an efficient recursive algorithm to compute the exact loss distribution and employ flexible mixture distributions to enhance empirical fit. Empirical validation on iTraxx indices demonstrates that our model significantly outperforms conventional copula-based approaches, delivering markedly improved pricing accuracy for multi-tranche synthetic CDO spreads. The framework thus provides a theoretically rigorous yet practically effective advancement in credit risk modeling and derivative valuation.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Modeling credit portfolio loss with infectious default contagion
• Developing efficient recursive algorithm for loss distribution
• Extending framework to integrate systematic factors for better fit

Innovation

• Recursive algorithm for loss distribution
• Flexible distributions with contagion component
• Empirical application pricing synthetic CDO tranches