Credit Risk Propagation in Structural-Form Models

Chu-Lan Kao*, Cheng Der Fuh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Existing empirical studies on correlated defaults have shown that the default
of a firm impacts other firms; however, this impact has yet to be theoretically validated and quantified, especially under a structural-form model with more than two firms, and with multiple firms that are all likely to default with almost equal weight. To fill the gap, this paper studies how the firm value processes interact with each other in the presence of correlated defaults as well as a large number of firms. To this end, a new renewal theory is developed. The results show that even under a simple one-factor model, the idiosyncratic moments of the defaulted firm transfer to other firms at the time of default, causing a propagation in credit risk. Furthermore, we can quantify this propagation via
asymptotic theory, which provides a multi-name distance-to-default type risk
measure for a system of firms. The results potentially constitute a new method
in studying contagion and other correlated default effects, and therefore provide new measurements in credit risk management. Numerical and empirical studies are presented to illustrate our claim.
Original languageAmerican English
Pages (from-to)1340–1373
Number of pages34
JournalSIAM Journal on Financial Mathematics
Issue number4
StateAccepted/In press - 28 Jul 2021


  • structural-form model
  • correlated defaults
  • renewal theory
  • multi-name distance-to-defaults


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