From Fault Tree to Credit Risk Assessment: A Case Study

Reliability has been largely applied to industrial systems in order to study the
various possibilities of systems' failure. It targets the chain of events leading to any
system’s failure, namely the top event. Looking for the minimal paths yielding any
system’s fault allows for a better control of systems' safety. To this end, reliability is
composed of a static approach (see Ngom et al. [1999] for example) as well as a dynamic
approach (see Reory and Andrews [2006] for example). In this paper, we extend the
framework of Gatfaoui (2006) who applies fault tree theory to credit risk assessment. The
author explains that fault tree is one alternative approach of reliability, which matches
default risk analysis in a simple framework. Our extension includes other distributions of
probability to model the lifetimes of French firms while studying the related empirical
default probabilities. We use mainly, but not exclusively, continuous distributions for
which the exponential law used by Gatfaoui (2006) constitutes a particular case. Our results
exhibit both the exponential nature of French firms' lifetimes as well as strong convex and
fast decreasing time varying failure rates. Such a feature has some non-negligible impact
insofar as it characterizes corresponding credit spreads' term structure.