From Fault Tree to Credit Risk Assessment: A Case Study
by Hayette Gatfaoui of the University of Technology, Sydney
Abstract: Reliability has been largely applied to industrial systems in order to study the various possibilities of systems' failure. The goal is to establish the chain of events leading to any system's failure, namely the top event. Looking for the minimal paths leading to 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.  [REF] for example) as well as a dynamic approach (see Reay & Andrews  for example). In this paper, we extend the framework stated by Gatfaoui (2003) allowing for the application of 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 (2003) 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.
Keywords: credit risk, default probability, failure rate, fault tree, reliability, survival probability.