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From Fault Tree to Credit Risk Assessment: An Empirical Attempt

By Hayette Gatfaoui

Abstract

Since 80’, fault tree theory has known a great development in industrial systems’ sector. Its first goal is to estimate and model the probability and events combination which could lead a given system to failure. Later static and dynamic studies arise such as Dugan, Venkataraman & Gulati (1997), Gulati & Dugan (1997) and Ngom et al. (1999) for example. Improvements are also proposed by Anand & Somani (1998)[REF], Zhu et al. (2001)[REF] and Reory & Andrews (2003)[REF] among others. Since credit risk valuation attempts to quantify firms’ default risk, we propose to apply one alternative approach of fault tree, or equivalently, reliability study to assess firms’ default risk. We set a very simple framework and use French firms’ bankruptcy statistics to quantify default probabilities. From these empirical default probabilities and under the assumption that the lifetime process follows an exponential law with a constant parameter, we estimate this constant parameter for French sectors. Each parameter’s estimation corresponds to the related hazard rate over the time horizon under consideration. Checking for the consistency of our constant parameter’s assumption, we compute the monthly implied parameters related to our exponential law setting. Results show a time varying behavior for those parameters. Indeed, each exponential law’s parameter is a convex decreasing function of time. Whatever, such an approach may be useful to give a statistical benchmark for common credit risk models’ improvement.credit risk default probability failure rate fault tree reliability survival

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