PDF Ebook Frailty Correlated Default: Preliminary and Incomplete Version
This paper introduces and estimates a new model of frailty-correlated defaults, according to which firms have an unobservable common source of “frailty,” a default risk factor that changes randomly over time. The posterior distribution of this frailty factor, conditional on past observable covariates and past defaults, represents a significant additional source of uncertainty to creditors. Our model is estimated for U.S. non-financial public firms for the period 1979-2004. The results show that the frailty factor induces a large estimated increase in default clustering, and significant additional fluctuation over time in the conditional expected level of default losses, above and beyond that predicted by our observable default covariates, including leverage, volatility, and interest rates.
The usual duration-based model of default probabilities is based on the doubly-stochastic assumption, by which firms’ default times are conditionally independent given the paths of observable factors influencing their credit qualities. Under this assumption, different firms’ default times are correlated only to the extent implied by the correlation of observable factors determining their default intensities. For example, Couderc and Renault (2004), Shumway (2001), and Duffie, Saita, and Wang (2006) use this property to compute the likelihood function, which is to be maximized when estimating the coefficients of a default intensity model, as the product across firms of the covariate-conditional likelihoods of each firm’s default or survival. This significantly reduces the computational complexity of the estimation.
The doubly-stochastic assumption is violated in the presence of “frailty,” meaning unobservable explanatory variables that may be correlated across firms. For example, the defaults of Enron in 2001 and WorldCom in 2002 may have revealed faulty accounting practices that could have been used at other firms, and thus may have had an impact on the conditional default probabilities of other firms. Even if all relevant covariates are observable in principle, some will inevitably be ignored in practice. The impacts of missing and unobservable covariates are essentially equivalent from the viewpoint of estimating default probabilities or portfolio credit risk.
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PDF Ebook Frailty Correlated Default: Preliminary and Incomplete Version
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