Estimating correlation parameters in credit portfolio models under time-varying and nonhomogeneous default probabilities

Since the development of the first credit portfolio models at the end of the last century (eg, CreditMetrics by JP Morgan and CreditRisk+ by Credit Suisse First Boston), the estimation of correlation parameters has been widely discussed in the literature, and many different estimation methods have been proposed. Unfortunately, many of them assume an infinitely large portfolio of counterparties, and nearly all of them assume a homogeneous one. These two assumptions are not realistic for banks’ typical portfolio segments other than the retail banking segment. To remove these shortcomings, we introduce new maximum likelihood estimation methods that are much more flexible than existing estimators, with the ability to account for finite portfolio sizes, scarce default data and time-varying, nonhomogeneous default probabilities. The last two aspects are necessary for financial institutions who wish to estimate correlation parameters in a way that is consistent with the philosophy of their rating systems (ie, point-in-time or through-the-cycle) and to prevent misspecifications and double-counting. Through a simulation study, the performance of the new estimators is compared with that of a selection of well-known estimators. The results show that, in the context of practical applications, the new estimators often outperform their competitors.