Journal of Credit Risk

Risk.net

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

Kevin Jakob

  • New maximum likelihood estimation methods are introduced which are much more flexible when compared to the already-known estimators and can account for finite portfolio size, scarce default data, and time-varying and non-homogeneous default probabilities.
  • The methods can be used by financial institutions who wish to estimate correlation parameters consistently to the philosophy of their rating systems (i.e., point in time or through the cycle) and to prevent from misspecifications and double counting effects.
  • The results of a simulation study show that in the context of practical applications, the new estimators often outperform their competitors.

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.

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