Credit risk is defined as the risk of loss resulting from failure of obligors to honor their payment obligations. The 1988 Basel Accord (“Basel I”), issued by the Basel Committee on Banking Supervision, is a framework for credit risk measurement and requires banks to maintain a capital to risk-weighted asset ratio of at least 8%. The 2004 Basel Accord (“Basel II”) is a revision of Basel I, aiming to promote the soundness of the financial system. It is based on three pillars: (1) minimum capital requirements; (2) supervisory review processes; and (3) market discipline. Keeping the capital to risk-weighted asset ratio of at least 8% requirement of the first Basel accord, the revision adjusts capital requirements to credit risk, operational risk and market risk. Credit risk in this context is the focus of this paper.
Basel II allows banks to evaluate the credit risk using either a standardized approach or an internal ratings-based (IRB) approach. The standardized approach relies on external ratings, such as those assigned by external credit assessment institutions, to determine risk weights for capital charges, whereas the IRB allows banks to develop their own internal ratings for risk-weighting purposes subject to supervisory approval and strict disclosure requirements. Some large banks start with the IRB approach. However, most banks start with the standardized approach and progress toward the more advanced IRB approaches that generate lower capital charges as they meet incremental requirements.
The probability of default (PD) is one of the key IRB risk parameters. It plays a central role in pricing of credit assets, portfolio management, and capital allocation. Banks must categorize exposures into risk classes and for each class estimate a PD. This estimate is one of the inputs to a formula that gives risk capital requirements for an asset in a given class.
Three main issues have been raised in estimating the PD. The first issue is handling the missing values for obligors’ financial variables such as cash flow, net borrowing, and inventory turnover ratio. Internal data on such variables are the primary data source for the PD estimates. However, in practice, internal records are often incomplete and/or do not have long enough history to estimate the PD. Missing data are especially problematic in the case of low default portfolios characterized by no or very few default records.
A survey of five international journals in banking and finance shows that missing data are a common feature of many financial applications (Kofman and Sharpe, 2003). The easiest method to handle missing data is complete case analysis, where incomplete cases are removed from the study. However, this method, at best, gives unbiased but inefficient estimates, and at worst, biased estimates. An alternative is to use ad-hoc methods of single imputation, which substitute a plausible value such as average or median for each missing value. Biased estimates, understated variances and lower coverage rates are some of the major problems generally associated with these methods. In order to reflect uncertainty arising from imputation of missing values into the imputation procedure, maximization of the incomplete data likelihood (Dempster, Laird and Rubin, 1977) and maximization of the posterior distribution (Tanner and Wong, 1987) have also been suggested. However, as indicated by Schafer (1997) and King, Honaker, Joseph and Scheve (1998), such maximization methods can produce incorrect standard errors in financial applications where non-normality and small samples are common occurrences.
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