A Way to Condition Transition Matrix on Wind

May 1, 1999

Over the last several years a number of credit risk models have been developed to measure future credit loss based on transitions in credit ratings, including default. In such models, the matrix of ratings transition probabilities, the so-called transition matrix, plays a crucial role in the calculation of the joint distribution of ratings for bonds that compose a portfolio. Wilson (1997) suggests a basic concept for constructing the transition matrix by postulating that the matrix is conditional on macroeconomic states, Belkin, Forest, and Suchower (1998) present a one-parameter representation of credit risk and transition matrices, and Nickell, Perraudin, and Varotto (1998) show that different transition matrices are identified across various factors, such as the obligor's domicile and industry and the stage of business cycle. The Basle Committee on Banking Supervision (1999) also emphasizes the importance of the conditional transition matrix vis-a-vis its ability to improve the accuracy of the credit risk models.

Previous studies, however, are difficult to apply to current credit risk models, since they use a large amount of panel data and/or focus on fitting retrospectively, rather than forecasting or stress testing the future transition matrix. In this paper, we describe a proposed model for estimating the conditional transition matrix. The idea is to adopt an established framework with a minimal number of parameters and a minimal amount of required data, within which we could incorporate credit cycle dynamics into the transition matrix. The technique of conditional transition matrix improves the accuracy of credit loss simulation provided by the credit risk models and yields an efficient method for stress testing according to the analyst's view of the future economic state. To implement the technique, we first build a credit cycle index, which indicates the credit state of the financial market as a whole. The model of building the credit cycle index needs to include the most relevant macroeconomic and financial series, such that the forecasted credit cycle index represents the credit state well, even with only a small number of series. The next step is conditioning the transition matrix on the forecasted credit cycle index. The model of conditioning the transition matrix should cover events that lead to upgrading and downgrading, as well as default. Furthermore, the estimated results should be stable enough to apply to forecasting or stress testing of the transition matrix. To show how the technique of conditional transition matrix improves the accuracy of credit loss simulation, we present an example from CreditMetrics.