Multivariate ordinal models in credit risk: Three essays

This dissertation deals with the development, implementation and application of a multivariate statistical framework for credit risk modeling, which is able to incorporate both, default (or failure) information and credit ratings. Credit risk is the risk of a loss arising from a failure (or default) of a counterparty to meet its contractual obligations (e.g., McNeil et al., 2015). The modeling of credit risk in banks and insurance companies has received considerable attention from academics and practitioners over the last decades. From a regulatory point of view, the Basel Committee on Banking Supervision provides a sophisticated foundation for the assessment of credit risk (Basel I, 1988; Basel II, 2004; Basel III, 2011). According to this regulatory framework, credit risk management and the development of appropriate credit risk models have a crucial relevance for banks and insurance companies, influencing their capital requirements. The financial crisis of 2007-2009 has made the prediction of bankruptcies as well as the understanding of the drivers of creditworthiness an even more urgent matter. Credit rating agencies provide in their credit ratings a forward-looking opinion about the creditworthiness of firms and sovereigns. Even though external credit ratings from the big three players in the credit rating market (Standard and Poor’s (S&P), Moody’s and Fitch) where criticized in the aftermath of the financial crisis, they seem to remain the most common and widely used credit risk measure (Hilscher and Wilson, 2017). Alternatively to credit ratings, internal statistical models based on historical defaults, accounting and market information are often applied when modeling credit risk. Such internal credit risk models serve as a widely-used alternative to credit ratings. Among others Lipton et al. (2012) and Löffler (2013) argue that credit rating agencies react slowly to credit events and are outperformed by failure prediction models in terms of prediction accuracy. Nevertheless in scenarios where defaults are scarce credit ratings serve as an important measure of credit risk and present an alternative to statistical models. The thesis consists of three research articles. The first paper is concerned with a multivariate extension of ordinal regression models. The model class of multivariate ordinal regression models is motivated by the fact that correlated ordinal data arises naturally when modeling credit ratings. Existing model specifications are extended in several directions. E.g., we allow for a flexible covariate dependent correlation structure between the continuous variables underlying the ordinal credit ratings. Furthermore, in addition to an underlying multivariate normal distribution (multivariate probit link), a multivariate logistic distribution (multivariate logit link) is considered. Moreover, missing observations in the response variables can be dealt with by the model. An estimation algorithm based on composite maximum likelihood methods is implemented and the quality of the estimates is investigated by means of a comprehensive simulation study. The proposed model allows to obtain insights into the rating behaviour of the big three credit rating agencies. The second research article aims at making the algorithm for the estimation of multivariate ordinal regression models developed in the first paper accessible for the statistical community. A flexible modeling framework for multiple ordinal measurements on the same subject is set up and implemented in the form of an R package (R Core Team, 2019). The mvord package (Hirk et al., 2019b) is freely available on the “Comprehensive R Archive Network” (CRAN) and enhances the available statistical software for analyzing correlated ordinal data. The flexible and user-friendly model design allows practitioners and researchers, who deal with correlated ordinal data in various areas of application, for different error structures to capture the dependence among the multiple observations. In addition, flexible constraints on the regression coefficients and on the threshold parameters can be set. The third paper uses the framework developed and implemented in the first two research articles to propose a novel multivariate credit risk model, where default or failure information together with rating or expert information are jointly modeled. The proposed credit risk model uses financial variables typically used for bankruptcy predictions to provide probabilities of default conditional on the credit ratings from one or more credit rating agencies. The model is able to account for missing default and credit rating information. An empirical analysis on a data set of US firms over the period from 1985 to 2014 is conducted. Our findings suggest that the proposed joint modeling framework gives superior prediction accuracy and discriminatory power compared to state-of-the-art failure prediction models and shadow rating approaches.