Business — Banking — Management — Marketing & Sales

The usual qualitative assessment of individual risks of borrowers, other than individuals, relies on ratings. However, models of individual risks have existed for a long time. Due to the current emphasis on extensive data on individual borrowers risks, modelling became attractive for assessing risk in a comprehensive and objective manner, and for complying with the New Basel Accord recommendations.

Statistical models link observable attributes of borrowers to actual ratings or to observed default or no default events. The alternative view consists of considering that a drop of the asset value of a firm below the threshold of short-term debt obligations triggers the firms default. This second approach, based on the Merton (1974) model, relies on values derived from equity prices of publicly listed firms. Statistical techniques do not rely on conceptual models, as the Merton model does, but on statistical fits. This chapter addresses the statistical approaches. There are several generations of models of credit risk and default probabilities, starting from the early statistical models linking ratings to financial characteristics of firms, up to elaborate econometric techniques and neural network models. This chapter focuses on statistical techniques. The next chapter focuses on the option modelling of default probability, its conceptual foundations and implementation techniques.

Rating models make ratings (ordinal numbers) a function of observable attributes of borrowers. Default risk models focus on determining the default probability (cardinal numbers) based on similar attributes. The latter use information on default events rather than ratings, which are more judgmental than factual default events. Banks can map modelled ratings to statistical default rates, although this mapping is not equivalent to modelling directly default probabilities.

Credit scoring uses techniques for discriminating between defaulters and non-defaulters. A scoring function provides a score from observable attributes, which is a number. Score ranges map on a one-to-one basis to ratings or default frequencies. Scores use discriminant analysis to separate defaulters from non-defaulters, as the original Altmans zeta score does. Comparing scores to cut-off values separates firms according to risk. Scoring techniques also provide posterior default probabilities, or probabilities of default given the score values. Scoring applies well to individual borrowers in retail banking, because of the large volume of data. It serves when making lending decisions for consumers or mortgage loans to individuals. Scoring also applies to firms, although implementation is more challenging for corporations.

The probit-logit regression models have gained ground for both individual consumers and corporate borrowers. These multivariate techniques use observable attributes and provide similar outputs to those of scoring models, ratings or default probabilities, with a different technique. They apply to default probabilities because defaults are binary events, with probabilities within the 0 to 1 range. The logit-probit technique allows the modelled variable to comply with this specific constraint. This is the methodology of Moodys RiskCalc for modelling default rates.

The econometric techniques allow us to model the default rates of portfolio segments, or subpopulations of firms by risk class, from time series of default rates and economic factors. The Credit Portfolio View (CPV) approach illustrates the potential of the intuitive hint that economic cycles relate to default and migration risks. CPV provides a framework for capturing the cyclical dynamics of credit risk. It uses standard time series models combined with a logit model to obtain default rates by portfolio segment. Time series models predict economic variables, industry and economic indexes, later converted into default rates through the logit model. Ultimately, CPV aims at modelling portfolio risk, as detailed in subsequent chapters. Because of its dual contribution in defining inputs for portfolio models and modelling portfolio risk, CPV belongs to both classes of models: default probability and portfolio models.

Neural network techniques are newcomers for modelling ratings and default probabilities. Empirical observations show non-linear relations between financial attributes of firms and their ratings or default frequencies, such as the relationship between size of firms and credit risk. Moreover, financial attributes strongly correlate, which creates weaknesses in statistical models. Such peculiarities do not affect neural networks. The basic tools for measuring accuracy are misclassification matrices and power curves. Misclassification tables simply compare predicted outcomes with actual ones. Power curves characterize the discriminating power of models (between ratings or default-no default states) by a single number. Both techniques apply to all models.

A common feature of all models is that they necessarily make errors in predicting defaults from historical values of attributes of borrowers. However, their added complexity makes it more difficult to interpret why one borrower is more or less risky than another.

The first section explains the basic intuition behind statistical models of ratings or default probability. The second section explains the principle of scoring. The third section discusses the probit-logit techniques and details the basic equations. The fourth section shows how econometric modelling of defaults and migrations by CPV, which captures the cyclical dynamics of credit risk. The fifth section describes the principles of neural networks. Finally, the last section addresses misclassification matrices and power curves. See Caouette et al. (1998) for a comprehensive overview of the statistical techniques.