Default rates are unstable when time passes. The volatility of yearly historical default rates is the standard deviation of observed time series. The volatility increases with the level of default rate, when the rating decreases. Historical volatilities are available from rating agencies for default rates observed across varying horizons. If the volatility is high, the […]
When time drifts, the risk either improves or deteriorates. These shifts are captured by the transition frequencies between risk classes. Within a given period, transition rates between classes are transfer frequencies divided by the number of original firms in each risk class. It is possible to map rating classes with observed credit spreads in the […]
This section shows how to model the term structure of historical default rates from historical raw data. The technique allows us to assign probabilities of default at various forward periods. As mentioned above, there are various default rates, arithmetic or value weighted. The first step is to define the number of firms surviving at the […]
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 […]
The principle of all statistical models is to fit observable attributes, such as financial variables of firms, to variables to be predicted, such as default or non-default, or the rating of the firm. The simplest technique for doing so is the simple linear regression, or variations of this technique. This technique provides valuable findings. For […]
The principle of scoring is to use a metric for dividing good and bad credits into distinct distributions. The statistical technique is the standard discriminant analysis. Fisher Discriminant Analysis Discriminant analysis distinguishes statistically between two or more groups of unit observations (firms or individuals).
Scoring provides information on the credit standing of a firm. Therefore, the probability of default given the score S differs from the probability of default under no information on S. If we use scoring to discriminate between firms that are likely to default in the future and firms that are not, we can infer from […]
Scoring is widely used for consumer loans. Scoring allows us to automate the credit process because there is no real need to examine in detail the profile of individuals. There are plenty of reliable portfolio loss statistics, given the large number of individuals. The intensity of services provided to customers is a major source of […]
There are models dedicated to predicting binary events, such as defaults or non-defaults, or to scaling the probabilities that such events occur. Originally, they were behavioural models, used to predict two or more qualitative choices or behavioural responses, such as voting yes or no, ranking different products by consumer preferences, and so on. These models […]
This section presents the macro-economic modelling of default and migration rates. This is the CPV (Wilson, 1997a, b) framework, which addresses explicitly the cyclical dynamics of these variables. The model focuses on portfolio segments, rather than individual obligors, and default or migration rates rather than probabilities. The underlying assumption is that of the homogeneous behaviour […]
