The statistical modelling of preferences measured on an ordinal scale has again and again proven to be very challenging for researchers. “For the sake of simplicity, think of the ratings we give to ‘objects’ like hotels and restaurants on TripAdvisor or similar platforms. Our rating is our assessment of the hotel, information about whether we found it good or bad,” explains WU Professor Kurt Hornik. “We also find similar ratings in the banking sector, where they are particularly important.” In his research, Professor Hornik searches for ways of combining different ratings into a single consensus rating. “Particularly in the field of banking, it’s of particular interest to find out how existing credit ratings can be used to forecast future default.” It is especially important for large banks to be able to reliably model the creditworthiness of enterprises. On the one hand, such models can be based on existing credit default information, i.e. information about instances where borrowers failed to pay back their debt as agreed. On the other hand, credit ratings already exist for certain companies, for example the ratings issued by the big three credit rating agencies, which use ordinal scales for their ratings. These agencies issue their credit ratings in the form of rating categories such as AAA or B. Kurt Hornik and his fellow researchers looked for potential ways of aggregating and combining these types of information to develop better models for assessing creditworthiness.

Towards better credit ratings

The main challenge for the researchers was calibrating their models based on existing data – in other words, defining the parameters of the models in such a way that they match or closely approximate the available data. The composite likelihood method proved to be very practical in this regard. “This is a kind of trick that consists in looking not at the full likelihood of related observations but focusing on component likelihoods instead. In our case, it’s sufficient to use single observations or pairs of observations,” Hornik explains. Together with his fellow researchers, Hornik developed a very flexible model class. The new models allow for better assessments of companies’ creditworthiness.

A model used in the management of one of the world’s biggest credit portfolios

One variant of these models was developed jointly by Kurt Hornik and experts from the Austrian central bank (OeNB). Today, this model serves as the basis of one of the key monetary policy measures of the Eurosystem: the provision of fresh capital to banks, where sufficiently high-quality loans the banks have awarded to business enterprises are accepted as collateral. “This is one of the largest credit portfolios in the world, and our methods play an important role in managing this portfolio successfully,” Professor Hornik points out.

As one of the co-developers of the world-renowned programming language R, Kurt Hornik makes the new models available to the public as open source software, so that they can be calibrated efficiently and used free of charge. Their scope of application is not limited to credit ratings. They can also be used to combine other kinds of ordinal ratings.