2007: Estimating probabilities of default with support vector machines. The Journal of Banking and Finance

Application of statistical techniques to corporate bankruptcy started in the 60’s. The first technique introduced was discriminant analysis (DA) for uni-variate (Beaver, 1966) and multivariate models (Altman, 1968). After DA the logit and probit models were introduced in (Martin, 1977) and (Ohlson, 1980). Nowadays these models are widely used in practice, e.g. they are at the core of the rating solutions at most European central banks. The solution in the traditional framework is a linear function (a hyperplane in a multidimensional feature space) separating successful and failing companies. A company score is computed as a value of that function. In the case of the probit and logit models the score can be directly transformed into a probability of default (PD), which denotes the probability with which a company can go bankrupt within a certain period. The major disadvantages of these popular approaches is the linearity of the solution and, in the case of logit and probit models, the prespecified form of the link function between PDs and the linear combination of predictors (Figure 1.1). In Figure 1.1 successful and failing companies are denoted with black triangles and white quadrangles respectively. There is an equal number of companies of both classes in the sample. Following the DA and logit classi-fication rule, which give virtually the same result, we are more likely to find a failing company above and to the right from the straight line. This may lead to a conclusion that companies with significantly negative values of op