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Graphical Data Representation in Bankruptcy Analysis

by Wolfgang K. Härdle of Humboldt-Universität zu Berlin,
Rouslan A. Moro of Humboldt-Universität zu Berlin, and
Dorothea Schäfer of the German Institute for Economic Research

February 24, 2006

Abstract: Graphical data representation is an important tool for model selection in bankruptcy analysis since the problem is highly non-linear and its numerical representation is much less transparent. In classical rating models a convenient representation of ratings in a closed form is possible reducing the need for graphical tools. In contrast to that non-linear non-parametric models achieving better accuracy often rely on visualisation. We demonstrate an application of visualisation techniques at different stages of corporate default analysis based on Support Vector Machines (SVM). These stages are the selection of variables (predictors), probability of default (PD) estimation and the representation of PDs for two and higher dimensional models with colour coding. It is at this stage when the selection of a proper colour scheme becomes essential for a correct visualisation of PDs. The mapping of scores into PDs is done as a non-parametric regression with monotonisation. The SVM learns a non-parametric score function that is, in its turn, non-parametrically transformed into PDs. Since PDs cannot be represented in a closed form, some other ways of displaying them must be found. Graphical tools give this possibility.

JEL Classification: C14, G33, C45.

Keywords: company rating, default probability, support vector machines, colour coding.

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