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The Bayesian Additive Classification Tree Applied to Credit Risk Modelling

Author

Listed:
  • Junni L. Zhang
  • Wolfgang Härdle

Abstract

We propose a new nonlinear classification method based on a Bayesian "sum-of-trees" model, the Bayesian Additive Classification Tree (BACT), which extends the Bayesian Additive Regression Tree (BART) method into the classi- fication context. Like BART, the BACT is a Bayesian nonparametric additive model specified by a prior and a likelihood in which the additive components are trees, and it is fitted by an iterative MCMC algorithm. Each of the trees learns a different part of the underlying function relating the dependent variable to the input variables, but the sum of the trees offers a flexible and robust model. Through several benchmark examples, we show that the BACT has excellent performance. We apply the BACT technique to classify whether firms would be insolvent. This practical example is very important for banks to construct their risk profile and operate successfully. We use the German Creditreform database and classify the solvency status of German firms based on financial statement information. We show that the BACT outperforms the logit model, CART and the Support Vector Machine in identifying insolvent Firms.

Suggested Citation

  • Junni L. Zhang & Wolfgang Härdle, 2008. "The Bayesian Additive Classification Tree Applied to Credit Risk Modelling," SFB 649 Discussion Papers SFB649DP2008-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2008-003
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2008-003.pdf
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    References listed on IDEAS

    as
    1. Härdle, Wolfgang Karl & Moro, Rouslan A. & Schäfer, Dorothea, 2007. "Estimating probabilities of default with support vector machines," Discussion Paper Series 2: Banking and Financial Studies 2007,18, Deutsche Bundesbank.
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    More about this item

    Keywords

    Classi¯cation and Regression Tree; Financial Ratio; Misclassification Rate; Accuracy Ratio;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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