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Optimization Heuristics for Determining Internal Rating Grading Scales

Author

Listed:
  • Marianna Lyra
  • Johannes Paha
  • Sandra Paterlini
  • Peter Winker
Abstract
Basel II imposes regulatory capital on banks related to the de- fault risk of their credit portfolio. Banks using an internal rating approach compute the regulatory capital from pooled probabilities of default. These pooled probabilities can be calculated by clustering credit borrowers into di®erent buckets and computing the mean PD for each bucket. The clustering problem can become very complex when Basel II regulations and real-world constraints are taken into account. Search heuristics have already proven remarkable performance in tackling this problem. A Threshold Accepting algorithm is proposed, which exploits the inherent discrete nature of the clustering problem. This algorithm is found to outperform alternative methodologies already proposed in the literature, such as standard k-means and Di®erential Evolution. Besides considering several clustering objectives for a given number of buckets, we extend the analysis further by introducing new methods to determine the optimal number of buckets in which to cluster banks' clients.

Suggested Citation

  • Marianna Lyra & Johannes Paha & Sandra Paterlini & Peter Winker, 2009. "Optimization Heuristics for Determining Internal Rating Grading Scales," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0015, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    • Handle: RePEc:mod:wcefin:0015
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    References listed on IDEAS

    as
    1. Krink, Thiemo & Paterlini, Sandra & Resti, Andrea, 2008. "The optimal structure of PD buckets," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2275-2286, October.
    2. Winker, Peter & Gilli, Manfred, 2004. "Applications of optimization heuristics to estimation and modelling problems," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 211-223, September.
    3. Thiemo Krink & Sandra Paterlini, 2008. "Differential Evolution for Multiobjective Portfolio Optimization," Center for Economic Research (RECent) 021, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    4. Thiemo Krink & Sandra Paterlini, 2008. "Differential Evolution for Multiobjective Portfolio Optimization," Center for Economic Research (RECent) 021, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    5. Hunt, Daniel L. & Cheng, Cheng & Pounds, Stanley, 2009. "The beta-binomial distribution for estimating the number of false rejections in microarray gene expression studies," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1688-1700, March.
    6. Winker, Peter & Fang, Kai-Tai, 1995. "Application of threshold accepting to the evaluation of the discrepancy of a set of points," Discussion Papers, Series II 248, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    7. Peter Winker & Dietmar Maringer, 2004. "Optimal Lag Structure Selection in VEC-Models," Contributions to Economic Analysis, in: New Directions in Macromodelling, pages 213-234, Emerald Group Publishing Limited.
    8. A. Foglia & S. Iannotti & P. Marullo Reedtz, 2001. "The Definition of the Grading Scales in Banks’ Internal Rating Systems," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 30(3), pages 421-456, November.
    9. Paterlini, Sandra & Krink, Thiemo, 2006. "Differential evolution and particle swarm optimisation in partitional clustering," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1220-1247, March.
    10. Krink, Thiemo & Paterlini, Sandra & Resti, Andrea, 2007. "Using differential evolution to improve the accuracy of bank rating systems," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 68-87, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    : credit risk; probability of default; clustering; Threshold Accepting; Differential Evolution;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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