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Optimization Heuristics for Determining Internal Rating Grading Scales

  • Marianna Lyra


  • Johannes Paha


  • Sandra Paterlini


  • Peter Winker


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.

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Paper provided by Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi" in its series Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) with number 09031.

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Length: pages 31
Date of creation: Mar 2009
Date of revision:
Handle: RePEc:mod:wcefin:09031
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  1. 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.
  2. Dietmar Maringer & Peter Winker, 2004. "Optimal Lag Structure Selection in VEC-Models," Computing in Economics and Finance 2004 155, Society for Computational Economics.
  3. 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.
  4. Thiemo Krink & Sandra Paterlini, 2008. "Differential Evolution for Multiobjective Portfolio Optimization," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 08012, Universita di Modena e Reggio Emilia, Dipartimento di Economia "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 & Gilli, Manfred, 2004. "Applications of optimization heuristics to estimation and modelling problems," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 211-223, September.
  7. 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.
  8. 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.
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