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Confidence sets and confidence bands for a beta distribution with applications to credit risk management

Author

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  • Kiatsupaibul, Seksan
  • Hayter, Anthony J.
  • Somsong, Sarunya

Abstract

Incorporating statistical multiple comparisons techniques with credit risk measurement, a new methodology is proposed to construct exact confidence sets and exact confidence bands for a beta distribution. This involves simultaneous inference on the two parameters of the beta distribution, based upon the inversion of Kolmogorov tests. Some monotonicity properties of the distribution function of the beta distribution are established which enable the derivation of an efficient algorithm for the implementation of the procedure. The methodology has important applications to financial risk management. Specifically, the analysis of loss given default (LGD) data are often modeled with a beta distribution. This new approach properly addresses model risk caused by inadequate sample sizes of LGD data, and can be used in conjunction with the standard recommendations provided by regulators to provide enhanced and more informative analyses.

Suggested Citation

  • Kiatsupaibul, Seksan & Hayter, Anthony J. & Somsong, Sarunya, 2017. "Confidence sets and confidence bands for a beta distribution with applications to credit risk management," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 98-104.
    • Handle: RePEc:eee:insuma:v:75:y:2017:i:c:p:98-104
    DOI: 10.1016/j.insmatheco.2017.05.006
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    References listed on IDEAS

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    1. Frontczak, Robert & Rostek, Stefan, 2015. "Modeling loss given default with stochastic collateral," Economic Modelling, Elsevier, vol. 44(C), pages 162-170.
    2. Jones,Stewart & Hensher,David A. (ed.), 2008. "Advances in Credit Risk Modelling and Corporate Bankruptcy Prediction," Cambridge Books, Cambridge University Press, number 9780521689540, September.
    3. Wei, Li & Yuan, Zhongyi, 2016. "The loss given default of a low-default portfolio with weak contagion," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 113-123.
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    Cited by:

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