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Probabilistic Overview of Probabilities of Default for Low Default Portfolios by K. Pluto and D. Tasche

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  • Andrius Grigutis

Abstract

This article gives a probabilistic overview of the widely used method of default probability estimation proposed by K. Pluto and D. Tasche. There are listed detailed assumptions and derivation of the inequality where the probability of default is involved under the influence of systematic factor. The author anticipates adding more clarity, especially for early career analysts or scholars, regarding the assumption of borrowers' independence, conditional independence and interaction between the probability distributions such as binomial, beta, normal and others. There is also shown the relation between the probability of default and the joint distribution of $\sqrt{\varrho}X-\sqrt{1-\varrho}Y$, where $X$, including but not limiting, is the standard normal, $Y$ admits, including but not limiting, the beta-normal distribution and $X,\,Y$ are independent.

Suggested Citation

  • Andrius Grigutis, 2023. "Probabilistic Overview of Probabilities of Default for Low Default Portfolios by K. Pluto and D. Tasche," Papers 2303.06148, arXiv.org.
  • Handle: RePEc:arx:papers:2303.06148
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    References listed on IDEAS

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    1. Peter Xue‐Kun Song, 2000. "Multivariate Dispersion Models Generated From Gaussian Copula," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 305-320, June.
    2. Katja Pluto & Dirk Tasche, 2006. "Estimating Probabilities of Default for Low Default Portfolios," Springer Books, in: Bernd Engelmann & Robert Rauhmeier (ed.), The Basel II Risk Parameters, chapter 0, pages 79-103, Springer.
    3. Tasche, Dirk, 2013. "Bayesian estimation of probabilities of default for low default portfolios," Journal of Risk Management in Financial Institutions, Henry Stewart Publications, vol. 6(3), pages 302-326, July.
    4. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
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    Cited by:

    1. Ignas Gasparaviv{c}ius & Andrius Grigutis, 2024. "The Famous American Economist H. Markowitz and Mathematical Overview of his Portfolio Selection Theory," Papers 2402.10253, arXiv.org.

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