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Using the Censored Gamma Distribution for Modeling Fractional Response Variables with an Application to Loss Given Default

Author

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  • Sigrist, Fabio
  • Stahel, Werner A.

Abstract

Regression models for limited continuous dependent variables having a non-negligible probability of attaining exactly their limits are presented. The models differ in the number of parameters and in their flexibility. Fractional data being a special case of limited dependent data, the models also apply to variables that are a fraction or a proportion. It is shown how to fit these models and they are applied to a Loss Given Default dataset from insurance to which they provide a good fit.

Suggested Citation

  • Sigrist, Fabio & Stahel, Werner A., 2011. "Using the Censored Gamma Distribution for Modeling Fractional Response Variables with an Application to Loss Given Default," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 673-710, November.
    • Handle: RePEc:cup:astinb:v:41:y:2011:i:02:p:673-710_00
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    Cited by:

    1. Gourieroux, Christian & Lu, Yang, 2019. "Least impulse response estimator for stress test exercises," Journal of Banking & Finance, Elsevier, vol. 103(C), pages 62-77.
    2. Kaposty, Florian & Kriebel, Johannes & Löderbusch, Matthias, 2020. "Predicting loss given default in leasing: A closer look at models and variable selection," International Journal of Forecasting, Elsevier, vol. 36(2), pages 248-266.
    3. Sigrist, Fabio & Hirnschall, Christoph, 2019. "Grabit: Gradient tree-boosted Tobit models for default prediction," Journal of Banking & Finance, Elsevier, vol. 102(C), pages 177-192.
    4. Morne Joubert & Tanja Verster & Helgard Raubenheimer & Willem D. Schutte, 2021. "Adapting the Default Weighted Survival Analysis Modelling Approach to Model IFRS 9 LGD," Risks, MDPI, vol. 9(6), pages 1-17, June.
    5. Chih-Kang Chu & Ruey-Ching Hwang, 2019. "Predicting Loss Distributions for Small-Size Defaulted-Debt Portfolios Using a Convolution Technique that Allows Probability Masses to Occur at Boundary Points," Journal of Financial Services Research, Springer;Western Finance Association, vol. 56(1), pages 95-117, August.
    6. Salvatore D. Tomarchio & Antonio Punzo, 2019. "Modelling the loss given default distribution via a family of zero‐and‐one inflated mixture models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1247-1266, October.
    7. Lozinskaia Agata & Ozhegov Evgeniy, 2016. "Key Determinants of Demand, Credit Underwriting, and Performance on Government-Insured Mortgage Loans in Russia," EERC Working Paper Series 16/03e, EERC Research Network, Russia and CIS.
    8. Yuta Tanoue & Satoshi Yamashita & Hideaki Nagahata, 2020. "Comparison study of two-step LGD estimation model with probability machines," Risk Management, Palgrave Macmillan, vol. 22(3), pages 155-177, September.
    9. Hwang, Ruey-Ching & Chu, Chih-Kang & Yu, Kaizhi, 2020. "Predicting LGD distributions with mixed continuous and discrete ordinal outcomes," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1003-1022.
    10. Yurchenko, Yurii, 2019. "The impact of macroeconomic factors on collateral value within the framework of expected credit loss calculation," MPRA Paper 97135, University Library of Munich, Germany.
    11. Yashkir, Olga & Yashkir, Yuriy, 2013. "Loss Given Default Modelling: Comparative Analysis," MPRA Paper 46147, University Library of Munich, Germany.
    12. Ruey-Ching Hwang & Huimin Chung & C. K. Chu, 2016. "A Two-Stage Probit Model for Predicting Recovery Rates," Journal of Financial Services Research, Springer;Western Finance Association, vol. 50(3), pages 311-339, December.
    13. Ying Wu & Garvit Arora & Xuan Mei, 2024. "Using CPI in Loss Given Default Forecasting Models for Commercial Real Estate Portfolio," Papers 2402.15498, arXiv.org.
    14. Ruey-Ching Hwang & Chih-Kang Chu & Kaizhi Yu, 2021. "Predicting the Loss Given Default Distribution with the Zero-Inflated Censored Beta-Mixture Regression that Allows Probability Masses and Bimodality," Journal of Financial Services Research, Springer;Western Finance Association, vol. 59(3), pages 143-172, June.

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