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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. 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.
    2. Gourieroux, Christian & Lu, Yang, 2019. "Least impulse response estimator for stress test exercises," Journal of Banking & Finance, Elsevier, vol. 103(C), pages 62-77.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Yashkir, Olga & Yashkir, Yuriy, 2013. "Loss Given Default Modelling: Comparative Analysis," MPRA Paper 46147, University Library of Munich, Germany.

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