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A zero-adjusted gamma model for mortgage loan loss given default

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  • Tong, Edward N.C.
  • Mues, Christophe
  • Thomas, Lyn

Abstract

The Internal Ratings Based (IRB) approach introduced in the Basel II Accord requires financial institutions to estimate not just the probability of default, but also the Loss Given Default (LGD), i.e., the proportion of the outstanding loan that will be lost in the event of a default. However, modelling LGD poses substantial challenges. One of the key problems in building regression models for estimating the loan-level LGD in retail portfolios such as mortgage loans relates to the difficulty of modelling their distributions, as they typically contain extensive numbers of zeroes. In this paper, an alternative approach is proposed where a mixed discrete-continuous model for the total loss amount incurred on a defaulted loan is developed. The model accommodates the probability of a zero loss and the loss amount given that a loss occurs simultaneously. The approach is applied to a large dataset of defaulted home mortgages from a UK bank and compared to two well-known industry approaches. Our zero-adjusted gamma model is shown to present an alternative and competitive approach to LGD modelling.

Suggested Citation

  • Tong, Edward N.C. & Mues, Christophe & Thomas, Lyn, 2013. "A zero-adjusted gamma model for mortgage loan loss given default," International Journal of Forecasting, Elsevier, vol. 29(4), pages 548-562.
    • Handle: RePEc:eee:intfor:v:29:y:2013:i:4:p:548-562
    DOI: 10.1016/j.ijforecast.2013.03.003
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    Cited by:

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    3. Do, Hung Xuan & Rösch, Daniel & Scheule, Harald, 2018. "Predicting loss severities for residential mortgage loans: A three-step selection approach," European Journal of Operational Research, Elsevier, vol. 270(1), pages 246-259.
    4. Li, Aimin & Li, Zhiyong & Bellotti, Anthony, 2023. "Predicting loss given default of unsecured consumer loans with time-varying survival scores," Pacific-Basin Finance Journal, Elsevier, vol. 78(C).
    5. Jobst, Rainer & Kellner, Ralf & Rösch, Daniel, 2020. "Bayesian loss given default estimation for European sovereign bonds," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1073-1091.
    6. 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.
    7. Bambino-Contreras, Carlos & Morales-Oñate, Víctor, 2021. "Exposición al default: estimación para un portafolio de tarjeta de crédito [Exposure to default: estimation for a credit card portfolio]," MPRA Paper 112333, University Library of Munich, Germany.
    8. Chen, Rongda & Zhou, Hanxian & Jin, Chenglu & Zheng, Wei, 2019. "Modeling of recovery rate for a given default by non-parametric method," Pacific-Basin Finance Journal, Elsevier, vol. 57(C).
    9. Tiago M. Magalhães & Gustavo H. A. Pereira & Denise A. Botter & Mônica C. Sandoval, 2024. "Bartlett corrections for zero-adjusted generalized linear models," Statistical Papers, Springer, vol. 65(4), pages 2191-2209, June.
    10. Peter-Hendrik Ingermann & Frederik Hesse & Christian Bélorgey & Andreas Pfingsten, 2016. "The recovery rate for retail and commercial customers in Germany: a look at collateral and its adjusted market values," Business Research, Springer;German Academic Association for Business Research, vol. 9(2), pages 179-228, August.
    11. Peth, Denise & Mußhoff, Oliver & Funke, Katja & Hirschauer, Norbert, 2018. "Nudging Farmers to Comply With Water Protection Rules – Experimental Evidence From Germany," Ecological Economics, Elsevier, vol. 152(C), pages 310-321.
    12. 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.
    13. Tomazella, Vera & Pereira, Gustavo H.A. & Nobre, Juvêncio S. & Santos-Neto, Manoel, 2019. "Zero-adjusted reparameterized Birnbaum–Saunders regression model," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 142-145.
    14. Xia, Yufei & Zhao, Junhao & He, Lingyun & Li, Yinguo & Yang, Xiaoli, 2021. "Forecasting loss given default for peer-to-peer loans via heterogeneous stacking ensemble approach," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1590-1613.
    15. Thamayanthi Chellathurai, 2017. "Probability Density Of Recovery Rate Given Default Of A Firm’S Debt And Its Constituent Tranches," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-34, June.
    16. 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.
    17. Tong, Edward N.C. & Mues, Christophe & Brown, Iain & Thomas, Lyn C., 2016. "Exposure at default models with and without the credit conversion factor," European Journal of Operational Research, Elsevier, vol. 252(3), pages 910-920.
    18. Buchholz, Matthias & Holst, Gesa & Musshoff, Oliver, 2015. "Water and irrigation policy impact assessment using business simulation games: Evidence from northern Germany," DARE Discussion Papers 1505, Georg-August University of Göttingen, Department of Agricultural Economics and Rural Development (DARE).
    19. Nithi Sopitpongstorn & Param Silvapulle & Jiti Gao, 2017. "Local logit regression for recovery rate," Monash Econometrics and Business Statistics Working Papers 19/17, Monash University, Department of Econometrics and Business Statistics.
    20. Sopitpongstorn, Nithi & Silvapulle, Param & Gao, Jiti & Fenech, Jean-Pierre, 2021. "Local logit regression for loan recovery rate," Journal of Banking & Finance, Elsevier, vol. 126(C).
    21. Yao, Xiao & Crook, Jonathan & Andreeva, Galina, 2017. "Enhancing two-stage modelling methodology for loss given default with support vector machines," European Journal of Operational Research, Elsevier, vol. 263(2), pages 679-689.
    22. Frank Ranganai Matenda & Mabutho Sibanda & Eriyoti Chikodza & Victor Gumbo, 2022. "Corporate Loan Recovery Rates under Downturn Conditions in a Developing Economy: Evidence from Zimbabwe," Risks, MDPI, vol. 10(10), pages 1-24, October.

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