IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i10p2228-d1143118.html
   My bibliography  Save this article

Modelling the Time to Write-Off of Non-Performing Loans Using a Promotion Time Cure Model with Parametric Frailty

Author

Listed:
  • Janette Larney

    (Centre for Business Mathematics and Informatics, North-West University, Potchefstroom 2531, South Africa
    These authors contributed equally to this work.)

  • James Samuel Allison

    (School of Mathematical and Statistical Sciences, North-West University, Potchefstroom 2531, South Africa
    These authors contributed equally to this work.)

  • Gerrit Lodewicus Grobler

    (School of Mathematical and Statistical Sciences, North-West University, Potchefstroom 2531, South Africa
    These authors contributed equally to this work.)

  • Marius Smuts

    (School of Mathematical and Statistical Sciences, North-West University, Potchefstroom 2531, South Africa
    These authors contributed equally to this work.)

Abstract

Modelling the outcome after loan default is receiving increasing attention, and survival analysis is particularly suitable for this purpose due to the likely presence of censoring in the data. In this study, we suggest that the time to loan write-off may be influenced by latent competing risks, as well as by common, unobservable drivers, such as the state of the economy. We therefore expand on the promotion time cure model and include a parametric frailty parameter to account for common, unobservable factors and for possible observable covariates not included in the model. We opt for a parametric model due to its interpretability and analytical tractability, which are desirable properties in bank risk management. Both a gamma and inverse Gaussian frailty parameter are considered for the univariate case, and we also consider a shared frailty model. A Monte Carlo study demonstrates that the parameter estimation of the models is reliable, after which they are fitted to a real-world dataset in respect of large corporate loans in the US. The results show that a more flexible hazard function is possible by including a frailty parameter. Furthermore, the shared frailty model shows potential to capture dependence in write-off times within industry groups.

Suggested Citation

  • Janette Larney & James Samuel Allison & Gerrit Lodewicus Grobler & Marius Smuts, 2023. "Modelling the Time to Write-Off of Non-Performing Loans Using a Promotion Time Cure Model with Parametric Frailty," Mathematics, MDPI, vol. 11(10), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2228-:d:1143118
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/10/2228/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/10/2228/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Portier, Francois & El Ghouch, Anouar & Van Keilegom, Ingrid, 2017. "Efficiency and bootstrap in the promotion time cure model," LIDAM Reprints ISBA 2017019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Rodrigues, Josemar & Cancho, Vicente G. & de Castro, Mrio & Louzada-Neto, Francisco, 2009. "On the unification of long-term survival models," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 753-759, March.
    3. Khieu, Hinh D. & Mullineaux, Donald J. & Yi, Ha-Chin, 2012. "The determinants of bank loan recovery rates," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 923-933.
    4. Li, Chin-Shang & Taylor, Jeremy M. G. & Sy, Judy P., 2001. "Identifiability of cure models," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 389-395, October.
    5. Fenech, Jean Pierre & Yap, Ying Kai & Shafik, Salwa, 2016. "Modelling the recovery outcomes for defaulted loans: A survival analysis approach," Economics Letters, Elsevier, vol. 145(C), pages 79-82.
    6. Dirick, Lore & Claeskens, Gerda & Baesens, Bart, 2015. "An Akaike information criterion for multiple event mixture cure models," European Journal of Operational Research, Elsevier, vol. 241(2), pages 449-457.
    7. Jennifer Betz & Ralf Kellner & Daniel Rösch, 2021. "Time matters: How default resolution times impact final loss rates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(3), pages 619-644, June.
    8. Arno Botha & Conrad Beyers & Pieter de Villiers, 2020. "Simulation-based optimisation of the timing of loan recovery across different portfolios," Papers 2009.11064, arXiv.org, revised Apr 2021.
    9. Lore Dirick & Tony Bellotti & Gerda Claeskens & Bart Baesens, 2019. "Macro-Economic Factors in Credit Risk Calculations: Including Time-Varying Covariates in Mixture Cure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 40-53, January.
    10. Maria Stepanova & Lyn Thomas, 2002. "Survival Analysis Methods for Personal Loan Data," Operations Research, INFORMS, vol. 50(2), pages 277-289, April.
    11. Deresa, Negera Wakgari & Van Keilegom, Ingrid, 2020. "A multivariate normal regression model for survival data subject to different types of dependent censoring," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    12. L N Allen & L C Rose, 2006. "Financial survival analysis of defaulted debtors," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 630-636, June.
    13. Tong, Edward N.C. & Mues, Christophe & Thomas, Lyn C., 2012. "Mixture cure models in credit scoring: If and when borrowers default," European Journal of Operational Research, Elsevier, vol. 218(1), pages 132-139.
    14. Leow, Mindy & Mues, Christophe, 2012. "Predicting loss given default (LGD) for residential mortgage loans: A two-stage model and empirical evidence for UK bank data," International Journal of Forecasting, Elsevier, vol. 28(1), pages 183-195.
    15. Legrand, Catherine, 2021. "Advanced Survival Models," LIDAM Reprints ISBA 2021015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Deresa, N.W. & Van Keilegom, I. & Antonio, K., 2022. "Copula-based inference for bivariate survival data with left truncation and dependent censoring," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 1-21.
    17. J Banasik & J N Crook & L C Thomas, 1999. "Not if but when will borrowers default," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(12), pages 1185-1190, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Arno Botha & Tanja Verster & Roelinde Bester, 2024. "The TruEnd-procedure: Treating trailing zero-valued balances in credit data," Papers 2404.17008, arXiv.org, revised Nov 2024.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dirick, Lore & Claeskens, Gerda & Vasnev, Andrey & Baesens, Bart, 2022. "A hierarchical mixture cure model with unobserved heterogeneity for credit risk," Econometrics and Statistics, Elsevier, vol. 22(C), pages 39-55.
    2. Jiang, Cuiqing & Wang, Zhao & Zhao, Huimin, 2019. "A prediction-driven mixture cure model and its application in credit scoring," European Journal of Operational Research, Elsevier, vol. 277(1), pages 20-31.
    3. Lore Dirick & Gerda Claeskens & Bart Baesens, 2017. "Time to default in credit scoring using survival analysis: a benchmark study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(6), pages 652-665, June.
    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. Peláez, Rebeca & Van Keilegom, Ingrid & Cao, Ricardo & Vilar, Juan M., 2024. "Probability of default estimation in credit risk using mixture cure models," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    6. Richard Chamboko & Jorge M. Bravo, 2016. "On the modelling of prognosis from delinquency to normal performance on retail consumer loans," Risk Management, Palgrave Macmillan, vol. 18(4), pages 264-287, December.
    7. Calabrese, Raffaella & Crook, Jonathan, 2020. "Spatial contagion in mortgage defaults: A spatial dynamic survival model with time and space varying coefficients," European Journal of Operational Research, Elsevier, vol. 287(2), pages 749-761.
    8. Thi Mai Luong, 2020. "Selection Effects of Lender and Borrower Choices on Risk Measurement, Management and Prudential Regulation," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2020, January-A.
    9. Leow, Mindy & Crook, Jonathan, 2014. "Intensity models and transition probabilities for credit card loan delinquencies," European Journal of Operational Research, Elsevier, vol. 236(2), pages 685-694.
    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. Liu, Fan & Hua, Zhongsheng & Lim, Andrew, 2015. "Identifying future defaulters: A hierarchical Bayesian method," European Journal of Operational Research, Elsevier, vol. 241(1), pages 202-211.
    12. Mariusz Górajski & Dobromił Serwa & Zuzanna Wośko, 2019. "Measuring expected time to default under stress conditions for corporate loans," Empirical Economics, Springer, vol. 57(1), pages 31-52, July.
    13. Arno Botha & Tanja Verster & Roelinde Bester, 2024. "The TruEnd-procedure: Treating trailing zero-valued balances in credit data," Papers 2404.17008, arXiv.org, revised Nov 2024.
    14. Michal Rychnovský, 2018. "Survival Analysis As A Tool For Better Probability Of Default Prediction," Acta Oeconomica Pragensia, Prague University of Economics and Business, vol. 2018(1), pages 34-46.
    15. Mauro Ribeiro de Oliveira & Fernando Moreira & Francisco Louzada, 2017. "The zero-inflated promotion cure rate model applied to financial data on time-to-default," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1395950-139, January.
    16. Alexandre, Michel & Antônio Silva Brito, Giovani & Cotrim Martins, Theo, 2017. "Default contagion among credit modalities: evidence from Brazilian data," MPRA Paper 76859, University Library of Munich, Germany.
    17. 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.
    18. Dirick, Lore & Claeskens, Gerda & Baesens, Bart, 2015. "An Akaike information criterion for multiple event mixture cure models," European Journal of Operational Research, Elsevier, vol. 241(2), pages 449-457.
    19. 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.
    20. Richard Chamboko, 2024. "Digital financial services adoption: a retrospective time-to-event analysis approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-27, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2228-:d:1143118. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.