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Bootstrap Bandwidth Selection and Confidence Regions for Double Smoothed Default Probability Estimation

Author

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  • Rebeca Peláez

    (Research Group MODES, Department of Mathematics, CITIC, University of A Coruña, 15071 A Coruña, Spain)

  • Ricardo Cao

    (Research Group MODES, Department of Mathematics, CITIC, University of A Coruña, 15071 A Coruña, Spain)

  • Juan M. Vilar

    (Research Group MODES, Department of Mathematics, CITIC, University of A Coruña, 15071 A Coruña, Spain)

Abstract

For a fixed time, t , and a horizon time, b , the probability of default (PD) measures the probability that an obligor, that has paid his/her credit until time t , runs into arrears not later that time t + b . This probability is one of the most crucial elements that influences the risk in credits. Previous works have proposed nonparametric estimators for the probability of default derived from Beran’s estimator and a doubly smoothed Beran’s estimator of the conditional survival function for censored data. They have also found asymptotic expressions for the bias and variance of the estimators, but they do not provide any practical way to choose the smoothing parameters involved. In this paper, resampling methods based on bootstrap techniques are proposed to approximate the bandwidths on which Beran and smoothed Beran’s estimators of the PD depend. Bootstrap algorithms for the calculation of confidence regions of the probability of default are also proposed. Extensive simulation studies show the good behavior of the presented algorithms. The bandwidth selector and the confidence region algorithm are applied to a German credit dataset to analyze the probability of default conditional on the credit scoring.

Suggested Citation

  • Rebeca Peláez & Ricardo Cao & Juan M. Vilar, 2022. "Bootstrap Bandwidth Selection and Confidence Regions for Double Smoothed Default Probability Estimation," Mathematics, MDPI, vol. 10(9), pages 1-25, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1523-:d:807502
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    References listed on IDEAS

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    1. Glennon, Dennis & Nigro, Peter, 2005. "Measuring the Default Risk of Small Business Loans: A Survival Analysis Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(5), pages 923-947, October.
    2. Wiginton, John C., 1980. "A Note on the Comparison of Logit and Discriminant Models of Consumer Credit Behavior," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(3), pages 757-770, September.
    3. Ingrid Van Keilegom & Noël Veraverbeke, 1997. "Estimation and Bootstrap with Censored Data in Fixed Design Nonparametric Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 467-491, September.
    4. Steenackers, A. & Goovaerts, M. J., 1989. "A credit scoring model for personal loans," Insurance: Mathematics and Economics, Elsevier, vol. 8(1), pages 31-34, March.
    5. G. dos Reis & G. Smith, 2018. "Robust and consistent estimation of generators in credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 983-1001, June.
    6. 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.
    7. Naohiko Baba & Hiromichi Goko, 2006. "Survival Analysis of Hedge Funds," Bank of Japan Working Paper Series 06-E-5, Bank of Japan.
    8. Rebeca Peláez Suárez & Ricardo Cao Abad & Juan M. Vilar Fernández, 2021. "Correction to: Probability of default estimation in credit risk using a nonparametric approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 406-406, June.
    9. Srinivasan, Venkat & Kim, Yong H, 1987. "Credit Granting: A Comparative Analysis of Classification Procedures," Journal of Finance, American Finance Association, vol. 42(3), pages 665-681, July.
    10. Strzalkowska-Kominiak, Ewa & Cao, Ricardo, 2013. "Maximum likelihood estimation for conditional distribution single-index models under censoring," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 74-98.
    11. Rebeca Peláez Suárez & Ricardo Cao Abad & Juan M. Vilar Fernández, 2021. "Probability of default estimation in credit risk using a nonparametric approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 383-405, June.
    12. Gang Li & Somnath Datta, 2001. "A Bootstrap Approach to Nonparametric Regression for Right Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 708-729, December.
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    Cited by:

    1. Ashish Dhiman, 2023. "UQ for Credit Risk Management: A deep evidence regression approach," Papers 2305.04967, arXiv.org, revised May 2023.
    2. 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).

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