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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
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal International Journal of Forecasting.

    Volume (Year): 29 (2013)
    Issue (Month): 4 ()
    Pages: 548-562

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    Handle: RePEc:eee:intfor:v:29:y:2013:i:4:p:548-562

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    Web page: http://www.elsevier.com/locate/ijforecast

    Related research

    Keywords: Regression; Finance; Credit risk modelling; Mixture models; LGD; Basel II;

    References

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    1. Zhang, Jie & Thomas, Lyn C., 2012. "Comparisons of linear regression and survival analysis using single and mixture distributions approaches in modelling LGD," International Journal of Forecasting, Elsevier, Elsevier, vol. 28(1), pages 204-215.
    2. Joao A. Bastos, 2009. "Forecasting bank loans loss-given-default," CEMAPRE Working Papers 0901, Centre for Applied Mathematics and Economics (CEMAPRE), School of Economics and Management (ISEG), Technical University of Lisbon.
    3. Somers, Mark & Whittaker, Joe, 2007. "Quantile regression for modelling distributions of profit and loss," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1477-1487, December.
    4. Qi, Min & Yang, Xiaolong, 2009. "Loss given default of high loan-to-value residential mortgages," Journal of Banking & Finance, Elsevier, vol. 33(5), pages 788-799, May.
    5. Thomas, L.C. & Matuszyk, A. & Moore, A., 2012. "Comparing debt characteristics and LGD models for different collections policies," International Journal of Forecasting, Elsevier, Elsevier, vol. 28(1), pages 196-203.
    6. Fabio Sigrist & Werner A. Stahel, 2010. "Using The Censored Gamma Distribution for Modeling Fractional Response Variables with an Application to Loss Given Default," Papers 1011.1796, arXiv.org, revised May 2012.
    7. Loterman, Gert & Brown, Iain & Martens, David & Mues, Christophe & Baesens, Bart, 2012. "Benchmarking regression algorithms for loss given default modeling," International Journal of Forecasting, Elsevier, Elsevier, vol. 28(1), pages 161-170.
    8. Qi, Min & Zhao, Xinlei, 2011. "Comparison of modeling methods for Loss Given Default," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2842-2855, November.
    9. Calabrese, Raffaella & Zenga, Michele, 2010. "Bank loan recovery rates: Measuring and nonparametric density estimation," Journal of Banking & Finance, Elsevier, vol. 34(5), pages 903-911, May.
    10. Bellotti, Tony & Crook, Jonathan, 2012. "Loss given default models incorporating macroeconomic variables for credit cards," International Journal of Forecasting, Elsevier, Elsevier, vol. 28(1), pages 171-182.
    11. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554.
    12. D. Mikis Stasinopoulos & Robert A. Rigby, . "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, American Statistical Association, American Statistical Association, vol. 23(i07).
    13. 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, Elsevier, vol. 28(1), pages 183-195.
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