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Modelling the loss given default distribution via a family of zero‐and‐one inflated mixture models

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  • Salvatore D. Tomarchio
  • Antonio Punzo
Abstract
The empirical distribution of the loss given default (LGD) has support [0,1], contains an excess of 0s and 1s, and is often multimodal on (0,1). Though some parametric models have been used in the credit risk literature to model the LGD distribution, these peculiarities call for more flexible approaches. Thus, we introduce a zero‐and‐one inflated mixture where a three‐level multinomial model is considered for the membership of the LGD values to the sets {0}, (0,1) and {1}, whereas a finite mixture of distributions is used on (0,1). To allow for more flexible shapes on (0,1), we consider component distributions already defined on (0,1) and distributions on (−∞,∞) mapped on (0,1) via the inverse logit transformation. This yields a family of 13 zero‐and‐one inflated mixture models. They are applied to two data sets of LGDs on loans: one from a European Bank and the other from the Bank of Italy. The best performers in our family, selected via classical information criteria, are then compared with several well‐established semiparameteric or non‐parametric approaches via a convenient simulation‐based procedure.

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  • 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.
    • Handle: RePEc:bla:jorssa:v:182:y:2019:i:4:p:1247-1266
    DOI: 10.1111/rssa.12466
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    References listed on IDEAS

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    1. Michel Dietsch, 2004. "Should SME exposures be treated as retail or corporate exposures: a comparative analysis of probabilities of default and assets correlations in French and German SMEs," ULB Institutional Repository 2013/14164, ULB -- Universite Libre de Bruxelles.
    2. Daniel Rösch & Harald Scheule, 2006. "A Multi-Factor Approach for Systematic Default and Recovery Risk," Springer Books, in: Bernd Engelmann & Robert Rauhmeier (ed.), The Basel II Risk Parameters, chapter 0, pages 105-125, Springer.
    3. Gürtler, Marc & Hibbeln, Martin, 2013. "Improvements in loss given default forecasts for bank loans," Journal of Banking & Finance, Elsevier, vol. 37(7), pages 2354-2366.
    4. Jakub Seidler, 2008. "Implied Market Loss Given Default: structural-model approach," Working Papers IES 2008/26, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Oct 2008.
    5. Bastos, João A., 2010. "Forecasting bank loans loss-given-default," Journal of Banking & Finance, Elsevier, vol. 34(10), pages 2510-2517, October.
    6. 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.
    7. Raffaella Calabrese, 2014. "Predicting bank loan recovery rates with a mixed continuous‐discrete model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(2), pages 99-114, March.
    8. 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.
    9. Grunert, Jens & Weber, Martin, 2009. "Recovery rates of commercial lending: Empirical evidence for German companies," Journal of Banking & Finance, Elsevier, vol. 33(3), pages 505-513, March.
    10. Christian Gourieroux & Alain Monfort, 2006. "(Non) consistency of the Beta Kernel Estimator for Recovery Rate Distribution," Working Papers 2006-31, Center for Research in Economics and Statistics.
    11. 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.
    12. Loterman, Gert & Brown, Iain & Martens, David & Mues, Christophe & Baesens, Bart, 2012. "Benchmarking regression algorithms for loss given default modeling," International Journal of Forecasting, Elsevier, vol. 28(1), pages 161-170.
    13. Nazemi, Abdolreza & Fatemi Pour, Farnoosh & Heidenreich, Konstantin & Fabozzi, Frank J., 2017. "Fuzzy decision fusion approach for loss-given-default modeling," European Journal of Operational Research, Elsevier, vol. 262(2), pages 780-791.
    14. Miller, Patrick & Töws, Eugen, 2018. "Loss given default adjusted workout processes for leases," Journal of Banking & Finance, Elsevier, vol. 91(C), pages 189-201.
    15. Dietsch, Michel & Petey, Joel, 2004. "Should SME exposures be treated as retail or corporate exposures? A comparative analysis of default probabilities and asset correlations in French and German SMEs," Journal of Banking & Finance, Elsevier, vol. 28(4), pages 773-788, April.
    16. Miljkovic, Tatjana & Grün, Bettina, 2016. "Modeling loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 387-396.
    17. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    18. Ellen Tobback & David Martens & Tony Van Gestel & Bart Baesens, 2014. "Forecasting Loss Given Default models: impact of account characteristics and the macroeconomic state," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(3), pages 376-392, March.
    19. Hurlin, Christophe & Leymarie, Jérémy & Patin, Antoine, 2018. "Loss functions for Loss Given Default model comparison," European Journal of Operational Research, Elsevier, vol. 268(1), pages 348-360.
    20. Luca Bagnato & Antonio Punzo, 2013. "Finite mixtures of unimodal beta and gamma densities and the $$k$$ -bumps algorithm," Computational Statistics, Springer, vol. 28(4), pages 1571-1597, August.
    21. Calabrese, Raffaella, 2014. "Downturn Loss Given Default: Mixture distribution estimation," European Journal of Operational Research, Elsevier, vol. 237(1), pages 271-277.
    22. 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.
    23. Renault, Olivier & Scaillet, Olivier, 2004. "On the way to recovery: A nonparametric bias free estimation of recovery rate densities," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 2915-2931, December.
    24. Egon A. Kalotay & Edward I. Altman, 2017. "Intertemporal Forecasts of Defaulted Bond Recoveries and Portfolio Losses," Review of Finance, European Finance Association, vol. 21(1), pages 433-463.
    25. Düllmann, Klaus & Trapp, Monika, 2004. "Systematic Risk in Recovery Rates: An Empirical Analysis of US Corporate Credit Exposures," Discussion Paper Series 2: Banking and Financial Studies 2004,02, Deutsche Bundesbank.
    26. Schmit, Mathias, 2004. "Credit risk in the leasing industry," Journal of Banking & Finance, Elsevier, vol. 28(4), pages 811-833, April.
    27. 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.
    28. Rongda Chen & Ze Wang, 2013. "Curve Fitting of the Corporate Recovery Rates: The Comparison of Beta Distribution Estimation and Kernel Density Estimation," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-9, July.
    29. Bellotti, Tony & Crook, Jonathan, 2012. "Loss given default models incorporating macroeconomic variables for credit cards," International Journal of Forecasting, Elsevier, vol. 28(1), pages 171-182.
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