Loss Given Default Modelling: Comparative Analysis

Yashkir, Olga and Yashkir, Yuriy (2013): Loss Given Default Modelling: Comparative Analysis. Published in: Journal of Risk Model Validation , Vol. 7, No. 1 (27 March 2013)

Abstract

In this study we investigated several most popular Loss Given Default (LGD) models (LSM, Tobit, Three-Tiered Tobit, Beta Regression, Inflated Beta Regression, Censored Gamma Regression) in order to compare their performance. We show that for a given input data set, the quality of the model calibration depends mainly on the proper choice (and availability) of explanatory variables (model factors), but not on the fitting model. Model factors were chosen based on the amplitude of their correlation with historical LGDs of the calibration data set. Numerical values of non-quantitative parameters (industry, ranking, type of collateral) were introduced as their LGD average. We show that different debt instruments depend on different sets of model factors (from three factors for Revolving Credit or for Subordinated Bonds to eight factors for Senior Secured Bonds). Calibration of LGD models using distressed business cycle periods provide better fit than data from total available time span. Calibration algorithms and details of their realization using the R statistical package are presented. We demonstrate how LGD models can be used for stress testing. The results of this study can be of use to risk managers concerned with the Basel accord compliance.

• Item Type: MPRA Paper
• Language: English
• Keywords: LGD, Credit Risk, LGD model, Linear regression, Tobit model, Stress testing
• Subjects: G - Financial Economics > G1 - General Financial Markets > G14 - Information and Market Efficiency ; Event Studies ; Insider Trading; G - Financial Economics > G1 - General Financial Markets > G17 - Financial Forecasting and Simulation; G - Financial Economics > G1 - General Financial Markets > G19 - Other; G - Financial Economics > G2 - Financial Institutions and Services > G24 - Investment Banking ; Venture Capital ; Brokerage ; Ratings and Ratings Agencies

References

Edward Altman. Are historically based default and recovery models in the high-yield and distressed debt markets still relevant in today's credit environment? Stern School of Business, 2006. Special Report.

Edward Altman. Default recovery rates and lgd in credit risk modeling and practice: an updated review of the literature and empirical evidence. Working paper, 2006.

Edward Altman and Egon Kalotay. A flexible approach to modeling ultimate recoveries on defaulted loans and bonds. 2010.

Edward Altman, Brooks Brady, Andrea Resti, and Andrea Sironi. The link between default and recovery rates: Theory, empirical evidence, implications. Working Paper S-CDM-04-07, 2003. Series Credit and Debt Markets Research Group.

Edward Altman, Andrea Resti, and Andrea Sironi. Default recovery rates in credit risk modeling: A review of the literature, empirical evidence. Economic Notes, 33:183-208, 2004.

Benjamin Bade, Daniel Rosch, and Harald Scheule. Empirical performance of loss given default prediction models. The Journal of Risk Model Validation, 5(2):25-44, 2011.

J. Samuel Baixauli and Susanna Alvarez. The role of market-implied severity modeling for credit var. ANNALS OF ECONOMICS AND FINANCE, 11(2):337-353, 2010.

Michael Barco. Going downturn. Risk, 20(9):39-44, 2007.

Tony Bellotti and Jonathan Crook. Loss given default models incorporating macroeconomic variables for credit cards. International Journal of Forecasting, Special Section 2: Credit Risk Modelling and Forecasting, 28(1):171-182, January-March 2012.

Radovan Chalupka and Juraj Kopecsni. Modeling bank loan LGD of corporate, sme segments. a case study. Czech Journal of Economics and Finance, 59(4):360-382, 2009.

Craig Friedman and Sven Sandow. Ultimate recoveries. RISK, 16(8):69-73, 2003.

Greg M. Gupton. Advancing loss given default prediction models: How the quiet have quickened. Economic Notes by Banca Monte dei Paschi di Siena SpA, 34(2):185-230, 2005.

Greg M. Gupton and Roger M. Stein. Losscalc: Model for predicting loss given default (LGD). Federal Reserve Bank of New York (working paper), 2002.

Marc Gurtler and Martin Hibbeln. Pitfalls in modeling loss given default of bank loans. Working Paper, Technische Universität Braunschweig, 2011.

Martin Hillebrand. Modeling and estimating dependent loss given default. CRC working paper, 2006.

Stefan Hlawatsch and Sebastian Ostrowski. Simulation and estimation of loss given default. The Journal of Credit Risk, 7(3):39-73, 2011.

Xinzheng Huang and Cornelis W. Oosterlee. Generalized beta regression models for random loss given default. The Journal of Credit Risk, 7(4):45-70, 2012.

Michael Jacobs Jr. A two-factor structural model of ultimate loss-given-default: Capital structure and calibration to corporate recovery data. The Journal of Financial Transformation, 31(4):31-43, 2011.

David Li, Ruchi Bhariok, Sean Keenan, and Stefano Santilli. Validation techniques and performance metrics for loss given default models. The Journal of Risk Model Validation, 3(3):3-26, 2009.

Xiaolin Luo and Pavel V. Shevchenko. LGD credit risk model: estimation of capital with parameter uncertainty using mcmc. Working Paper, CSIRO Mathematics, Informatics and Statistics, 2010.

John F. McDonald and Robert A. Moffitt. The uses of tobit analysis. Review of Economics and Statistics, 62(2):318-321, 1980.

Tarciana L. Pereira and Francisko Cribari-Neto. A test for a correct model specification in inflated beta regressions. Working Paper, Instituto de Matemática, Estatística e Computação Científica Universidade Estadual de Campinas, 2010.

Daniel Rosch and Harald Scheule. Stress-testing credit risk parameters: an application to retail loan portfolios. Journal of Risk Model Validation, 1(1):55-75, 2007.

Til Schuermann. What do we know about loss given default? Federal Reserve Bank of New York (working paper), 2004.

Fabio Sigrist and Werner A. Stahel. Censored gamma regression models for limited dependent variables with an application to loss given default. In 28th European Meeting of Statisticians, August, 17-22, 2010, Piraeus, Greece, 2010.

Fabio Sigrist and Werner A. Stahel. Using the censored gamma distribution for modeling fractional response variables with an application to loss given default. ASTIN Bulletin, 41(2), 2011.

Standard&Poor's. Default, transition, and recovery: 2011 annual global corporate default study and rating transitions. 2012. Report.

Wemke van der Weija and Marcel den Hollandera. Improving PD and LGD models: following the changes in the market. SNS Reaal, 2009. Utrecht.

Bill Huajian Yang and Mykola Tkachenko. Modeling exposure at default and loss given default: empirical approaches and technical implementation. The Journal of Credit Risk, 8(2):81-102, 2012.